AP Chemistry Quiz: Gibbs Free Energy And Thermodynamic Favorability
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Gibbs Free Energy And Thermodynamic FavorabilityQuestion 1 of 20

In a laboratory demonstration, carbon dioxide is converted to solid dry ice:

CO2(g)→CO2(s)\text{CO}_2(g)\rightarrow \text{CO}_2(s)

For this phase change, ΔH<0\Delta H<0 and ΔS<0\Delta S<0. Which statement best describes when deposition is thermodynamically favorable (spontaneous) as written?

Spontaneous only at high temperature
Nonspontaneous at all temperatures
Spontaneous only at low temperature
Spontaneous at all temperatures
Spontaneous only if ΔS>0\Delta S>0
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AP Chemistry Quiz

AP Chemistry Quiz: Gibbs Free Energy And Thermodynamic Favorability

Practice Gibbs Free Energy And Thermodynamic Favorability in AP Chemistry with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Gibbs Free Energy And Thermodynamic Favorability, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Chemistry.

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Question 1

In a laboratory demonstration, carbon dioxide is converted to solid dry ice:

CO2(g)→CO2(s)\text{CO}_2(g)\rightarrow \text{CO}_2(s)

For this phase change, ΔH<0\Delta H<0 and ΔS<0\Delta S<0. Which statement best describes when deposition is thermodynamically favorable (spontaneous) as written?

  1. Spontaneous only at high temperature
  2. Nonspontaneous at all temperatures
  3. Spontaneous only at low temperature (correct answer)
  4. Spontaneous at all temperatures
  5. Spontaneous only if ΔS>0\Delta S>0

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. For deposition with ΔH < 0 and ΔS < 0, ΔG = ΔH - TΔS is negative at low temperatures where the negative ΔH outweighs the small positive -TΔS term. At high temperatures, the entropy term dominates, making ΔG positive and the process nonspontaneous. Hence, deposition is thermodynamically favorable only at low temperatures. A tempting distractor is 'Spontaneous at all temperatures,' which is incorrect because it assumes exothermic phase changes are always spontaneous, failing to account for the entropy decrease's growing influence with temperature. Always analyze spontaneity by evaluating ΔG's sign, considering both thermodynamic parameters and temperature.

Question 2

Consider the reaction

2SO2(g)+O2(g)→2SO3(g)2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g)

At 298 K, the value of the Gibbs free energy change for the reaction is ΔG=−71kJ mol−1\Delta G = -71 \text{kJ mol}^{-1} (as written). Based on this information, which statement best describes the thermodynamic favorability of the reaction at 298 K?

  1. The reaction is thermodynamically favorable (spontaneous) at 298 K. (correct answer)
  2. The reaction is thermodynamically unfavorable (nonspontaneous) at 298 K.
  3. The reaction is thermodynamically favorable (spontaneous) only at high temperature.
  4. The reaction is thermodynamically unfavorable (nonspontaneous) only at low temperature.
  5. The reaction is thermodynamically favorable (spontaneous) only if a catalyst is added.

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. A negative ΔG\Delta G (−71 kJ/mol-71 \, \text{kJ/mol}) at 298 K means the reaction is spontaneous at that temperature. ΔG<0\Delta G < 0 favors the forward direction thermodynamically. This holds regardless of rate. A tempting distractor is choice B, 'Thermodynamically unfavorable (nonspontaneous) at 298 K,' perhaps from misinterpreting the sign. Use given ΔG\Delta G values directly to assess favorability at specified conditions.

Question 3

A reaction has ΔH<0\Delta H<0 and ΔS<0\Delta S<0. Which statement best describes its thermodynamic favorability at high temperature?

  1. Spontaneous at all temperatures
  2. Spontaneous only at low temperature
  3. Nonspontaneous at all temperatures
  4. Spontaneous only at high temperature
  5. Nonspontaneous at high temperature (correct answer)

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. With ΔH < 0 and ΔS < 0, ΔG = ΔH - TΔS becomes positive at high temperatures as -TΔS grows large positive. At low T, ΔG is negative. This shows nonspontaneity at high T. A tempting distractor is choice A, 'Spontaneous at all temperatures,' based on the misconception that exothermic reactions are invariably spontaneous. Evaluate ΔG at specific temperatures to ascertain thermodynamic behavior.

Question 4

A student studies the dissolution process

NH4NO3(s)→NH4+(aq)+NO3−(aq)\text{NH}_4\text{NO}_3(s) \rightarrow \text{NH}_4^+(aq) + \text{NO}_3^-(aq)

For this process, ΔH>0\Delta H > 0 and ΔS>0\Delta S > 0. Under which temperature condition, if any, is the process thermodynamically favorable (spontaneous) based on ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S?

  1. The process is thermodynamically favorable (spontaneous) only at low temperature.
  2. The process is thermodynamically favorable (spontaneous) at all temperatures.
  3. The process is thermodynamically favorable (spontaneous) only at high temperature. (correct answer)
  4. The process is thermodynamically unfavorable (nonspontaneous) at all temperatures.
  5. The process is thermodynamically favorable (spontaneous) only if it occurs rapidly.

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. ΔG = ΔH - TΔS determines spontaneity if negative. For this dissolution with ΔH > 0 and ΔS > 0, at high temperatures, TΔS exceeds ΔH, making ΔG negative. At low T, it's positive and nonspontaneous. A tempting distractor is choice C, 'Spontaneous at all temperatures,' which ignores the need for high T to overcome positive ΔH. Apply the ΔG equation to find temperature thresholds for phase or dissolution processes.

Question 5

A reaction has ΔH<0\Delta H<0 and ΔS>0\Delta S>0. Which statement best describes its thermodynamic favorability at any temperature?

  1. Spontaneous only at low temperature
  2. Nonspontaneous at all temperatures
  3. Spontaneous at all temperatures (correct answer)
  4. Spontaneous only at high temperature
  5. Nonspontaneous only if the products are more disordered

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. When ΔH < 0 and ΔS > 0, ΔG = ΔH - TΔS is always negative, as both terms contribute negatively. Negative ΔH and negative -TΔS favor spontaneity at all temperatures. Entropy's effect strengthens with T. A tempting distractor is choice A, 'Spontaneous only at low temperature,' mistakenly prioritizing enthalpy over entropy at high T. Classify reactions by ΔH and ΔS signs to predict ΔG behavior across temperatures.

Question 6

For the reaction N2(g)+O2(g)→2NO(g)\text{N}_2(g) + \text{O}_2(g) \rightarrow 2\text{NO}(g), ΔH>0\Delta H > 0 and ΔS<0\Delta S < 0. Which statement best describes the thermodynamic favorability of the reaction as written?

  1. Spontaneous only at high temperature.
  2. Spontaneous at all temperatures because ΔS\Delta S is negative.
  3. Nonspontaneous at all temperatures. (correct answer)
  4. Spontaneous only at low temperature.
  5. Spontaneous only if a catalyst is present.

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. The Gibbs free energy change, ΔG, determines spontaneity, where ΔG < 0 indicates a spontaneous reaction. For this reaction with ΔH > 0 and ΔS < 0, both terms oppose: positive ΔH and positive -TΔS make ΔG always positive. Thus, the reaction is nonspontaneous at all temperatures. A tempting distractor is choice A, which incorrectly suggests spontaneity at high temperatures, assuming entropy drives it despite negative ΔS. Always use ΔG to judge spontaneity, not catalysts which affect only rate.

Question 7

Consider the reaction N2(g)+3H2(g)→2NH3(g)\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g). For this process, ΔH<0\Delta H < 0 and ΔS<0\Delta S < 0. Under which conditions is the reaction thermodynamically favorable (spontaneous)?

  1. Spontaneous at all temperatures because ΔH\Delta H is negative.
  2. Spontaneous only at low temperature. (correct answer)
  3. Nonspontaneous at all temperatures because ΔS\Delta S is negative.
  4. Spontaneous only at high temperature.
  5. Spontaneous only if the reaction is fast.

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. The Gibbs free energy change, ΔG, determines spontaneity, where ΔG < 0 indicates a spontaneous reaction. For this reaction with ΔH < 0 and ΔS < 0, ΔG = ΔH - TΔS shows that the negative ΔH favors spontaneity, but the negative ΔS makes -TΔS positive, opposing it. At low temperatures, the TΔS term is small, so ΔG is negative and the reaction is spontaneous; at high temperatures, the TΔS term dominates, making ΔG positive. A tempting distractor is choice A, which incorrectly assumes that exothermic reactions are always spontaneous, ignoring the entropy contribution at higher temperatures. Remember that spontaneity depends on the sign of ΔG, not on whether the reaction is exothermic alone.

Question 8

A sample of solid ammonium nitrate dissolves in water: NH4NO3(s)→NH4+(aq)+NO3−(aq)\text{NH}_4\text{NO}_3(s) \rightarrow \text{NH}_4^+(aq) + \text{NO}_3^-(aq). For this process, ΔH>0\Delta H > 0 and ΔS>0\Delta S > 0. Under which conditions is the dissolution thermodynamically favorable (spontaneous)?

  1. Nonspontaneous at all temperatures because ΔH\Delta H is positive.
  2. Spontaneous at all temperatures because ΔS\Delta S is positive.
  3. Spontaneous only at high temperature. (correct answer)
  4. Spontaneous only at low temperature.
  5. Spontaneous only if a catalyst is added.

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. The Gibbs free energy change, ΔG, determines spontaneity, where ΔG < 0 indicates a spontaneous process. For this dissolution with ΔH > 0 and ΔS > 0, ΔG = ΔH - TΔS shows that the positive ΔH opposes spontaneity, but the positive ΔS makes -TΔS negative, favoring it. At high temperatures, the TΔS term dominates, making ΔG negative and the process spontaneous; at low temperatures, ΔH dominates, making ΔG positive. A tempting distractor is choice A, which incorrectly assumes endothermic processes are nonspontaneous at all temperatures, disregarding the entropy increase. Always evaluate spontaneity based on ΔG, not just the sign of ΔH.

Question 9

A reaction has ΔG=+12 kJ mol−1\Delta G = +12\ \text{kJ mol}^{-1} at 298 K298\ \text{K} and 1 bar1\ \text{bar}. Which statement best describes the thermodynamic favorability of the reaction as written under these conditions?

  1. Spontaneous under these conditions because ΔG\Delta G is positive.
  2. Nonspontaneous under these conditions because ΔG\Delta G is positive. (correct answer)
  3. Spontaneous only at low temperature because ΔG\Delta G is positive.
  4. Spontaneous only at high temperature because ΔG\Delta G is positive.
  5. Spontaneous only if the reaction occurs rapidly.

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. The Gibbs free energy change, ΔG, directly determines spontaneity, with ΔG < 0 for spontaneous reactions, ΔG > 0 for nonspontaneous, and ΔG = 0 for equilibrium. Here, ΔG = +12 kJ mol⁻¹ indicates the reaction is nonspontaneous under the given conditions. This positive ΔG means the reverse reaction would be favored. A tempting distractor is choice A, which mistakenly assumes positive ΔG means spontaneous, confusing the sign convention for ΔG. Always verify spontaneity by checking if ΔG is negative, not by confusing it with reaction rate.

Question 10

The reaction H2(g)+Cl2(g)→2HCl(g)\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g) has ΔH<0\Delta H < 0 and ΔS<0\Delta S < 0. Under which conditions is the reaction thermodynamically favorable (spontaneous)?

  1. Spontaneous only at low temperature. (correct answer)
  2. Spontaneous at all temperatures because ΔH\Delta H is negative.
  3. Spontaneous only at high temperature.
  4. Spontaneous only if the reaction is fast.
  5. Nonspontaneous at all temperatures because ΔS\Delta S is negative.

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. The Gibbs free energy change, ΔG, determines spontaneity, where ΔG < 0 indicates a spontaneous reaction. For this reaction with ΔH < 0 and ΔS < 0, ΔG = ΔH - TΔS means negative ΔH favors, but positive -TΔS opposes. At low temperatures, ΔG is negative; at high temperatures, it's positive. A tempting distractor is choice B, which assumes all exothermic reactions are spontaneous at all temperatures, ignoring entropy. Spontaneity depends on ΔG, not reaction speed.

Question 11

The dissolution of calcium chloride in water is represented as CaCl2(s)→Ca2+(aq)+2Cl−(aq)\text{CaCl}_2(s) \rightarrow \text{Ca}^{2+}(aq) + 2\text{Cl}^-(aq). For this process, ΔH<0\Delta H < 0 and ΔS>0\Delta S > 0. Which statement best describes the thermodynamic favorability of the dissolution as written?

  1. Spontaneous only if a catalyst is added.
  2. Nonspontaneous at all temperatures because ΔH\Delta H is negative.
  3. Spontaneous only at high temperature.
  4. Spontaneous only at low temperature.
  5. Spontaneous at all temperatures. (correct answer)

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. The Gibbs free energy change, ΔG, determines spontaneity, where ΔG < 0 indicates a spontaneous process. For this dissolution with ΔH < 0 and ΔS > 0, both terms favor: negative ΔH and negative -TΔS ensure ΔG < 0 always. Thus, it's spontaneous at all temperatures. A tempting distractor is choice A, which assumes negative ΔH means nonspontaneous, reversing the enthalpy effect. Remember, spontaneity depends on ΔG, not catalysts which affect kinetics.

Question 12

For the reaction 2NO2(g)→2NO(g)+O2(g)\mathrm{2NO_2(g) \rightarrow 2NO(g) + O_2(g)}, ΔH>0\Delta H>0 and ΔS>0\Delta S>0. Which statement best describes the thermodynamic favorability (spontaneity) of the reaction as written?

  1. Spontaneous only if ΔS<0\Delta S<0
  2. Spontaneous only at high temperature (correct answer)
  3. Spontaneous only at low temperature
  4. Spontaneous at all temperatures
  5. Nonspontaneous at all temperatures

Explanation: This question tests understanding of Gibbs free energy and thermodynamic favorability. For NO₂ decomposition, we have ΔH > 0 (endothermic) and ΔS > 0 (increase in entropy as 2 moles of gas form 3 moles). Using ΔG = ΔH - TΔS, when both terms are positive, spontaneity depends on their relative magnitudes. At low temperatures, the positive ΔH dominates over the small TΔS term, making ΔG positive and the reaction nonspontaneous. At high temperatures, the TΔS term becomes large enough to overcome the positive ΔH, making ΔG negative and the reaction spontaneous. Choice E incorrectly states that negative ΔS would make the reaction spontaneous, but with positive ΔH, this would make it nonspontaneous at all temperatures. Remember: when ΔH > 0 and ΔS > 0, reactions become spontaneous only at high temperatures.

Question 13

The decomposition reaction CaCO3(s)→CaO(s)+CO2(g)\mathrm{CaCO_3(s) \rightarrow CaO(s) + CO_2(g)} has ΔH>0\Delta H>0 and ΔS>0\Delta S>0. At what temperature conditions is this process thermodynamically favorable (spontaneous) as written?

  1. Spontaneous at all temperatures
  2. Nonspontaneous at all temperatures
  3. Spontaneous only at high temperature (correct answer)
  4. Spontaneous only at low temperature
  5. Spontaneous only if ΔS\Delta S is negative

Explanation: This question tests understanding of Gibbs free energy and thermodynamic favorability. For calcium carbonate decomposition, we have ΔH > 0 (endothermic) and ΔS > 0 (increase in entropy due to gas formation). Using ΔG = ΔH - TΔS, when both terms are positive, the reaction's spontaneity depends on their relative magnitudes. At low temperatures, the positive ΔH dominates over the small TΔS term, making ΔG positive and the reaction nonspontaneous. At high temperatures, the TΔS term becomes large enough to overcome the positive ΔH, making ΔG negative and the reaction spontaneous. Choice E incorrectly suggests that a negative ΔS would make the reaction spontaneous, but this would actually make it nonspontaneous at all temperatures when combined with positive ΔH. Remember: when ΔH > 0 and ΔS > 0, reactions become spontaneous only at high temperatures where the entropy term dominates.

Question 14

A process has ΔH>0\Delta H>0 and ΔS<0\Delta S<0 under the stated conditions. Which statement best describes the thermodynamic favorability (spontaneity) of this process?

  1. Spontaneous only at high temperature
  2. Spontaneous at all temperatures
  3. Nonspontaneous at all temperatures (correct answer)
  4. Spontaneous only at low temperature
  5. Spontaneous only if ΔH\Delta H is positive

Explanation: This question tests understanding of Gibbs free energy and thermodynamic favorability. With ΔH > 0 (endothermic) and ΔS < 0 (decrease in entropy), we can analyze using ΔG = ΔH - TΔS. The positive ΔH contributes positively to ΔG, making the process less favorable. The negative ΔS means -TΔS is positive (since -T × negative = positive), also contributing positively to ΔG. Since both terms in the ΔG equation are positive regardless of temperature, ΔG will always be positive, making the process nonspontaneous at all temperatures. Choice E incorrectly suggests that positive ΔH could make a process spontaneous, but positive ΔH actually opposes spontaneity. Remember: when ΔH > 0 and ΔS < 0, both terms work against spontaneity, making the process nonspontaneous at all temperatures.

Question 15

When NH4NO3(s)\mathrm{NH_4NO_3(s)} dissolves in water to form an aqueous solution, the process has ΔH>0\Delta H>0 and ΔS>0\Delta S>0. Under which conditions is the dissolution thermodynamically favorable (spontaneous)?

  1. Spontaneous only at high temperature (correct answer)
  2. Spontaneous only at low temperature
  3. Nonspontaneous at all temperatures
  4. Spontaneous at all temperatures
  5. Spontaneous only when ΔH<0\Delta H<0

Explanation: This question tests understanding of Gibbs free energy and thermodynamic favorability. For ammonium nitrate dissolution, we have ΔH > 0 (endothermic) and ΔS > 0 (increase in entropy as solid dissolves). Using ΔG = ΔH - TΔS, both terms are positive, so spontaneity depends on temperature. At low temperatures, the positive ΔH dominates over the small TΔS term, making ΔG positive and dissolution nonspontaneous. At high temperatures, the TΔS term becomes large enough to overcome the positive ΔH, making ΔG negative and dissolution spontaneous. Choice E incorrectly implies that only the sign of ΔH determines spontaneity, but with positive ΔS, an endothermic process can still be spontaneous at sufficiently high temperatures. Remember: when ΔH > 0 and ΔS > 0, processes become spontaneous at high temperatures where entropy dominates.

Question 16

For the reaction N2(g)+3H2(g)→2NH3(g)\mathrm{N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)}, ΔH<0\Delta H<0 and ΔS<0\Delta S<0. Under which conditions is the reaction thermodynamically favorable (spontaneous) as written?

  1. Spontaneous only at high temperature
  2. Nonspontaneous at all temperatures
  3. Spontaneous only at low temperature (correct answer)
  4. Spontaneous only when the reaction is fast
  5. Spontaneous at all temperatures

Explanation: This question tests understanding of Gibbs free energy and thermodynamic favorability. For the ammonia synthesis reaction, we have ΔH < 0 (exothermic) and ΔS < 0 (decrease in entropy due to fewer moles of gas products). Using ΔG = ΔH - TΔS, when both ΔH and ΔS are negative, the -TΔS term becomes positive, opposing the negative ΔH. At low temperatures, the TΔS term is small, so the negative ΔH dominates, making ΔG negative and the reaction spontaneous. At high temperatures, the positive TΔS term becomes large enough to overcome the negative ΔH, making ΔG positive and the reaction nonspontaneous. Choice E incorrectly confuses reaction rate with thermodynamic favorability—spontaneity depends on ΔG, not how fast a reaction proceeds. Remember: when ΔH < 0 and ΔS < 0, reactions are spontaneous only at low temperatures where the enthalpy term dominates.

Question 17

For the reaction 2H2(g)+O2(g)→2H2O(l)\mathrm{2H_2(g) + O_2(g) \rightarrow 2H_2O(l)}, ΔH<0\Delta H<0 and ΔS<0\Delta S<0. Which statement best describes when the reaction is thermodynamically favorable (spontaneous) as written?

  1. Nonspontaneous at all temperatures
  2. Spontaneous only at high temperature
  3. Spontaneous at all temperatures
  4. Spontaneous only at low temperature (correct answer)
  5. Spontaneous only if the reaction is slow

Explanation: This question tests understanding of Gibbs free energy and thermodynamic favorability. For water formation from gases, we have ΔH < 0 (highly exothermic) and ΔS < 0 (decrease in entropy as gases form liquid). Using ΔG = ΔH - TΔS, when both terms are negative, the -TΔS becomes positive, opposing the negative ΔH. At low temperatures, the TΔS term is small, so the negative ΔH dominates, making ΔG negative and the reaction spontaneous. At high temperatures, the positive TΔS term becomes large enough to overcome the negative ΔH, making ΔG positive and the reaction nonspontaneous. Choice E incorrectly relates reaction speed to spontaneity—thermodynamic favorability depends on ΔG, not kinetics. Remember: when ΔH < 0 and ΔS < 0, reactions are spontaneous only at low temperatures.

Question 18

The process CO2(g)→CO2(s)\text{CO}_2(g)\rightarrow \text{CO}_2(s) (deposition) at 1 atm has ΔH<0\Delta H<0 and ΔS<0\Delta S<0. Which statement best describes when this process is thermodynamically favorable (spontaneous)?

  1. The process is spontaneous only at low temperature. (correct answer)
  2. The process is spontaneous only at high temperature.
  3. The process is spontaneous at all temperatures because ΔH<0\Delta H<0.
  4. The process is nonspontaneous at all temperatures because ΔS<0\Delta S<0.
  5. The process is spontaneous only if it is rapid.

Explanation: This question tests understanding of Gibbs free energy and thermodynamic favorability. For the deposition CO₂(g) → CO₂(s), we have ΔH < 0 (exothermic) and ΔS < 0 (gas to solid). Using ΔG = ΔH - TΔS, at low temperatures, the negative ΔH term dominates over the small positive -TΔS term, making ΔG < 0 and the process spontaneous. At high temperatures, the -TΔS term becomes large and positive, making ΔG > 0 and deposition nonspontaneous. Choice C incorrectly assumes that all exothermic processes are spontaneous at all temperatures, ignoring the unfavorable entropy decrease. The principle is that phase transitions with ΔH < 0 and ΔS < 0 favor the more ordered phase at low temperatures.

Question 19

The reaction 2NO2(g)→N2O4(g)2\text{NO}_2(g)\rightarrow \text{N}_2\text{O}_4(g) is exothermic (ΔH<0\Delta H<0) and results in fewer moles of gas, so ΔS<0\Delta S<0. Based on these signs, which statement best describes the thermodynamic favorability of the reaction?

  1. The reaction is spontaneous at all temperatures because ΔH<0\Delta H<0.
  2. The reaction is spontaneous only at low temperature. (correct answer)
  3. The reaction is spontaneous only at high temperature.
  4. The reaction is nonspontaneous at all temperatures because ΔS<0\Delta S<0.
  5. The reaction is spontaneous only if a catalyst is present.

Explanation: This question tests understanding of Gibbs free energy and thermodynamic favorability. For the dimerization reaction 2NO₂(g) → N₂O₄(g), we have ΔH < 0 (exothermic) and ΔS < 0 (fewer moles of gas). Using ΔG = ΔH - TΔS, at low temperatures, the negative ΔH term dominates over the small positive -TΔS term, making ΔG < 0 and the reaction spontaneous. At high temperatures, the -TΔS term becomes large and positive, potentially making ΔG > 0 and the reaction nonspontaneous. Choice A incorrectly assumes that all exothermic reactions are spontaneous at all temperatures, ignoring the unfavorable entropy change. The principle is that reactions with ΔH < 0 and ΔS < 0 are spontaneous only at temperatures below T = ΔH/ΔS.

Question 20

A student studies the reaction

2NO(g)+O2(g)→2NO2(g)2\text{NO}(g)+\text{O}_2(g)\rightarrow 2\text{NO}_2(g)

Thermodynamic signs for the reaction are ΔH<0\Delta H<0 and ΔS<0\Delta S<0. Under which conditions is the reaction thermodynamically favorable (spontaneous)?

  1. Spontaneous only at low temperature (correct answer)
  2. Spontaneous only at high temperature
  3. Spontaneous at all temperatures
  4. Nonspontaneous at all temperatures
  5. Spontaneous only when ΔS>0\Delta S>0

Explanation: This question assesses the skill of Gibbs free energy and thermodynamic favorability. Spontaneity is governed by ΔG=ΔH−TΔS\Delta G = \Delta H - T \Delta S, and for ΔH<0\Delta H < 0 and ΔS<0\Delta S < 0, ΔG\Delta G is negative when ∣ΔH∣>T∣ΔS∣|\Delta H| > T|\Delta S|, which happens at low temperatures. At high temperatures, the −TΔS-T \Delta S term becomes more positive, making ΔG\Delta G positive and the reaction nonspontaneous. Therefore, the reaction is thermodynamically favorable only at low temperatures. A tempting distractor is 'Spontaneous at all temperatures,' which is incorrect because it assumes exothermic reactions are always spontaneous, disregarding the negative entropy effect at high temperatures. Remember, spontaneity depends on the sign of ΔG\Delta G, not solely on the sign of ΔH\Delta H.