General Chemistry II Exam 2 Study Guidance: Kinetics, Radioactivity, and Reaction Mechanisms

{"type":"doc","content":[{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1a. What is the rate constant for the decay of Am-241? What units does the rate constant have?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Radioactive Decay Kinetics"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of first-order kinetics as applied to radioactive decay, specifically how to relate half-life to the rate constant."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Half-life ("},{"type":"inlineMath","attrs":{"latex":"t_{1/2}"}},{"type":"text","text":"): The time required for half of a radioactive sample to decay."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rate constant ("},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":"): A proportionality constant in the rate law for a first-order process."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Key formula for first-order decay:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"t_{1/2} = \\frac{0.693}{k}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the half-life given: "},{"type":"inlineMath","attrs":{"latex":"t_{1/2} = 432.6"}},{"type":"text","text":" years."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the formula relating half-life and rate constant for a first-order process: "},{"type":"inlineMath","attrs":{"latex":"t_{1/2} = \\frac{0.693}{k}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rearrange the formula to solve for "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":": "},{"type":"inlineMath","attrs":{"latex":"k = \\frac{0.693}{t_{1/2}}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Consider the units: Since half-life is in years, "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" will have units of "},{"type":"inlineMath","attrs":{"latex":"\\text{year}^{-1}"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"k = 0.00160\\ \\text{year}^{-1}"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The rate constant is calculated using "},{"type":"inlineMath","attrs":{"latex":"k = \\frac{0.693}{432.6}"}},{"type":"text","text":", and the units are "},{"type":"inlineMath","attrs":{"latex":"\\text{year}^{-1}"}},{"type":"text","text":" because the half-life was given in years."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1b. How much radiation will be emitted after 30 years?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Radioactive Decay Calculations"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the first-order decay equation to determine the remaining activity (or amount) after a certain time."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Initial activity ("},{"type":"inlineMath","attrs":{"latex":"A_0"}},{"type":"text","text":"): The starting amount of radioactivity, here "},{"type":"inlineMath","attrs":{"latex":"1\\ \\mu\\text{Ci}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Remaining activity ("},{"type":"inlineMath","attrs":{"latex":"A"}},{"type":"text","text":"): The amount left after time "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"First-order decay equation: "},{"type":"inlineMath","attrs":{"latex":"A = A_0 e^{-kt}"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the known values: "},{"type":"inlineMath","attrs":{"latex":"A_0 = 1\\ \\mu\\text{Ci}"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" from part (a), "},{"type":"inlineMath","attrs":{"latex":"t = 30"}},{"type":"text","text":" years."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the first-order decay equation: "},{"type":"inlineMath","attrs":{"latex":"A = A_0 e^{-kt}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug in the values for "},{"type":"inlineMath","attrs":{"latex":"A_0"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":" (be sure $k$ and $t$ are in compatible units)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the exponent: "},{"type":"inlineMath","attrs":{"latex":"-kt"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"A = 0.955\\ \\mu\\text{Ci}"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"After 30 years, the activity is calculated using "},{"type":"inlineMath","attrs":{"latex":"A = 1 \\times e^{-0.00160 \\times 30}"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1c. How long will it be before the radiation is less than 0.100 μCi?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving for Time in First-Order Decay"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question asks you to determine the time required for the activity to decrease to a specified value using the first-order decay equation."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"First-order decay equation: "},{"type":"inlineMath","attrs":{"latex":"A = A_0 e^{-kt}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"To solve for "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":", rearrange: "},{"type":"inlineMath","attrs":{"latex":"t = \\frac{1}{k} \\ln\\left(\\frac{A_0}{A}\\right)"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the known values: "},{"type":"inlineMath","attrs":{"latex":"A_0 = 1\\ \\mu\\text{Ci}"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"A = 0.100\\ \\mu\\text{Ci}"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" from part (a)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the rearranged decay equation: "},{"type":"inlineMath","attrs":{"latex":"t = \\frac{1}{k} \\ln\\left(\\frac{A_0}{A}\\right)"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug in the values for "},{"type":"inlineMath","attrs":{"latex":"A_0"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"A"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the natural logarithm: "},{"type":"inlineMath","attrs":{"latex":"\\ln\\left(\\frac{1}{0.100}\\right)"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"t = 1,440\\ \\text{years}"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This is found by calculating "},{"type":"inlineMath","attrs":{"latex":"t = \\frac{1}{0.00160} \\ln(10)"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1d. BONUS: What is an alpha particle? Why is it safe for a radioactive source to be mandated by law to be installed in all buildings? What is the daughter nucleus after it decays?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Nuclear Chemistry and Radiation Safety"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of nuclear decay particles, safety considerations for alpha emitters, and nuclear decay products."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Alpha particle: A type of nuclear radiation consisting of 2 protons and 2 neutrons (a helium-4 nucleus)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Daughter nucleus: The new nucleus formed after radioactive decay."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Define what an alpha particle is (composition and charge)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Explain why alpha particles are generally considered safe in smoke detectors (penetration power, containment)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the nuclear equation for Am-241 alpha decay and identify the daughter nucleus (subtract 2 protons and 4 mass units from the parent)."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try answering in your own words before checking the explanation!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"An alpha particle is a helium-4 nucleus ("},{"type":"inlineMath","attrs":{"latex":"^4_2\\text{He}"}},{"type":"text","text":"). Alpha particles have low penetration and are stopped by air or a thin barrier, making them safe in smoke detectors. The daughter nucleus after Am-241 alpha decay is Neptunium-237 ("},{"type":"inlineMath","attrs":{"latex":"^{237}_{93}\\text{Np}"}},{"type":"text","text":")."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2a. Label each plot according to the order it represents."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Reaction Order and Integrated Rate Laws"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to recognize the graphical forms of zero, first, and second order reactions based on how concentration changes with time."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Zero order: "},{"type":"inlineMath","attrs":{"latex":"[A]"}},{"type":"text","text":" vs. "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":" is linear."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"First order: "},{"type":"inlineMath","attrs":{"latex":"\\ln([A])"}},{"type":"text","text":" vs. "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":" is linear."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Second order: "},{"type":"inlineMath","attrs":{"latex":"1/[A]"}},{"type":"text","text":" vs. "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":" is linear."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Recall the integrated rate law forms for each order and their linear plots."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Match each plot to the correct order based on which gives a straight line."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Label the axes and note which variable is plotted against time in each case."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try matching the plots before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Zero order: "},{"type":"inlineMath","attrs":{"latex":"[A]"}},{"type":"text","text":" vs. "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":" is linear. First order: "},{"type":"inlineMath","attrs":{"latex":"\\ln([A])"}},{"type":"text","text":" vs. $t$ is linear. Second order: "},{"type":"inlineMath","attrs":{"latex":"1/[A]"}},{"type":"text","text":" vs. $t$ is linear."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2b. What is the order of the reaction? How do you know?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Determining Reaction Order from Plots"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to interpret experimental data and determine the reaction order based on which plot is linear."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Order of reaction: The exponent to which the concentration term is raised in the rate law."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Linear plot: Indicates the correct integrated rate law for the reaction order."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Examine the plots from part (a) and identify which one is linear."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Recall which order corresponds to a linear plot of "},{"type":"inlineMath","attrs":{"latex":"[A]"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"\\ln([A])"}},{"type":"text","text":", or "},{"type":"inlineMath","attrs":{"latex":"1/[A]"}},{"type":"text","text":" vs. "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"State the order and justify your answer based on the plot's linearity."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try reasoning through the plots before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The reaction is first order because the "},{"type":"inlineMath","attrs":{"latex":"\\ln([A])"}},{"type":"text","text":" vs. "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":" plot is linear."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2c. What is the rate constant? What units does the rate constant have?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Determining the Rate Constant from Plots"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to extract the rate constant from the slope of a linearized integrated rate law plot and to assign correct units."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For first order: "},{"type":"inlineMath","attrs":{"latex":"\\ln([A]) = -kt + \\ln([A]_0)"}},{"type":"text","text":", so slope = "},{"type":"inlineMath","attrs":{"latex":"-k"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Units for first order "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":": "},{"type":"inlineMath","attrs":{"latex":"\\text{time}^{-1}"}},{"type":"text","text":" (e.g., "},{"type":"inlineMath","attrs":{"latex":"\\text{min}^{-1}"}},{"type":"text","text":")."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the slope of the linear plot ("},{"type":"inlineMath","attrs":{"latex":"\\ln([A])"}},{"type":"text","text":" vs. "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":")."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Recall that for first order, the slope is "},{"type":"inlineMath","attrs":{"latex":"-k"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Take the absolute value of the slope to find "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Assign the correct units based on the time axis (e.g., if "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":" is in minutes, "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" is in "},{"type":"inlineMath","attrs":{"latex":"\\text{min}^{-1}"}},{"type":"text","text":")."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try extracting the value from the plot before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"k = 0.554\\ \\text{min}^{-1}"}},{"type":"text","text":" (example value; use the actual slope from your plot). Units are "},{"type":"inlineMath","attrs":{"latex":"\\text{min}^{-1}"}},{"type":"text","text":"."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2d. What is the half-life of the reaction?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Half-life for First-Order Reactions"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the rate constant to calculate the half-life for a first-order reaction."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"First-order half-life: "},{"type":"inlineMath","attrs":{"latex":"t_{1/2} = \\frac{0.693}{k}"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Recall the formula for first-order half-life: "},{"type":"inlineMath","attrs":{"latex":"t_{1/2} = \\frac{0.693}{k}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the value of "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" from part (c)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the calculation, but do not compute the final value yet."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the calculation before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"t_{1/2} = \\frac{0.693}{0.554} = 1.25\\ \\text{min}"}},{"type":"text","text":" (example; use your "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" value)."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2e. What will the concentration of A be after 1.25 minutes?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Integrated Rate Law for First-Order Reactions"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the first-order integrated rate law to find the concentration at a given time."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"First-order integrated rate law: "},{"type":"inlineMath","attrs":{"latex":"[A] = [A]_0 e^{-kt}"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the initial concentration "},{"type":"inlineMath","attrs":{"latex":"[A]_0 = 6.50\\ \\text{M}"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" from part (c), and "},{"type":"inlineMath","attrs":{"latex":"t = 1.25"}},{"type":"text","text":" min."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the equation: "},{"type":"inlineMath","attrs":{"latex":"[A] = [A]_0 e^{-kt}"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug in the values for "},{"type":"inlineMath","attrs":{"latex":"[A]_0"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"t"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the exponent "},{"type":"inlineMath","attrs":{"latex":"-kt"}},{"type":"text","text":" for calculation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the calculation before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"[A] = 6.50 \\times e^{-0.554 \\times 1.25} = 2.60\\ \\text{M}"}},{"type":"text","text":" (example; use your "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" value)."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2f. When will the concentration of A be 0.50 M?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Solving for Time in First-Order Kinetics"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to rearrange the first-order integrated rate law to solve for time."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"First-order integrated rate law: "},{"type":"inlineMath","attrs":{"latex":"[A] = [A]_0 e^{-kt}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rearranged: "},{"type":"inlineMath","attrs":{"latex":"t = \\frac{1}{k} \\ln\\left(\\frac{[A]_0}{[A]}\\right)"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify "},{"type":"inlineMath","attrs":{"latex":"[A]_0 = 6.50\\ \\text{M}"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"[A] = 0.50\\ \\text{M}"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" from part (c)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the rearranged equation: "},{"type":"inlineMath","attrs":{"latex":"t = \\frac{1}{k} \\ln\\left(\\frac{[A]_0}{[A]}\\right)"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug in the values for "},{"type":"inlineMath","attrs":{"latex":"[A]_0"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"[A]"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the natural logarithm for calculation."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the calculation before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"t = \\frac{1}{0.554} \\ln\\left(\\frac{6.50}{0.50}\\right) = 3.60\\ \\text{min}"}},{"type":"text","text":" (example; use your "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" value)."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2g. If the activation energy of this reaction is 36.8 kJ/mol, what is the rate constant at 35.4°C?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Arrhenius Equation and Temperature Dependence of Rate Constants"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the Arrhenius equation to calculate the rate constant at a new temperature."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Arrhenius equation (two-point form): "},{"type":"inlineMath","attrs":{"latex":"\\ln\\left(\\frac{k_2}{k_1}\\right) = \\frac{E_a}{R}\\left(\\frac{1}{T_1} - \\frac{1}{T_2}\\right)"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"E_a"}},{"type":"text","text":": Activation energy (in J/mol)"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"R"}},{"type":"text","text":": Gas constant ("},{"type":"inlineMath","attrs":{"latex":"8.314\\ \\text{J/mol}\\cdot\\text{K}"}},{"type":"text","text":")"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"T_1"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"T_2"}},{"type":"text","text":": Temperatures in Kelvin"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Convert both temperatures to Kelvin: "},{"type":"inlineMath","attrs":{"latex":"T_1 = 18.3 + 273.15"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"T_2 = 35.4 + 273.15"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the rate constant "},{"type":"inlineMath","attrs":{"latex":"k_1"}},{"type":"text","text":" from earlier at "},{"type":"inlineMath","attrs":{"latex":"T_1"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug "},{"type":"inlineMath","attrs":{"latex":"E_a"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"R"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"T_1"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"T_2"}},{"type":"text","text":" into the Arrhenius equation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the equation to solve for "},{"type":"inlineMath","attrs":{"latex":"k_2"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the calculation before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"k_2 = k_1 \\times \\exp\\left[\\frac{36800}{8.314}\\left(\\frac{1}{291.45} - \\frac{1}{308.55}\\right)\\right]"}},{"type":"text","text":" (example; use your "},{"type":"inlineMath","attrs":{"latex":"k_1"}},{"type":"text","text":" value)."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q3. For each of the following, determine if the statement is true (T or +) or false (F or -)."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Chemical Kinetics Concepts"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your conceptual understanding of rate laws, reaction mechanisms, and terminology in kinetics."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rate law: An expression relating the rate of a reaction to the concentration of reactants (and sometimes catalysts)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Order: The exponent of a concentration term in the rate law."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Transition state: A high-energy, unstable arrangement of atoms during a reaction."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Bimolecular: A step involving two reactant species."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Enzyme: A biological catalyst; substrate: the reactant in an enzyme-catalyzed reaction."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Read each statement carefully and recall the relevant definition or concept."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For each, ask yourself: Does this match what you know from class or the textbook?"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Mark each as true or false, but be sure to justify your reasoning for each."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try answering each statement before checking the explanations!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a. F b. T c. F d. F e. F f. T g. T"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"See your notes or textbook for explanations of each statement."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q4. For each of the following orders, note the units for k."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Units of the Rate Constant"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to determine the units of the rate constant for different reaction orders."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"General rate law: "},{"type":"inlineMath","attrs":{"latex":"\\text{rate} = k [A]^n"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Units of rate: "},{"type":"inlineMath","attrs":{"latex":"\\text{M}/\\text{time}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Units of "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" depend on the overall order "},{"type":"inlineMath","attrs":{"latex":"n"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the general rate law for each order."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the units for rate and concentration."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Algebraically solve for the units of "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" for each order."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Express the units in terms of "},{"type":"inlineMath","attrs":{"latex":"\\text{M}"}},{"type":"text","text":" and "},{"type":"inlineMath","attrs":{"latex":"\\text{time}"}},{"type":"text","text":" (or \"time\")."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try deriving the units for each order before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"0th order: "},{"type":"inlineMath","attrs":{"latex":"\\text{M}/\\text{time}"}},{"type":"text","text":" 1st order: "},{"type":"inlineMath","attrs":{"latex":"1/\\text{time}"}},{"type":"text","text":" 2nd order: "},{"type":"inlineMath","attrs":{"latex":"1/(\\text{M}\\cdot\\text{time})"}},{"type":"text","text":" 7th order: "},{"type":"inlineMath","attrs":{"latex":"1/(\\text{M}^6\\cdot\\text{time})"}}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q5. What are the requirements for an effective collision?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Collision Theory"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of what is necessary for molecules to react when they collide."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Effective collision: A collision that leads to a chemical reaction."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Activation energy: The minimum energy required for a reaction to occur."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Orientation: The relative positioning of molecules during a collision."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Recall the two main requirements for an effective collision: sufficient energy and proper orientation."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Explain what is meant by each requirement."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Consider examples of ineffective collisions (e.g., low energy, wrong orientation)."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try listing the requirements before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"1. Colliding molecules must have energy equal to or greater than the activation energy. 2. Molecules must be oriented properly to allow bond breaking/forming."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q6a. What is the initial rate for Al?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Stoichiometry and Rate Relationships"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to relate the rate of disappearance of one reactant to another using the stoichiometry of the reaction."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rate of reaction: "},{"type":"inlineMath","attrs":{"latex":"\\text{rate} = -\\frac{1}{a} \\frac{d[A]}{dt}"}},{"type":"text","text":" for reactant A with coefficient "},{"type":"inlineMath","attrs":{"latex":"a"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Stoichiometric relationships: Use the balanced equation to relate rates."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the balanced equation: "},{"type":"inlineMath","attrs":{"latex":"2\\text{Al} + 3\\text{S}_8 \\rightarrow \\text{Al}_2\\text{S}_3"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the rate expressions for each species using their stoichiometric coefficients."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Relate the rate of disappearance of Al to the given rate for S"},{"type":"inlineMath","attrs":{"latex":"_8"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the proportional relationship using the coefficients."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the relationship before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Initial rate for Al: "},{"type":"inlineMath","attrs":{"latex":"-\\frac{2}{3} \\times 0.667 = -0.445\\ \\text{M/s}"}}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q6b. What is the initial rate for Al2S3?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Stoichiometry and Rate Relationships"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to relate the rate of appearance of a product to the rate of disappearance of a reactant."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rate of formation: "},{"type":"inlineMath","attrs":{"latex":"\\text{rate} = \\frac{1}{c} \\frac{d[C]}{dt}"}},{"type":"text","text":" for product C with coefficient "},{"type":"inlineMath","attrs":{"latex":"c"}},{"type":"text","text":"."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the balanced equation from part (a)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the rate expression for Al"},{"type":"inlineMath","attrs":{"latex":"_2"}},{"type":"text","text":"S"},{"type":"inlineMath","attrs":{"latex":"_3"}},{"type":"text","text":" using its coefficient."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Relate the rate of formation of Al"},{"type":"inlineMath","attrs":{"latex":"_2"}},{"type":"text","text":"S"},{"type":"inlineMath","attrs":{"latex":"_3"}},{"type":"text","text":" to the rate of disappearance of S"},{"type":"inlineMath","attrs":{"latex":"_8"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the proportional relationship using the coefficients."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try setting up the relationship before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Initial rate for Al"},{"type":"inlineMath","attrs":{"latex":"_2"}},{"type":"text","text":"S"},{"type":"inlineMath","attrs":{"latex":"_3"}},{"type":"text","text":": "},{"type":"inlineMath","attrs":{"latex":"\\frac{1}{3} \\times 0.667 = 0.222\\ \\text{M/s}"}}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q6c–h. Orders and Rate Law Effects"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Rate Laws and Reaction Order"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"These questions test your understanding of how the rate law is affected by changes in concentration and the meaning of reaction order."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Given rate law: "},{"type":"inlineMath","attrs":{"latex":"\\text{rate} = k[\\text{S}_8]^2"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Order in a reactant: The exponent of its concentration in the rate law."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Overall order: Sum of exponents in the rate law."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For each part, identify the relevant order from the rate law."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For changes in concentration, use the rate law to predict the effect (e.g., tripling "},{"type":"inlineMath","attrs":{"latex":"[\\text{S}_8]"}},{"type":"text","text":" increases rate by "},{"type":"inlineMath","attrs":{"latex":"3^2"}},{"type":"text","text":")."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For reactants not in the rate law, changing their concentration has no effect on rate."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try reasoning through each scenario before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c. Order in Al: 0 d. Order in S"},{"type":"inlineMath","attrs":{"latex":"_8"}},{"type":"text","text":": 2 e. Overall order: 2 f. Tripling S$_8$ increases rate by 9x g. Halving Al has no effect h. Quartering S$_8$ decreases rate by 16x; tripling Al has no effect"}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q7. Determine the rate law and rate constants for the above reaction."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Experimental Determination of Rate Laws"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use initial rate data to determine the order of reaction with respect to each reactant and the rate constant."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"General rate law: "},{"type":"inlineMath","attrs":{"latex":"\\text{rate} = k [\\text{N}_2]^x [\\text{H}_2]^y [\\text{Fe}]^z"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"To find order: Compare experiments where only one reactant changes."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"To find "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":": Plug in values from any experiment after determining orders."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Compare experiments where only "},{"type":"inlineMath","attrs":{"latex":"[\\text{N}_2]"}},{"type":"text","text":" changes to find "},{"type":"inlineMath","attrs":{"latex":"x"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Compare experiments where only "},{"type":"inlineMath","attrs":{"latex":"[\\text{H}_2]"}},{"type":"text","text":" changes to find "},{"type":"inlineMath","attrs":{"latex":"y"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Compare experiments where only "},{"type":"inlineMath","attrs":{"latex":"[\\text{Fe}]"}},{"type":"text","text":" changes to find "},{"type":"inlineMath","attrs":{"latex":"z"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Add up the exponents to get the overall order."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Plug in concentrations and rate from any experiment to solve for "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Write the full rate law with determined orders and "},{"type":"inlineMath","attrs":{"latex":"k"}},{"type":"text","text":" value."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try analyzing the data before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a. Order in N"},{"type":"inlineMath","attrs":{"latex":"_2"}},{"type":"text","text":": 0 b. Order in H$_2$: 1 c. Order in Fe: 1 d. Overall order: 2 e. "},{"type":"inlineMath","attrs":{"latex":"k = 0.0322\\ \\text{M}^{-1}\\text{s}^{-1}"}},{"type":"text","text":" f. Rate law: "},{"type":"inlineMath","attrs":{"latex":"\\text{rate} = 0.0322 [\\text{H}_2][\\text{Fe}]"}}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q8. Consider the following mechanism."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Reaction Mechanisms, Intermediates, and Catalysts"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to identify intermediates and catalysts in a mechanism and to write rate laws based on the slow step."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms and Formulas"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Intermediate: Produced in one step, consumed in another."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Catalyst: Present at start and end, not consumed."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Rate law for slow step: Based on reactants in that step."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"List all species in the mechanism and track their appearance/disappearance."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify intermediates and catalysts."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For each possible slow step, write the rate law using the reactants in that step."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For the last part, use all information to deduce which step is likely slow and justify."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try identifying intermediates and writing rate laws before checking the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Intermediates: FeN"},{"type":"inlineMath","attrs":{"latex":"_2"}},{"type":"text","text":", FeN$_2$H$_2$, FeNH Catalyst: Fe Rate law for slow step: Use reactants of that step (e.g., if first step is slow, rate = k[Fe][N$_2$]) Mechanism deduction: The step whose rate law matches the experimentally determined rate law is likely the slow step."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q9. Draw an appropriate reaction coordinate diagram and label all features."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Reaction Coordinate Diagrams"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to represent the energy changes during a reaction, including reactants, products, transition states, intermediates, activation energy, and enthalpy change."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Reaction coordinate: Progress of the reaction from reactants to products."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Transition state: Peak(s) on the diagram."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Intermediates: Valleys between peaks."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Activation energy: Energy difference from reactants to transition state."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Enthalpy change ("},{"type":"inlineMath","attrs":{"latex":"\\Delta H"}},{"type":"text","text":"): Energy difference between reactants and products."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Draw the energy axis (vertica