CHE 104 General Chemistry II Exam 3A – Guided Study Notes

Q1. Which of the following statements is/are correct?

Background

Topic: Acid-Base Equilibria and Relationships

This question tests your understanding of the relationships between the ion-product constant for water ($K_w$), the relationship between pH and pOH, and the relationship between $K_a$ and $K_b$ for conjugate acid-base pairs.

Key Terms and Formulas:

• $K_w = [H_3O^+][OH^-]$

• $pH + pOH = 14$ (at 25°C)

• $K_a \times K_b = K_w$ (for a conjugate acid-base pair)

Step-by-Step Guidance

1. Review each statement (i, ii, iii) and recall the definitions and relationships above.

2. For (i): Consider the definition of the ion-product constant for water.

3. For (ii): Recall the relationship between pH and pOH at standard temperature (25°C).

4. For (iii): Think about how $K_a$ and $K_b$ relate for conjugate acid-base pairs.

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Q2. What is the pH of a weak base (Kb = 2.82 \times 10^{-6}) with a solution concentration of 0.375 M?

Background

Topic: Weak Base Equilibria and pH Calculation

This question tests your ability to calculate the pH of a solution containing a weak base, using its base dissociation constant ($K_b$) and concentration.

Key Terms and Formulas:

• $K_b$ = base dissociation constant

• ICE table (Initial, Change, Equilibrium) for weak base equilibrium

• $K_b = \frac{[BH^+][OH^-]}{[B]}$

• $pOH = -\log[OH^-]$

• $pH = 14 - pOH$

Step-by-Step Guidance

1. Write the equilibrium equation for the weak base in water: $B + H_2O \rightleftharpoons BH^+ + OH^-$

2. Set up an ICE table using the initial concentration of the base (0.375 M) and let $x$ be the amount that reacts.

3. Express the equilibrium concentrations in terms of $x$ and substitute into the $K_b$ expression.

4. Solve for $x$ (which equals $[OH^-]$), and then calculate $pOH$ using $pOH = -\log[OH^-]$.

5. Use $pH = 14 - pOH$ to find the pH.

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Q3. Which of the following would be a buffer?

Background

Topic: Buffer Solutions

This question tests your understanding of what constitutes a buffer solution and how to recognize buffer pairs.

Key Terms and Concepts:

• Buffer: A solution that resists changes in pH when small amounts of acid or base are added.

• Composed of a weak acid and its conjugate base, or a weak base and its conjugate acid.

Step-by-Step Guidance

1. For each option, identify if the pair consists of a weak acid and its conjugate base, or a weak base and its conjugate acid.

2. Eliminate options that contain strong acids or bases, as these do not form buffers with their salts.

3. Check if the concentrations are similar, which is typical for effective buffers.

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Q4. Which of the following is the strongest acid?

Background

Topic: Acid Strength and pKa

This question tests your ability to compare acid strengths using pKa values.

Key Terms and Concepts:

• pKa: The negative logarithm of the acid dissociation constant ($K_a$); lower pKa means a stronger acid.

Step-by-Step Guidance

1. Recall that a lower pKa value indicates a stronger acid.

2. Compare the pKa values given for each acid.

3. Identify the acid with the lowest pKa value.

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Q5. What mass (in g) of sodium bicarbonate (84.01 g/mol) is needed to prepare a 6.6 pH buffer solution when mixed with 10.0 mL of a 3.0 M solution of carbonic acid? The Ka of carbonic acid is 4.3 \times 10^{-7}.

Background

Topic: Buffer Preparation and Henderson-Hasselbalch Equation

This question tests your ability to use the Henderson-Hasselbalch equation to prepare a buffer of a specific pH.

Key Terms and Formulas:

• Henderson-Hasselbalch equation: $pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• $[A^-]$ = concentration of conjugate base (sodium bicarbonate)

• $[HA]$ = concentration of weak acid (carbonic acid)

• To find mass: $\text{mass} = \text{moles} \times \text{molar mass}$

Step-by-Step Guidance

1. Calculate $pK_a$ from the given $K_a$ using $pK_a = -\log(K_a)$.

2. Use the Henderson-Hasselbalch equation to solve for the required ratio $\frac{[A^-]}{[HA]}$ for the desired pH.

3. Calculate the moles of carbonic acid ($HA$) present using volume and concentration.

4. Use the ratio from step 2 and the moles of $HA$ to find the required moles of sodium bicarbonate ($A^-$).

5. Convert moles of sodium bicarbonate to grams using its molar mass.

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Q6. At what temperature must entropy be equal to zero?

Background

Topic: Third Law of Thermodynamics

This question tests your understanding of the third law of thermodynamics and the concept of absolute entropy.

Key Terms and Concepts:

• Third Law of Thermodynamics: The entropy of a perfect crystal at absolute zero is zero.

• Absolute zero: 0 K

Step-by-Step Guidance

1. Recall the definition of entropy and the third law of thermodynamics.

2. Identify the temperature corresponding to absolute zero.

3. Match this temperature to the options provided.

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Q7. Which of the following is expected to have an increase in entropy?

Background

Topic: Entropy Changes in Physical and Chemical Processes

This question tests your ability to predict the sign of entropy change for various processes.

Key Terms and Concepts:

• Entropy ($S$): A measure of disorder or randomness in a system.

• Processes that increase disorder (e.g., melting, vaporization, dissolution) increase entropy.

Step-by-Step Guidance

1. For each process, determine if the system becomes more disordered (solid to liquid/gas, dissolution, etc.).

2. Identify which processes involve an increase in the number of microstates or dispersal of energy.

3. Select the option(s) that correspond to an increase in entropy.

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Q8. Calculate the change in entropy for the following reaction: 4 Al (s) + 3 MnO2 (s) → 2 Al2O3 (s) + 3 Mn (s)

Background

Topic: Standard Entropy Change for a Reaction

This question tests your ability to calculate the standard entropy change ($\Delta S^\circ$) for a reaction using standard molar entropies.

Key Terms and Formulas:

• $\Delta S^\circ_{rxn} = \sum n S^\circ_{products} - \sum n S^\circ_{reactants}$

• Use the provided $S^\circ$ values for each substance.

Step-by-Step Guidance

1. List the standard molar entropy ($S^\circ$) values for each reactant and product from the table.

2. Multiply each $S^\circ$ value by its stoichiometric coefficient in the balanced equation.

3. Sum the total $S^\circ$ for products and for reactants separately.

4. Subtract the sum for reactants from the sum for products to find $\Delta S^\circ_{rxn}$.

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Q9. A chemical reaction is endothermic and has a decrease in entropy. Which of the following statements is correct?

Background

Topic: Spontaneity, Enthalpy, and Entropy

This question tests your understanding of how enthalpy ($\Delta H$) and entropy ($\Delta S$) changes affect the spontaneity of a reaction.

Key Terms and Formulas:

• Gibbs Free Energy: $\Delta G = \Delta H - T\Delta S$

• Spontaneity: $\Delta G < 0$ means spontaneous

• Endothermic: $\Delta H > 0$; Decrease in entropy: $\Delta S < 0$

Step-by-Step Guidance

1. Substitute the signs for $\Delta H$ and $\Delta S$ into the Gibbs free energy equation.

2. Analyze how increasing temperature ($T$) affects $\Delta G$ with these signs.

3. Determine if $\Delta G$ can ever be negative (spontaneous) under any temperature conditions.

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Q10. What is the change in free energy at 80.0 ºC for the reaction: Zn (s) + 2 HCl (aq) → ZnCl2 (aq) + H2 (g)?

Background

Topic: Gibbs Free Energy Change at Non-Standard Temperature

This question tests your ability to calculate $\Delta G$ at a temperature other than 25°C using $\Delta H^\circ$ and $\Delta S^\circ$.

Key Terms and Formulas:

• $\Delta G = \Delta H - T\Delta S$

• Convert temperature to Kelvin: $T(K) = T(°C) + 273.15$

• Ensure units for $\Delta S$ are in kJ (divide by 1000 if necessary)

Step-by-Step Guidance

1. Convert 80.0 ºC to Kelvin.

2. Convert $\Delta S^\circ$ from J/mol·K to kJ/mol·K if needed.

3. Plug $\Delta H^\circ$, $T$, and $\Delta S^\circ$ into the Gibbs free energy equation.

4. Set up the calculation for $\Delta G$ but stop before the final arithmetic step.

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Q11. What is the boiling point of mercury?

Background

Topic: Physical Properties of Elements

This question tests your knowledge of the boiling point of mercury, a commonly referenced element in chemistry.

Key Terms:

• Boiling point: The temperature at which a substance changes from liquid to gas at atmospheric pressure.

Step-by-Step Guidance

1. Recall or look up the boiling point of mercury in standard reference tables.

2. Compare the value to the options provided.

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Q12. What is the value of Kw at 98.0 ºC?

Background

Topic: Temperature Dependence of the Ion-Product Constant for Water

This question tests your understanding of how $K_w$ changes with temperature.

Key Terms and Concepts:

• $K_w$: Ion-product constant for water

• As temperature increases, $K_w$ increases

Step-by-Step Guidance

1. Recall the trend that $K_w$ increases with temperature.

2. Compare the given options to the standard value at 25°C ($1.0 \times 10^{-14}$) and select the value that makes sense for 98.0 ºC.

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Q13. What is the correct cell notation for the following electrochemical cell?

Background

Topic: Electrochemical Cell Notation

This question tests your ability to write the correct cell notation for a galvanic cell.

Key Terms and Concepts:

• Cell notation: Anode | Anode solution || Cathode solution | Cathode

• Anode: Site of oxidation; Cathode: Site of reduction

Step-by-Step Guidance

1. Identify which species is oxidized (anode) and which is reduced (cathode).

2. Write the cell notation in the correct order: anode on the left, cathode on the right.

3. Match your notation to the options provided.

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Q14. What is the standard cell potential for the spontaneous reaction between Ni/Ni2+ and Fe/Fe2+?

Background

Topic: Standard Cell Potentials

This question tests your ability to calculate the standard cell potential ($E^\circ_{cell}$) using standard reduction potentials.

Key Terms and Formulas:

• $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$

• Identify which half-reaction is the cathode (reduction) and which is the anode (oxidation).

Step-by-Step Guidance

1. Write the half-reactions and their standard reduction potentials.

2. Determine which species is oxidized and which is reduced in the spontaneous reaction.

3. Plug the values into the $E^\circ_{cell}$ formula.

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Q15. Which of the following statements will increase the spontaneous cell potential for an electrochemical reaction?

Background

Topic: Factors Affecting Cell Potential

This question tests your understanding of how changes in concentration and temperature affect the cell potential.

Key Terms and Concepts:

• Nernst equation: $E = E^\circ - \frac{0.0592}{n} \log Q$

• Increasing cathode concentration or decreasing anode concentration generally increases cell potential.

Step-by-Step Guidance

1. For each statement, consider how it affects the reaction quotient $Q$ in the Nernst equation.

2. Recall that increasing the concentration of the cathode ion or decreasing the anode ion increases $E_{cell}$.

3. Consider the effect of temperature on cell potential.

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Q16. What is the cell potential for the spontaneous reaction between Mn/Mn2+ (0.025 M) and Cr/Cr3+ (11.5 M) at 50. ºC?

Background

Topic: Nernst Equation and Non-Standard Conditions

This question tests your ability to use the Nernst equation to calculate cell potential under non-standard concentrations and temperature.

Key Terms and Formulas:

• Nernst equation: $E = E^\circ - \frac{0.0592}{n} \log Q$ (at 25°C; adjust for other temperatures)

• Reaction quotient $Q$ based on ion concentrations

• Convert temperature to Kelvin

Step-by-Step Guidance

1. Write the half-reactions and determine which is the anode and which is the cathode.

2. Calculate $E^\circ_{cell}$ using standard reduction potentials.

3. Write the expression for $Q$ using the given concentrations.

4. Plug values into the Nernst equation, adjusting the constant for the temperature if necessary.

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Q17. What is the initial pH of the 0.120 M solution of nitrous acid before any sodium hydroxide titrant is added?

Background

Topic: Weak Acid Equilibria

This question tests your ability to calculate the pH of a weak acid solution using its $K_a$ and concentration.

Key Terms and Formulas:

• ICE table for weak acid dissociation: $HNO_2 \rightleftharpoons H^+ + NO_2^-$

• $K_a = \frac{[H^+][NO_2^-]}{[HNO_2]}$

• $pH = -\log[H^+]$

Step-by-Step Guidance

1. Set up an ICE table for the dissociation of nitrous acid.

2. Let $x$ be the amount of $HNO_2$ that dissociates; write equilibrium concentrations in terms of $x$.

3. Substitute into the $K_a$ expression and solve for $x$ ($[H^+]$).

4. Calculate $pH$ using $pH = -\log[H^+]$.

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Q18. What is the pH when 24.0 mL of 0.100 M sodium hydroxide is added to the 30.0 mL of 0.120 M nitrous acid?

Background

Topic: Buffer Calculations During Titration

This question tests your ability to calculate the pH of a buffer solution after partial neutralization during a titration.

Key Terms and Formulas:

• Henderson-Hasselbalch equation: $pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• Stoichiometry: Calculate moles of acid and base, and determine amounts of $HA$ and $A^-$ after reaction.

Step-by-Step Guidance

1. Calculate the initial moles of $HNO_2$ and $OH^-$ added.

2. Determine how much $HNO_2$ is neutralized and how much $NO_2^-$ is formed.

3. Calculate the new concentrations of $HA$ and $A^-$ in the total volume.

4. Plug these values into the Henderson-Hasselbalch equation to find the pH.

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Q19. What is the pH when 36.0 mL of 0.100 M sodium hydroxide is added to the 30.0 mL of 0.120 M nitrous acid?

Background

Topic: Titration Beyond the Equivalence Point

This question tests your ability to calculate the pH after all the weak acid has been neutralized and excess base is present.

Key Terms and Formulas:

• Stoichiometry: Calculate moles of $OH^-$ in excess after neutralization.

• $[OH^-] = \frac{\text{excess moles}}{\text{total volume}}$

• $pOH = -\log[OH^-]$; $pH = 14 - pOH$

Step-by-Step Guidance

1. Calculate the moles of $HNO_2$ and $OH^-$ added.

2. Determine the excess moles of $OH^-$ after all $HNO_2$ is neutralized.

3. Calculate the concentration of $OH^-$ in the new total volume.

4. Find $pOH$ and then $pH$.

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Q20. What is the pH when 48.0 mL of 0.100 M sodium hydroxide is added to the 30.0 mL of 0.120 M nitrous acid?

Background

Topic: Titration with Excess Strong Base

This question tests your ability to calculate the pH when a large excess of strong base is present after complete neutralization of the weak acid.

Key Terms and Formulas:

• Stoichiometry: Find excess $OH^-$ after all $HNO_2$ is neutralized.

• $[OH^-] = \frac{\text{excess moles}}{\text{total volume}}$

• $pOH = -\log[OH^-]$; $pH = 14 - pOH$

Step-by-Step Guidance

1. Calculate the moles of $HNO_2$ and $OH^-$ added.

2. Determine the excess moles of $OH^-$ after all $HNO_2$ is neutralized.

3. Calculate the concentration of $OH^-$ in the total solution volume.

4. Find $pOH$ and then $pH$.

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