AP Unit 9 Problems

Predict the sign of the system entropy change for (a) melting a solid, (b) expanding an ideal gas isothermally, (c) N₂(g) + 3H₂(g) → 2NH₃(g), and (d) heating a gas at fixed volume. For (b) and (d), connect the macroscopic change to particle locations or energy distribution. Explain why entropy change of the system alone does not decide whether every process is thermodynamically favored.

Compare the size of the change

Consider three separate isothermal expansions of ideal argon at 298 K. Supplied model data: expanding 1.00 mol from 10.0 L to 20.0 L gives ΔS = +5.76 J K−1; expanding 1.00 mol from 10.0 L to 40.0 L gives ΔS = +11.5 J K−1. Sample A is 1.00 mol expanding 10.0 → 20.0 L; sample B is 2.00 mol expanding 20.0 → 40.0 L; sample C is 1.00 mol expanding 10.0 → 40.0 L.

1. Calculate the entropy change for B using the amount and the common expansion ratio. Rank A, B and C by the magnitude of ΔS, within the rounding of the data.
2. Explain why C has a larger increase than A even though both signs are positive, and why B has twice the increase of A. Use particle access to space and amount, rather than visual disorder.
3. Could you rank the entropy changes of unrelated melting and reaction processes from their positive signs alone? Explain what information would be needed.

At 298 K the standard molar entropies are S°(N2(g)) = 191.6, S°(H2(g)) = 130.7, and S°(NH3(g)) = 192.8 J mol−1 K−1. Calculate ΔS° for N2(g) + 3H2(g) → 2NH3(g). Explain why assigning zero entropy to elemental N2 and H2 is wrong, and why the sign agrees with particle reasoning.

A hypothetical process has ΔH° = +40.0 kJ mol−1 and ΔS° = +100. J mol−1 K−1. Treat these as constant over the stated range. Calculate ΔG° at 298 K and 600 K, determine the approximate boundary temperature, and identify where the forward process is favored under standard conditions. Explain why a favorable answer does not promise a rapid reaction. Also identify which ΔH°/ΔS° sign combination is favored at all positive temperatures within this approximation.

Read the standard-state symbol and complete the sign cases

1. An aqueous solute in a real reaction mixture is 0.100 M at 350 K. In the AP concentration approximation, what solute concentration does the ° reference use? Is this mixture itself at that reference concentration? Does ° require 298 K? Explain why ΔG° alone does not determine the driving force of this nonstandard mixture.
2. Classify all four ΔH°/ΔS° sign pairs as favored at every positive T, at no positive T, only above a boundary, or only below a boundary. Explain the two cases not used in the first calculation by considering −TΔS°.
3. For a second process with ΔH° = −40.0 kJ mol−1 and ΔS° = −100. J mol−1 K−1, find the approximate boundary and identify the favored temperature interval. State what ΔG° = 0 means at the boundary.
4. At an independently specified 350 K, identify the standard-state references for a pure solid, a pure liquid and a gas under the AP pressure convention. Assume each named phase is stable at that temperature and reference pressure. Which references depend on purity, and which specifies gas pressure? Explain how the temperature and phase assumptions differ from the ° symbol.

At 298 K, ΔGf°(H2O(l)) = −237.1 kJ mol−1 and ΔGf°(H2O(g)) = −228.6 kJ mol−1. Use these formation values to find ΔG° for H2O(g) → H2O(l). Explain the meaning of the negative sign for the written standard-state process and why this is not a claim that any unsaturated water vapor in air must immediately condense.

A reaction has ΔG° < 0 but produces no detectable change over a class period at the stated composition, for which forward reaction is thermodynamically favored. A catalyst makes product appear rapidly. Explain the initial lack of observable change using an energy profile and distinguish kinetic control from equilibrium. Predict whether the catalyst changes ΔG° or K at the same temperature.

Create a labeled qualitative free-energy profile, with reaction progress on the horizontal axis and relative free energy on the vertical axis. Mark the activation barrier and the reactant-to-product free-energy difference separately.

At 298 K, a reaction has ΔG° = −11.4 kJ mol−1. Calculate K using R = 8.314 J mol−1 K−1. Estimate qualitatively whether K is close to one before calculating. Then another reaction has K = 0.250 at 298 K; determine the sign and magnitude of its ΔG°. Explain why ΔG° = 0 differs from the statement that an arbitrary mixture is at equilibrium.

Two reactions at the same temperature have ΔG° values −0.10RT and −10RT. Compare their equilibrium constants without inserting a numerical temperature. A student claims they have almost the same K because both free-energy changes are negative. Evaluate the claim, and predict K if the second reaction is reversed.

Two hypothetical salts have standard dissolution values at 298 K: salt A, ΔH° = +12.0 kJ mol−1 and ΔS° = +60.0 J mol−1 K−1; salt B, ΔH° = −10.0 kJ mol−1 and ΔS° = −60.0 J mol−1 K−1. Calculate each ΔG° and identify the favored standard dissolution. Explain how an endothermic dissolution can be favored and why dispersed ions do not guarantee positive total dissolution entropy. Distinguish this reference result from the actual driving force in a saturated solution.

Account for the three competing pieces

For salt A, use the following hypothetical component estimates per mole dissolved at 298 K. The path is a bookkeeping model, not three separately observed stages. The unsigned magnitudes are supplied; infer their signs from the stated changes.

1. Assign and explain the sign of each ΔH and ΔS contribution. Compare the sizes of the opposing enthalpy terms and of the entropy terms.
2. Calculate each component ΔG at 298 K and sum the contributions. Confirm consistency with A’s supplied net values.
3. Would changing only the hydration enthalpy estimate from a release of 803 to 795 kJ mol−1 change the sign of the predicted net ΔG°? Calculate and explain why cancellation makes the prediction sensitive. State why this hypothetical standard-state comparison is not itself a measured solubility.

A proposed coupled pathway has A + I → P with ΔG° = +18.0 kJ mol−1 and D → I with ΔG° = −30.0 kJ mol−1. Write the overall equation, identify the shared intermediate, calculate overall ΔG°, and explain how coupling can permit production of P. Would running the reactions in entirely disconnected containers prove that the first reaction has been driven? Give one other type of external energy input that can drive an unfavorable process.

An idealized galvanic cell operates by Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s). Its half-cells are joined by a wire, a conducting load, and an inert-ion salt bridge. Draw and label a cell representation with the anode, cathode, half-reactions, electron direction, bridge-ion directions, and predicted metal-mass changes. Explain why removing the bridge interrupts sustained operation and why electrons should not be drawn through the solution.

Measure without confusing the two paths

Add an idealized high-resistance voltmeter and an ammeter to your operating-cell drawing. Label which quantity each measures and how each is connected relative to the cell/load. Explain why a voltage reading with only the high-resistance voltmeter connected does not imply appreciable sustained current. Does either measuring device supply the driving energy in this galvanic cell? Explain.

A supplied electrolytic model decomposes molten MX into M metal and X2 gas, with M+ and X− as its only ions and inert electrodes. Write each half-reaction, identify anode and cathode, and explain the role of the external power source. Describe which species change at each electrode and why this molten model does not automatically predict products of aqueous MX electrolysis.

Use the supplied rounded standard reduction potentials: Ti2+(aq) + 2e− → Ti(s), E° = −1.63 V; Zn2+(aq) + 2e− → Zn(s), E° = −0.76 V. In an idealized galvanic standard-state model, identify the cathode and anode, balance the net equation, calculate E°cell and ΔG° for the balanced equation, and explain what happens to E°cell and ΔG° if the equation is doubled. Use F = 96485 C mol−1 of electrons. Ignore passivation and competing chemistry; this is a model, not a proposed titanium-cell experiment.

For a proposed written reaction, the assigned cathode has E°red = +0.20 V and the assigned anode has E°red = +0.65 V; the balanced reaction transfers two electrons. Calculate its standard cell potential and free-energy change using F = 96485 C mol−1. Is the written reaction galvanically favored under standard conditions? Explain how the reverse would differ and what an external electrical source would need to do to run the original direction.

For the written reaction Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s), E° > 0 at the stated temperature and Q = [Zn2+]/[Cu2+] in the ideal dilute model. Compare E with E° when Q = 0.10 and Q = 10, using E = E° − (RT/nF) ln Q qualitatively. As the cell reacts forward toward its equilibrium, explain how Q and E change. Why is applying Le Châtelier’s principle to “shift an equilibrium cell” inappropriate for this operating galvanic cell?

A concentration cell has identical M(s)/M2+(aq) electrodes, with one side dilute and the other concentrated. Standard reduction potentials cancel, so E°cell = 0. Without calculating a numerical Nernst voltage, determine which side oxidizes, which side reduces, the external electron direction, and how the reacting-ion concentrations approach equality. Explain how it can have nonzero voltage despite E°cell = 0.

In a supplied-data copper electroplating model, Cu2+ + 2e− → Cu occurs with a constant current of 1.50 A for 20.0 min. Calculate charge, moles of electrons, and theoretical copper mass deposited. Use F = 96485 C mol−1 e− and MCu = 63.55 g mol−1. The measured deposited mass is 0.500 g. Calculate current efficiency and give a plausible explanation for a lower actual mass without treating this as a lab procedure.

An idealized M3+ + 3e− → M deposition transfers enough charge to deposit 0.0100 mol metal. Calculate the required charge and time at constant 2.00 A, using F = 96485 C mol−1 e−. Another ion N2+ is deposited using exactly the same charge with 100% efficiency. Compare the deposited metal moles and explain why equal charge does not mean equal mass. No molar masses are supplied.