Gibbs Free Energy and Thermodynamic Favorability

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AP Chemistry › Gibbs Free Energy and Thermodynamic Favorability

Questions 1 - 10
1

A student studies the reaction

$$2\text{NO}(g)+\text{O}_2(g)\rightarrow 2\text{NO}_2(g)$$

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

Spontaneous only when $\Delta S>0$

Spontaneous only at low temperature

Spontaneous only at high temperature

Nonspontaneous at all temperatures

Spontaneous at all temperatures

Explanation

This question assesses the skill of Gibbs free energy and thermodynamic favorability. Spontaneity is governed by $\Delta G = \Delta H - T \Delta S$, and for $\Delta H < 0$ and $\Delta S < 0$, $\Delta G$ is negative when $|\Delta H| > T|\Delta S|$, which happens at low temperatures. At high temperatures, the $-T \Delta S$ term becomes more positive, making $\Delta G$ 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 $\Delta G$, not solely on the sign of $\Delta H$.

2

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

Spontaneous at all temperatures

Nonspontaneous at all temperatures

Spontaneous only at low temperature

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.

3

Consider the decomposition reaction

$$2\text{HgO}(s)\rightarrow 2\text{Hg}(l)+\text{O}_2(g)$$

For this reaction, $\Delta H>0$ and $\Delta S>0$. At which temperature regime is the reaction thermodynamically favorable (spontaneous)?

Spontaneous only if $\Delta H<0$

Spontaneous only at low temperature

Nonspontaneous at all temperatures

Spontaneous at all temperatures

Spontaneous only at high temperature

Explanation

This question assesses the skill of Gibbs free energy and thermodynamic favorability. For this decomposition with $\Delta H > 0$ and $\Delta S > 0$, $\Delta G = \Delta H - T\Delta S$ becomes negative at high temperatures where $T\Delta S$ outweighs $\Delta H$. At low temperatures, $\Delta G$ is positive because the entropy term is insufficient to overcome the endothermic enthalpy. Hence, the reaction is spontaneous only in the high-temperature regime. A tempting distractor is 'Spontaneous at all temperatures,' which is incorrect because it assumes positive entropy always drives spontaneity, ignoring the endothermic nature requiring high temperature. To predict favorability, always consider how temperature modulates the contributions of $\Delta H$ and $\Delta S$ to $\Delta G$.

4

A chemist analyzes the reaction

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

Thermodynamic signs are $\Delta H<0$ and $\Delta S<0$. Under which temperature regime is the reaction thermodynamically favorable (spontaneous) as written?

Spontaneous because $\Delta H<0$ regardless of $\Delta S$

Spontaneous at all temperatures

Nonspontaneous at all temperatures

Spontaneous only at low temperature

Spontaneous only at high temperature

Explanation

This question assesses the skill of Gibbs free energy and thermodynamic favorability. For $\Delta H < 0$ and $\Delta S < 0$, $\Delta G = \Delta H - T \Delta S$ is negative in the low-temperature regime where $T |\Delta S| < |\Delta H|$. As temperature increases, the $-T \Delta S$ term grows more positive, eventually making $\Delta G$ positive and the reaction nonspontaneous. Thus, thermodynamic favorability occurs only at low temperatures. A tempting distractor is 'Spontaneous at all temperatures,' which is incorrect because it assumes negative $\Delta H$ guarantees spontaneity, disregarding the opposing entropy effect at high temperatures. Use the relationship $\Delta G = \Delta H - T \Delta S$ to assess how temperature influences spontaneity based on thermodynamic signs.

5

Hydrogen and chlorine form hydrogen chloride: $\text{H}_2(g)+\text{Cl}_2(g)\rightarrow 2\text{HCl}(g)$. For this reaction, $\Delta H<0$ and $\Delta S<0$. At room temperature (moderate temperature), which statement best describes the thermodynamic favorability?

Spontaneous only at low temperature

Spontaneous at all temperatures

Spontaneous only if $\Delta S$ is positive

Nonspontaneous at all temperatures

Spontaneous only at high temperature

Explanation

This question assesses the skill of Gibbs free energy and thermodynamic favorability. ΔG = ΔH - TΔS determines if a reaction is spontaneous when negative. With ΔH < 0 and ΔS < 0, at moderate room temperature, ΔG is typically negative as |ΔH| > |TΔS|, but it becomes positive at higher temperatures. Thus, the reaction is spontaneous only at low to moderate temperatures. A tempting distractor is choice D, 'Spontaneous at all temperatures,' which assumes exothermic reactions are always spontaneous, ignoring the entropy penalty at high temperatures. Evaluate spontaneity using ΔG, not just the sign of ΔH or reaction rate.

6

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

Nonspontaneous only if $\Delta H$ is negative

Spontaneous at all temperatures

Spontaneous only at high temperature

Explanation

This question assesses the skill of Gibbs free energy and thermodynamic favorability. For ΔH > 0 and ΔS < 0, ΔG = ΔH - TΔS is always positive since both terms are positive. Positive ΔH and positive -TΔS ensure nonspontaneity at any temperature. No temperature can make ΔG negative. A tempting distractor is choice A, 'Spontaneous only at high temperature,' which wrongly assumes negative ΔS could be overcome by high T. Spontaneity is determined solely by ΔG's sign, integrating all factors.

7

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 unfavorable (nonspontaneous) only at low temperature.

The reaction is thermodynamically favorable (spontaneous) at 298 K.

The reaction is thermodynamically unfavorable (nonspontaneous) at 298 K.

The reaction is thermodynamically favorable (spontaneous) only at high 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.

8

A reaction has $\Delta G=+12\ \text{kJ mol}^{-1}$ at 298 K for the reaction as written. Which statement describes the thermodynamic favorability at 298 K?

Nonspontaneous at 298 K

Spontaneous at all temperatures

Spontaneous only at low temperature

Spontaneous only at high temperature

Nonspontaneous only if the reaction is slow

Explanation

This question assesses the skill of Gibbs free energy and thermodynamic favorability. A positive ΔG (+12 kJ/mol) at 298 K indicates the reaction is nonspontaneous under those conditions. ΔG directly determines spontaneity: positive means nonspontaneous, negative means spontaneous. This value shows the forward reaction does not proceed favorably at 298 K. A tempting distractor is choice A, 'Spontaneous at all temperatures,' which confuses positive ΔG with overall temperature independence, assuming no context for change. Remember, ΔG assesses thermodynamic favorability at specific conditions, independent of reaction kinetics.

9

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

Spontaneous only at low temperature

Spontaneous at all temperatures

Nonspontaneous at all temperatures

Spontaneous only at high temperature

Nonspontaneous at high temperature

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.

10

At 298 K, a reaction as written has $\Delta G=-0.5\ \text{kJ mol}^{-1}$. Which statement best describes the thermodynamic favorability at 298 K?

Nonspontaneous only if the reaction is fast

Nonspontaneous at 298 K

Spontaneous at 298 K

Spontaneous only at low temperature

Spontaneous only at high temperature

Explanation

This question assesses the skill of Gibbs free energy and thermodynamic favorability. A negative ΔG (-0.5 kJ/mol) at 298 K signifies the reaction is spontaneous at that temperature. ΔG < 0 drives the forward reaction thermodynamically. Even small negative values indicate favorability. A tempting distractor is choice A, 'Nonspontaneous at 298 K,' possibly from overlooking the negative sign. Confirm spontaneity by checking ΔG's sign, separate from kinetic considerations.

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