General Chemistry Exam 3 Study Guide – Step-by-Step Guidance

Q1. What is a greenhouse gas?

Background

Topic: Environmental Chemistry – Greenhouse Gases

This question tests your understanding of what defines a greenhouse gas and why certain gases in the atmosphere contribute to the greenhouse effect.

Key Terms:

• Greenhouse gas: A gas that absorbs and emits infrared radiation, contributing to the greenhouse effect.

• Greenhouse effect: The warming of Earth's surface due to atmospheric gases trapping heat.

Step-by-Step Guidance

1. Recall that greenhouse gases are molecules in the atmosphere that can absorb infrared (IR) radiation emitted by the Earth's surface.

2. Think about which gases have molecular structures that allow them to vibrate in ways that interact with IR radiation (e.g., CO2, H2O, CH4).

3. Consider why some gases (like N2 and O2) are not greenhouse gases, based on their molecular symmetry and lack of IR absorption.

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Q2. How does the concentration of greenhouse gases influence absorption in the atmosphere? (Consider Beer's Law, $A = ebc$)

Background

Topic: Spectroscopy and Atmospheric Chemistry

This question tests your understanding of how the amount of a greenhouse gas affects the absorption of radiation, using Beer's Law.

Key Terms and Formula:

• Beer's Law: $A = \varepsilon b c$

• $A$ = absorbance (unitless)

• $\varepsilon$ = molar absorptivity (L·mol–1·cm–1)

• $b$ = path length (cm)

• $c$ = concentration (mol/L)

Step-by-Step Guidance

1. Recall the relationship given by Beer's Law: $A = \varepsilon b c$.

2. Think about how increasing the concentration ($c$) of a greenhouse gas affects the absorbance ($A$), assuming $\varepsilon$ and $b$ are constant.

3. Consider what this means for the amount of energy absorbed by the atmosphere as greenhouse gas concentration changes.

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Q3. What wavelength/frequency regime interacts with molecular vibration of greenhouse gases?

Background

Topic: Molecular Vibrations and Electromagnetic Spectrum

This question tests your knowledge of which part of the electromagnetic spectrum is absorbed by greenhouse gases due to molecular vibrations.

Key Terms:

• Wavelength ($\lambda$): The distance between successive peaks of a wave (measured in meters or micrometers).

• Frequency ($\nu$): The number of wave cycles per second (measured in Hz).

• Infrared (IR) region: The part of the electromagnetic spectrum associated with molecular vibrations.

Step-by-Step Guidance

1. Recall that molecular vibrations are typically excited by photons in the infrared (IR) region of the electromagnetic spectrum.

2. Think about the approximate wavelength range for IR radiation (e.g., 700 nm to 1 mm).

3. Consider why visible or ultraviolet light does not usually cause vibrational transitions in greenhouse gases.

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Q4. What is symmetry breaking for vibrational modes of molecules? Why don’t O2(g) or N2(g) have symmetry breaking?

Background

Topic: Molecular Vibrations and IR Activity

This question tests your understanding of molecular symmetry and why some molecules do not absorb IR radiation.

Key Terms:

• Symmetry breaking: A change in the distribution of charge during vibration that allows a molecule to interact with IR light.

• IR active: A vibrational mode that results in a change in dipole moment and can absorb IR radiation.

Step-by-Step Guidance

1. Recall that for a vibrational mode to be IR active, it must involve a change in the dipole moment of the molecule.

2. Think about the symmetry of diatomic molecules like O2 and N2 and whether their vibrations cause a dipole moment change.

3. Consider why molecules with more than two atoms (like CO2 or H2O) can have IR active modes due to symmetry breaking.

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Q5. What is resonance in the case of energy transfer and what is required for resonance to happen? (Examples: moving a swing or demonstrating a slinky with frequency matching)

Background

Topic: Resonance and Energy Transfer

This question tests your understanding of resonance as it applies to physical systems and energy transfer, including molecular vibrations.

Key Terms:

• Resonance: The condition where a system absorbs energy most efficiently when the frequency of the external force matches the system's natural frequency.

• Natural frequency: The frequency at which a system naturally oscillates.

Step-by-Step Guidance

1. Recall that resonance occurs when the frequency of an external force matches the natural frequency of a system (e.g., pushing a swing at the right moment).

2. Think about how this concept applies to molecules absorbing energy from electromagnetic radiation (the frequency of light matches the vibrational frequency).

3. Consider what is required for resonance: matching frequencies and a system capable of oscillating at that frequency.

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Q6. Balance the following chemical equation: C3H8 + O2 → CO2 + H2O

Background

Topic: Chemical Equations and Stoichiometry

This question tests your ability to balance a combustion reaction and understand the conservation of mass.

Key Terms:

• Combustion reaction: A reaction where a hydrocarbon reacts with O2 to produce CO2 and H2O.

• Balancing equations: Ensuring the same number of each type of atom on both sides of the equation.

Step-by-Step Guidance

1. Write the unbalanced equation: $\mathrm{C_3H_8 + O_2 \rightarrow CO_2 + H_2O}$

2. Start by balancing the carbon atoms. There are 3 carbons in C3H8, so place a coefficient of 3 in front of CO2.

3. Next, balance the hydrogen atoms. There are 8 hydrogens in C3H8, so place a coefficient of 4 in front of H2O.

4. Now, count the total number of oxygen atoms on the product side and adjust the O2 coefficient accordingly.

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Q7. What is a limiting reactant? How do you identify it in a chemical reaction?

Background

Topic: Stoichiometry – Limiting Reactant

This question tests your understanding of how to determine which reactant will be consumed first in a chemical reaction.

Key Terms:

• Limiting reactant: The reactant that is completely consumed first, limiting the amount of product formed.

• Excess reactant: The reactant that remains after the reaction is complete.

Step-by-Step Guidance

1. Write the balanced chemical equation for the reaction.

2. Convert the amounts of each reactant (in grams or moles) to moles if necessary.

3. Use stoichiometry to determine how much product each reactant could produce.

4. The reactant that produces the least amount of product is the limiting reactant.

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Q8. Calculate the percentage yield if you start with 10.0 g of reactant and recover 7.5 g of product. (Assume the theoretical yield is 9.0 g.)

Background

Topic: Stoichiometry – Percentage Yield

This question tests your ability to calculate the efficiency of a chemical reaction.

Key Formula:

• Percentage yield = $\frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$

Step-by-Step Guidance

1. Identify the actual yield (amount of product recovered) and the theoretical yield (maximum possible amount based on stoichiometry).

2. Plug the values into the percentage yield formula: $\frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$

3. Calculate the percentage yield using the given numbers (actual yield = 7.5 g, theoretical yield = 9.0 g).

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Q9. Define molarity and show how to calculate the number of moles in 250 mL of a 0.200 M NaCl solution.

Background

Topic: Solution Chemistry – Molarity

This question tests your understanding of molarity and how to use it to find the amount of solute in a given volume of solution.

Key Formula:

• Molarity ($M$) = $\frac{\text{moles of solute}}{\text{liters of solution}}$

• Number of moles = $M \times V$ (where $V$ is in liters)

Step-by-Step Guidance

1. Convert the volume from mL to L: $250\ \text{mL} = 0.250\ \text{L}$

2. Use the formula: number of moles = $M \times V$

3. Plug in the values: $0.200\ \text{mol/L} \times 0.250\ \text{L}$

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Q10. What is the dilution equation and when should you use it?

Background

Topic: Solution Chemistry – Dilutions

This question tests your understanding of how to prepare solutions of lower concentration from a more concentrated stock solution.

Key Formula:

• Dilution equation: $M_1 V_1 = M_2 V_2$

• $M_1$ = initial molarity, $V_1$ = initial volume

• $M_2$ = final molarity, $V_2$ = final volume

Step-by-Step Guidance

1. Use the dilution equation when you are diluting a stock solution to a lower concentration.

2. Set up the equation with the known values and solve for the unknown (either $M_2$, $V_2$, $M_1$, or $V_1$).

3. Remember, this equation assumes no chemical reaction occurs during dilution—just mixing with solvent.

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Q11. Assign oxidation numbers to each element in H2O2.

Background

Topic: Redox Chemistry – Oxidation Numbers

This question tests your ability to assign oxidation numbers to elements in a compound.

Key Terms and Rules:

• Oxidation number of hydrogen is usually +1.

• Oxygen is usually –2, but in peroxides (like H2O2), it is –1.

• The sum of oxidation numbers in a neutral molecule is zero.

Step-by-Step Guidance

1. Assign the oxidation number of hydrogen as +1.

2. Let the oxidation number of oxygen be $x$.

3. Set up the equation: $2(+1) + 2(x) = 0$

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Q12. Calculate $\Delta H$ for the reaction: C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(l) using the heats of formation provided.

Background

Topic: Thermochemistry – Heats of Formation and Hess's Law

This question tests your ability to use standard enthalpies of formation to calculate the enthalpy change for a reaction.

Key Formula:

• $\Delta H = \sum n \Delta H_\mathrm{f}^\circ(\text{products}) - \sum n \Delta H_\mathrm{f}^\circ(\text{reactants})$

Step-by-Step Guidance

1. List the heats of formation for each compound (from the provided table): C3H8(g): –104 kJ/mol CO2(g): –393.5 kJ/mol H2O(l): –285.8 kJ/mol O2(g): 0 kJ/mol

2. Multiply each $\Delta H_\mathrm{f}^\circ$ by the number of moles in the balanced equation.

3. Sum the products' enthalpies and the reactants' enthalpies separately.

4. Subtract the sum for reactants from the sum for products using the formula above.

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