AP Chemistry · Learn by Concept

AP Chemistry Help: Gibbs Free Energy And Thermodynamic Favorability

Review real example questions for Gibbs Free Energy And Thermodynamic Favorability in AP Chemistry.

Question 1 / 10

0 of 10 answered

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

$\text{CO}_2(g)\rightarrow \text{CO}_2(s)$

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

All questions

Question 1

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

$\text{CO}_2(g)\rightarrow \text{CO}_2(s)$

For this phase change, $\Delta H<0$ and $\Delta S<0$ . 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 (correct answer)
Spontaneous at all temperatures
Spontaneous only if $\Delta S>0$

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

$2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g)$

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

The reaction is thermodynamically favorable (spontaneous) at 298 K. (correct answer)
The reaction is thermodynamically unfavorable (nonspontaneous) at 298 K.
The reaction is thermodynamically favorable (spontaneous) only at high temperature.
The reaction is thermodynamically unfavorable (nonspontaneous) only at low temperature.
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 $\Delta G$ ( $-71 \, \text{kJ/mol}$ ) at 298 K means the reaction is spontaneous at that temperature. $\Delta G < 0$ 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 $\Delta G$ values directly to assess favorability at specified conditions.

Question 3

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

Spontaneous at all temperatures
Spontaneous only at low temperature
Nonspontaneous at all temperatures
Spontaneous only at high temperature
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

$\text{NH}_4\text{NO}_3(s) \rightarrow \text{NH}_4^+(aq) + \text{NO}_3^-(aq)$

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

The process is thermodynamically favorable (spontaneous) only at low temperature.
The process is thermodynamically favorable (spontaneous) at all temperatures.
The process is thermodynamically favorable (spontaneous) only at high temperature. (correct answer)
The process is thermodynamically unfavorable (nonspontaneous) at all temperatures.
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 $\Delta H<0$ and $\Delta S>0$ . Which statement best describes its thermodynamic favorability at any temperature?

Spontaneous only at low temperature
Nonspontaneous at all temperatures
Spontaneous at all temperatures (correct answer)
Spontaneous only at high temperature
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 $\text{N}_2(g) + \text{O}_2(g) \rightarrow 2\text{NO}(g)$ , $\Delta H > 0$ and $\Delta S < 0$ . Which statement best describes the thermodynamic favorability of the reaction as written?

Spontaneous only at high temperature.
Spontaneous at all temperatures because $\Delta S$ is negative.
Nonspontaneous at all temperatures. (correct answer)
Spontaneous only at low temperature.
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 $\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g)$ . For this process, $\Delta H < 0$ and $\Delta S < 0$ . Under which conditions is the reaction thermodynamically favorable (spontaneous)?

Spontaneous at all temperatures because $\Delta H$ is negative.
Spontaneous only at low temperature. (correct answer)
Nonspontaneous at all temperatures because $\Delta S$ is negative.
Spontaneous only at high temperature.
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: $\text{NH}_4\text{NO}_3(s) \rightarrow \text{NH}_4^+(aq) + \text{NO}_3^-(aq)$ . For this process, $\Delta H > 0$ and $\Delta S > 0$ . Under which conditions is the dissolution thermodynamically favorable (spontaneous)?

Nonspontaneous at all temperatures because $\Delta H$ is positive.
Spontaneous at all temperatures because $\Delta S$ is positive.
Spontaneous only at high temperature. (correct answer)
Spontaneous only at low temperature.
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 $\Delta G = +12\ \text{kJ mol}^{-1}$ at $298\ \text{K}$ and $1\ \text{bar}$ . Which statement best describes the thermodynamic favorability of the reaction as written under these conditions?

Spontaneous under these conditions because $\Delta G$ is positive.
Nonspontaneous under these conditions because $\Delta G$ is positive. (correct answer)
Spontaneous only at low temperature because $\Delta G$ is positive.
Spontaneous only at high temperature because $\Delta G$ is positive.
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 $\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g)$ has $\Delta H < 0$ and $\Delta S < 0$ . Under which conditions is the reaction thermodynamically favorable (spontaneous)?

Spontaneous only at low temperature. (correct answer)
Spontaneous at all temperatures because $\Delta H$ is negative.
Spontaneous only at high temperature.
Spontaneous only if the reaction is fast.
Nonspontaneous at all temperatures because $\Delta S$ 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.