Entropy and spontaneity: notes and practice questions

Consider the synthesis of ammonia in the Haber process. What is the expected sign of the standard entropy change, $\Delta S^{\ominus}$, for this reaction?

$N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$

A. Positive

B. Negative

C. Approximately zero

D. Cannot be determined without thermodynamic data

The Haber-Bosch process is a crucial industrial method for synthesizing ammonia from nitrogen and hydrogen gases. Consider the reaction:

$\text{N}_2(\text{g}) + 3\text{H}_2(\text{g}) \rightleftharpoons 2\text{NH}_3(\text{g})$

Using the standard molar entropy data provided, calculate the standard entropy change, $\Delta S^{\ominus}$, for this reaction.

A $-198.7 \ J \ K^{-1} \ mol^{-1}$

B $198.7 \ J \ K^{-1} \ mol^{-1}$

C $62.7 \ J \ K^{-1} \ mol^{-1}$

D $-391.2 \ J \ K^{-1} \ mol^{-1}$

What is the expected sign of the standard entropy change, $\Delta S^\ominus$, for the thermal decomposition of calcium carbonate? [1]

$CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$

A. Positive

B. Negative

C. Approximately zero

D. Cannot be determined without enthalpy data

The synthesis of ammonia is a crucial industrial process. Consider the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$ at $298 \ K$. Calculate the standard Gibbs free energy change, $\Delta G^\circ$, for this reaction using the following thermodynamic data:

A $-151 \ kJ \ mol^{-1}$

B $151 \ kJ \ mol^{-1}$

C $59.2 \ kJ \ mol^{-1}$

D $-33.0 \ kJ \ mol^{-1}$

Urea, $(NH_2)_2CO$, is synthesized industrially from ammonia and carbon dioxide. The overall reaction is shown below.

$2NH_3(g) + CO_2(g) \rightarrow (NH_2)_2CO(s) + H_2O(l)$

Deduce the sign of the standard entropy change, $\Delta S^{\ominus}$, for this process.

A. Positive

B. Negative

C. Approximately zero

D. Cannot be determined without standard entropy values

The decomposition of aqueous hydrogen peroxide is an exothermic reaction, as shown by the equation:

$2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)$

Which statement correctly describes the spontaneity of this reaction?

A. The reaction is spontaneous at all temperatures.

B. The reaction is non-spontaneous at all temperatures.

C. The reaction is spontaneous only above a certain temperature.

D. The reaction is spontaneous only below a certain temperature.

Which process involves a decrease in entropy?

A. $I_2(s) \rightarrow I_2(g)$

B. $CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$

C. $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$

D. $C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(g)$

Under which conditions is a chemical reaction always spontaneous, regardless of the temperature?

A. $\Delta H^{\ominus} > 0$ and $\Delta S^{\ominus} > 0$

B. $\Delta H^{\ominus} < 0$ and $\Delta S^{\ominus} < 0$

C. $\Delta H^{\ominus} > 0$ and $\Delta S^{\ominus} < 0$

D. $\Delta H^{\ominus} < 0$ and $\Delta S^{\ominus} > 0$

In which reaction is the change in entropy, $\Delta S$, positive?

A. $2H_2O_2(l) \rightarrow 2H_2O(l) + O_2(g)$

B. $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$

C. $Ag^+(aq) + Cl^-(aq) \rightarrow AgCl(s)$

D. $2NO(g) + O_2(g) \rightarrow 2NO_2(g)$

A particular reaction is spontaneous at $25 \,^\circ\text{C}$ but becomes non-spontaneous at $500 \,^\circ\text{C}$. Which combination describes the signs of the enthalpy and entropy changes for this reaction?

A. $\Delta H: -$, $\Delta S: -$

B. $\Delta H: +$, $\Delta S: +$

C. $\Delta H: -$, $\Delta S: +$

D. $\Delta H: +$, $\Delta S: -$

Which reaction is predicted to have the largest increase in entropy ($\Delta S$)?

A. $2SO_2(g) + O_2(g) \rightarrow 2SO_3(g)$

B. $C(s) + O_2(g) \rightarrow CO_2(g)$

C. $2KClO_3(s) \rightarrow 2KCl(s) + 3O_2(g)$

D. $N_2O_4(g) \rightarrow 2NO_2(g)$

For a reversible reaction at constant temperature, the value of the reaction quotient, $Q$, is found to be less than the equilibrium constant, $K_c$. Which statement is correct for the forward reaction under these conditions?

A. $\Delta G$ is positive.

B. The reaction is at equilibrium.

C. $\Delta G$ is negative.

D. $\Delta G^{\ominus}$ is zero.