Thermodynamics, Entropy, and Equilibrium: Step-by-Step General Chemistry Guidance

Q1. Above what temperature does the following reaction become nonspontaneous?

FeO(s) + CO(g) → CO2(g) + Fe(s) ΔH = -11.0 kJ; ΔS = -17.4 J/K

Background

Topic: Thermodynamics – Spontaneity of Reactions

This question tests your understanding of how enthalpy (ΔH) and entropy (ΔS) affect the spontaneity of a reaction, using the Gibbs free energy equation.

Key formula:

$\Delta G = \Delta H - T\Delta S$

• $\Delta G$ = Gibbs free energy change

• $\Delta H$ = enthalpy change (in kJ)

• $\Delta S$ = entropy change (in J/K)

• $T$ = temperature (in K)

Step-by-Step Guidance

1. Recall that a reaction is nonspontaneous when $\Delta G > 0$.

2. Set up the equation: $\Delta G = \Delta H - T\Delta S$ and solve for the temperature where $\Delta G = 0$ (the threshold between spontaneous and nonspontaneous).

3. Convert $\Delta H$ to J if needed, so units match with $\Delta S$.

4. Rearrange the equation to solve for $T$: $T = \frac{\Delta H}{\Delta S}$.

Try solving on your own before revealing the answer!

Q2. Which of the following processes have a ΔS < 0?

Background

Topic: Entropy Changes in Physical Processes

This question tests your ability to recognize when entropy decreases (ΔS < 0) in phase changes or temperature changes.

Key Terms:

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

• ΔS < 0: Indicates a decrease in entropy (system becomes more ordered).

Step-by-Step Guidance

1. Identify which processes involve a transition to a more ordered state (solidification, condensation, cooling).

2. Recall that freezing, condensation, and deposition (gas to solid) all decrease entropy.

3. Consider the effect of lowering temperature on a gas: less molecular motion, more order.

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Q3. Consider the figure which shows ΔG° for a chemical process plotted against absolute temperature. What can you conclude?

Background

Topic: Gibbs Free Energy and Temperature Dependence

This question tests your ability to interpret a plot of ΔG° versus temperature and relate it to the signs of ΔH° and ΔS°.

Key formula:

$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$

Step-by-Step Guidance

1. Observe the slope of the line: If ΔG° increases with T, then $-\Delta S^\circ$ is positive, so $\Delta S^\circ$ is negative.

2. Check the y-intercept: At $T = 0$, $\Delta G^\circ = \Delta H^\circ$.

3. Determine the sign of $\Delta H^\circ$ from the y-intercept (positive or negative).

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Q4. ΔG° for the reaction A(aq) + B(aq) ⇄ C(aq) is -4.95 kJ/mol at 25°C. If [A] = 0.30 M, [B] = 0.40 M, and [C] = 12.6 M, what will occur?

Background

Topic: Reaction Direction and Gibbs Free Energy

This question tests your ability to use ΔG° and concentrations to predict the direction of a reaction.

Key formula:

$\Delta G = \Delta G^\circ + RT \ln Q$

• $Q$ = reaction quotient, calculated from concentrations

• $R$ = gas constant ($8.314 \text{ J/mol·K}$)

• $T$ = temperature in Kelvin

Step-by-Step Guidance

1. Calculate $Q = \frac{[C]}{[A][B]}$ using the given concentrations.

2. Plug $Q$, $\Delta G^\circ$, $R$, and $T$ into the formula to find $\Delta G$.

3. Determine whether $\Delta G$ is positive or negative to predict the direction of the reaction.

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Q5. Of the following, which has the largest entropy?

Background

Topic: Entropy and States of Matter

This question tests your understanding of how entropy varies between different phases and substances.

Key Terms:

• Entropy ($S$): Higher in gases than liquids, higher in liquids than solids.

Step-by-Step Guidance

1. Recall the order: $S_{\text{gas}} > S_{\text{liquid}} > S_{\text{solid}}$.

2. Compare the substances and their phases to determine which is most disordered.

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Q6. Which of the following does not have a ΔG° value of zero?

Background

Topic: Standard Free Energy of Formation

This question tests your knowledge of which substances have a standard free energy of formation ($\Delta G^\circ_f$) of zero.

Key Terms:

• Standard state: Most stable form of an element at 1 atm and 25°C.

• $\Delta G^\circ_f = 0$ for elements in their standard state.

Step-by-Step Guidance

1. Identify which substances are elements in their standard state.

2. Recall that only these have $\Delta G^\circ_f = 0$.

Try solving on your own before revealing the answer!

Q7. Which of the following statements is true?

Background

Topic: Laws of Thermodynamics and Entropy

This question tests your understanding of the second law of thermodynamics, entropy, and standard states.

Key Terms:

• Second law: Entropy of the universe increases for spontaneous processes.

• Standard entropy ($S^\circ$): Absolute values can be measured.

Step-by-Step Guidance

1. Review each statement and compare it to thermodynamic principles.

2. Identify which statement accurately reflects the laws or properties discussed.

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Q8. A container is filled with Ne gas. Which change increases the entropy of the system?

Background

Topic: Entropy and Molecular Motion

This question tests your understanding of how changes in volume, temperature, number of particles, and type of gas affect entropy.

Key Terms:

• Entropy increases with more particles, higher temperature, larger volume, and heavier atoms.

Step-by-Step Guidance

1. Consider how each change affects the disorder or randomness of the system.

2. Recall that increasing any of these factors generally increases entropy.

Try solving on your own before revealing the answer!

Q9. Balance the following reactions:

Zn(s) + ReO4-(aq) → Re(s) + Zn2+(aq) in acidic solution CN-(aq) + Fe3+(aq) → CNO-(aq) + Fe2+(aq) in basic solution

Background

Topic: Redox Reactions and Balancing Equations

This question tests your ability to balance redox reactions in acidic and basic solutions.

Key Steps:

• Assign oxidation states to each element.

• Write half-reactions for oxidation and reduction.

• Balance atoms and charges using electrons, H+, and OH- as appropriate.

Step-by-Step Guidance

1. Write the oxidation and reduction half-reactions for each equation.

2. Balance atoms other than H and O.

3. Balance O using H2O, H using H+ (acidic) or OH- (basic).

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Q10. Calculate ΔG° (kJ) for the reaction CO(g) → C(s) + 1/2 O2(g) given:

CO2(g) → C(s) + O2(g), ΔG°rxn = +394.4 kJ CO(g) + 1/2 O2(g) → CO2(g), ΔG°rxn = -257.2 kJ

Background

Topic: Thermodynamic Cycles and Hess's Law

This question tests your ability to use Hess's Law to combine reactions and calculate ΔG° for a new reaction.

Key Steps:

• Reverse and/or multiply reactions as needed to match the target reaction.

• Add the ΔG° values accordingly.

Step-by-Step Guidance

1. Write the target reaction and compare it to the given reactions.

2. Manipulate the given reactions (reverse, multiply) to construct the target reaction.

3. Add the ΔG° values, considering sign changes for reversed reactions.

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Q11. a. Determine the standard molar entropy change of vaporization (ΔSvap) for CH3OH(l) → CH3OH(g) at its boiling point.

Background

Topic: Phase Changes and Entropy

This question tests your ability to calculate entropy changes for phase transitions using enthalpy and temperature.

Key formula:

$\Delta S = \frac{\Delta H}{T}$

• $\Delta H$ = enthalpy change (in J/mol)

• $T$ = temperature (in K)

Step-by-Step Guidance

1. Convert enthalpy of vaporization from kJ/mol to J/mol.

2. Plug values into $\Delta S = \frac{\Delta H}{T}$ using the boiling point.

Try solving on your own before revealing the answer!

Q11b. Determine the standard molar entropy change of fusion (ΔSfus) for CH3OH(s) → CH3OH(l) at its freezing point.

Background

Topic: Phase Changes and Entropy

This question tests your ability to calculate entropy changes for fusion using enthalpy and temperature.

Key formula:

$\Delta S = \frac{\Delta H}{T}$

Step-by-Step Guidance

1. Convert enthalpy of fusion from kJ/mol to J/mol.

2. Plug values into $\Delta S = \frac{\Delta H}{T}$ using the freezing point.

Try solving on your own before revealing the answer!

Q11c. Explain why one of the values is higher than the other.

Background

Topic: Entropy Changes in Phase Transitions

This question tests your understanding of why vaporization generally has a larger entropy change than fusion.

Key Concepts:

• Vaporization involves a greater increase in disorder than fusion.

Step-by-Step Guidance

1. Compare the physical changes: solid to liquid vs. liquid to gas.

2. Discuss the difference in molecular freedom and randomness.

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Q12a. Determine the boiling point (in Kelvin) of benzene (C6H6).

Background

Topic: Phase Equilibria and Thermodynamics

This question tests your ability to use thermodynamic data to determine boiling points.

Key formula:

$\Delta G = \Delta H - T\Delta S$ (at boiling point, $\Delta G = 0$)

Step-by-Step Guidance

1. Set $\Delta G = 0$ at the boiling point.

2. Rearrange to $T = \frac{\Delta H}{\Delta S}$ using values for benzene.

Try solving on your own before revealing the answer!

Q12b. Determine the vapor pressure of benzene at 25°C.

Background

Topic: Vapor Pressure and Thermodynamics

This question tests your ability to use thermodynamic relationships to calculate vapor pressure.

Key formula:

$\Delta G = RT \ln \left(\frac{P}{P^\circ}\right)$

Step-by-Step Guidance

1. Use $\Delta G$ for vaporization at 25°C.

2. Plug values into the formula and solve for $P$.

Try solving on your own before revealing the answer!

Q12c. If the pressure was lower than your answer for part b, what would be the sign of ΔG? Explain.

Background

Topic: Thermodynamics of Phase Changes

This question tests your understanding of how vapor pressure and ΔG relate.

Key Concepts:

• If $P < P^\circ$, $\ln \left(\frac{P}{P^\circ}\right)$ is negative, so $\Delta G$ is positive.

Step-by-Step Guidance

1. Explain mathematically using the formula.

2. Discuss the physical meaning: vaporization is nonspontaneous if pressure is below equilibrium.

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Q13a. Calculate Ksp for the reaction AgBr(s) → Ag+(aq) + Br-(aq) at 25°C.

Background

Topic: Solubility Product and Thermodynamics

This question tests your ability to relate ΔG° to Ksp using thermodynamic equations.

Key formula:

$\Delta G^\circ = -RT \ln K_{sp}$

Step-by-Step Guidance

1. Find ΔG° for the dissolution reaction from the provided data.

2. Plug values into $\Delta G^\circ = -RT \ln K_{sp}$ and solve for $K_{sp}$.

Try solving on your own before revealing the answer!

Q13b. Determine the concentration (M) of Ag+(aq) at 25°C.

Background

Topic: Solubility Equilibria

This question tests your ability to use Ksp to find ion concentrations.

Key formula:

$K_{sp} = [Ag^+][Br^-]$

Step-by-Step Guidance

1. Assume equal concentrations of Ag+ and Br- for a 1:1 salt.

2. Set $[Ag^+] = [Br^-] = x$ and solve $K_{sp} = x^2$ for $x$.

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Q13c. Determine the temperature (K) necessary to make the concentration of both ions 0.010 M.

Background

Topic: Solubility and Temperature Dependence

This question tests your ability to relate solubility, Ksp, and temperature using thermodynamic equations.

Key formula:

$\Delta G^\circ = -RT \ln K_{sp}$

Step-by-Step Guidance

1. Set $K_{sp} = (0.010)^2$.

2. Plug values into the formula and solve for $T$.

Try solving on your own before revealing the answer!