Q: A reaction at 25°C has an equilibrium constant $$K_{eq} = 2.1 \times 10^4$. What is the Gibbs free energy change ($$\Delta G^\circ$$) for this reaction? (Use R = 8.314$ J/mol·K)

$$\Delta G^\circ = -RT \ln K_{eq}$$; \newline \Delta G^\circ = -(8.314)(298) \ln(2.1 \times $$10^4$$) \approx -24.0$ kJ/mol

Q: Given the reaction $$\text{SF}_6 (g) \rightarrow \text{SF}_4 (g) + \text{F}_2 (g)$$ with $$\Delta G^\circ = -374 kJ/$$mol, and partial pressures $$P_{SF_6$} = 0.43$$ atm, $$P_{SF_4$} = 0.65$$ atm, $$P_{F_2$} = 1.7$$ atm, calculate $$\Delta G$$ for the reaction at these conditions. ($$R = 8.314 J/$$mol·K, $$T = 298 K)$$

$$\Delta G = \Delta G^\circ + RT \ln Q$$; \newline $$Q = \dfrac{P_{SF_4$} \times P_{F_2$}}{P_{SF_6$}} = \dfrac{0.65 \times 1.7}{0.43} \approx 2.57$$; \newline $$\Delta G = -374000 + (8.314 \times 298) \ln(2.57) \approx -373.1 kJ/$$mol

Q: A hypothetical reaction at 35°C: X (aq) + 2Y (aq) $$\rightarrow Z (aq) $$has $$\Delta G^\circ = 3.2 kJ/$$mol. If $$[X] = 1.1 M$$, $$[Y] = 0.94 M$$, $$[Z] = 0.54 M$$, what is the value of $$K_{eq}$$ for this reaction?

$$K_{eq} = e$$^{-\Delta G^\circ / RT}$$; \newline T = 308$ K; $$\Delta G^\circ = 3200$$ J/mol; \newline K$$_{eq} = $$e^{-3200/(8.314 \times 308)}$$ \approx 0.29$$

Question 1

Which equation correctly relates the Gibbs free energy change to the equilibrium constant $$K_{eq} at $$standard conditions?

Accepted Answer

$$\Delta G^\circ = -RT \ln K_{eq}$$

Question 2

A reaction at 25°C has an equilibrium constant $$K_{eq} = 2.1 	imes 10^4$. What is the Gibbs free energy change ($$\Delta G^\circ$$) for this reaction? (Use R = 8.314$ J/mol·K)

Accepted Answer

$$\Delta G^\circ = -RT \ln K_{eq}$$; 
ewline \Delta G^\circ = -(8.314)(298) \ln(2.1 	imes $$10^4$$) \approx -24.0$ kJ/mol

Question 3

For the reaction Ag$$_2CO$_3 (s$$) $$\rightleftharpoons 2Ag$^+ (aq) + CO$_3$$^{2-}$$ (aq), $$\Delta H^\circ = 31.4$$ kJ/mol, $$\Delta S^\circ = 102.2$$ J/mol·K. What is the equilibrium constant K$$_{eq}$$ at 298.15 K?

Accepted Answer

First, calculate $$\Delta G^\circ$$: $$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ = 31400 - (298.15 	imes 102.2) = 31400 - 30474 \approx 926 J/$$mol. 
ewline Then, $$K_{eq} = e$$^{-\Delta G^\circ / RT}$$ = e$$^{-926/(8.314 	imes 298.15)}$$ \approx 0.71$$

Question 4

Which of the following statements best describes the relationship between $$\Delta G^\circ$$ and $$K_{eq}$$?

Accepted Answer

If $$\Delta G^\circ is $$negative, $$K_{eq} is $$greater than 1, favoring products.

Question 5

Given the reaction $$	ext{SF}_6 (g) ightarrow 	ext{SF}_4 (g) + 	ext{F}_2 (g)$$ with $$\Delta G^\circ = -374 kJ/$$mol, and partial pressures $$P_{SF_6$} = 0.43$$ atm, $$P_{SF_4$} = 0.65$$ atm, $$P_{F_2$} = 1.7$$ atm, calculate $$\Delta G$$ for the reaction at these conditions. ($$R = 8.314 J/$$mol·K, $$T = 298 K)$$

Accepted Answer

$$\Delta G = \Delta G^\circ + RT \ln Q$$; 
ewline $$Q = \dfrac{P_{SF_4$} 	imes P_{F_2$}}{P_{SF_6$}} = \dfrac{0.65 	imes 1.7}{0.43} \approx 2.57$$; 
ewline $$\Delta G = -374000 + (8.314 	imes 298) \ln(2.57) \approx -373.1 kJ/$$mol

Question 6

A hypothetical reaction at 35°C: X (aq) + 2Y (aq) $$\rightarrow Z (aq) $$has $$\Delta G^\circ = 3.2 kJ/$$mol. If $$[X] = 1.1 M$$, $$[Y] = 0.94 M$$, $$[Z] = 0.54 M$$, what is the value of $$K_{eq}$$ for this reaction?

Accepted Answer

$$K_{eq} = e$$^{-\Delta G^\circ / RT}$$; 
ewline T = 308$ K; $$\Delta G^\circ = 3200$$ J/mol; 
ewline K$$_{eq} = $$e^{-3200/(8.314 	imes 308)}$$ \approx 0.29$$

Question 7

If $$\Delta G^\circ$$ for a reaction is zero, what is the value of $$K_{eq}$$?

Accepted Answer

$$K_{eq} = 1$$

Question 8

Which of the following best describes the effect of increasing temperature on the equilibrium constant $$K_{eq}$$ for an endothermic reaction?

Accepted Answer

$$K_{eq}$$ increases as temperature increases.

Question 9

For a reaction where $$\Delta G^\circ is $$positive, which of the following is true about the equilibrium position?

Accepted Answer

The reaction favors reactants; $$K_{eq} \u003c 1.$$

Question 10

Which formula should be used to calculate the Gibbs free energy change ($$\Delta G) $$under non-standard conditions?

Accepted Answer

$$\Delta G = \Delta G^\circ + RT \ln Q$$

Question 11

A reaction has $$\Delta G^\circ = -40 kJ/$$mol at 298 K. What is the value of $$K_{eq}$$? ($$R = 8.314 J/$$mol·K)

Accepted Answer

$$K_{eq} = e$$^{-\Delta G^\circ / RT}$$ = e$$^{-(-40000)/(8.314 	imes 298)}$$ = e$$^{16.1}$$ \approx 1.0 	imes 10^7$

Question 12

Which of the following is NOT a correct use of the Gibbs free energy formula?

Accepted Answer

Using $$\Delta G = \Delta G^\circ + RT \ln K_{eq}$$ for equilibrium conditions.

Question 13

A reaction mixture has $$Q = 5.0$$ and $$K_{eq} = 2.0. $$What can be said about the direction in which the reaction will proceed?

Accepted Answer

The reaction will shift toward reactants to reach equilibrium.

Question 14

If $$\Delta G$$ for a reaction is negative under current conditions, what does this indicate?

Accepted Answer

The reaction is spontaneous in the forward direction.

Question 15

Which of the following is the correct expression for the reaction quotient $$Q$$ for the reaction $$aA + bB \rightarrow cC + dD$$?

Accepted Answer

$$Q = \dfrac{[C]^c [D]^d}{[A]^a [B]^b}$$

Question 16

A reaction has $$\Delta G^\circ = 15 kJ/$$mol and $$T = 298 K. $$What is the value of $$K_{eq}$$? ($$R = 8.314 J/$$mol·K)

Accepted Answer

$$K_{eq} = e$$^{-\Delta G^\circ / RT}$$ = e$$^{-15000/(8.314 	imes 298)}$$ = e$$^{-6.05}$$ \approx 0.0024$$

Question 17

Which of the following best explains why $$K_{eq} is $$temperature dependent?

Accepted Answer

Because $$\Delta G^\circ$$ depends on temperature through $$\Delta H^\circ$$ and $$\Delta S^\circ.$$

Question 18

For the reaction $$A ightleftharpoons B$$, if $$K_{eq} = 1.0 	imes 10$$^{-5}$$ at 298 K, what is the sign of $$\Delta G^\circ$$?

Accepted Answer

$$\Delta G^\circ is $$positive.

Question 19

Which of the following is true at equilibrium for any chemical reaction?

Accepted Answer

$$\Delta G = 0$$

Gibbs Free Energy, Equilibrium, and Reaction Quotient in Chemical Thermodynamics

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