Q: If the rate constant $$k$$ for a reaction increases by a factor of 10 when the temperature is raised from $$300 \ \text{K} to$$ $$310 \ \text{K}$$, what is the activation energy $$E_a$$? Use the Arrhenius equation: $$\ln \left( \frac{k_2$}{k_1$} \right) = -\frac{E_a}{R} \left( \frac{1}{T_2$} - \frac{1}{T_1$} \right).$$

$$E_a \approx 53.1 \ \frac{\text{kJ}}{\text{mol}}$$

Q: A student is asked to calculate the change in free energy for a reaction using $$\Delta G = \Delta G^\circ + RT \ln Q. If$$ $$\Delta G^\circ = -40 \ \frac{\text{kJ}}{\text{mol}}$$, $$R = 8.314 \ \frac{\text{J}}{\text{mol} \cdot \text{K}}$$, $$T = 298 \ \text{K}$$, and $$Q = 10$$, what is $$\Delta G$$?

$$\Delta G = -33.1 \ \frac{\text{kJ}}{\text{mol}}$$

Question 1

A chemist is studying the concentration of a reactant in a solution. The concentration at time $$t is $$given by $$C(t) = C(0) + \log \left( \frac{R t_0$ 	ext{ mmol}}{t_0$ 	ext{ mmol}} ight). If$$ $$C(0) = 9.26$$ and $$C(t) = 9.56$$, what is the value of $$R$$? (Assume $$t_0$$ cancels out.)

Accepted Answer

$$R = 0.04$$

Question 2

Given the equation $$\Delta G = \Delta G^\circ + RT \ln Q$$, calculate $$Q$$ when $$\Delta G = -68.9 \ \frac{	ext{kJ}}{	ext{mol}}$$, $$\Delta G^\circ = -53.5 \ \frac{	ext{kJ}}{	ext{mol}}$$, $$R = 8.314 \ \frac{	ext{J}}{	ext{mol} \cdot 	ext{K}}$$, and $$T = 305.1 \ 	ext{K}.$$

Accepted Answer

$$Q = 0.0523$$

Question 3

For a reaction, the temperature dependence of the equilibrium constant is given by $$\ln \left( \frac{K_2$}{K_1$} ight) = -\frac{E_a}{R} \left( \frac{1}{T_2$} - \frac{1}{T_1$} ight). If$$ $$K_1 = 18.6$$ \ \frac{1}{	ext{mol}}$$, K_2$ = 204 \ \frac{1}{	ext{mol}}$$, $$E_a = 40.5 \ \frac{	ext{kJ}}{	ext{mol}}$$, $$R = 8.314 \ \frac{	ext{J}}{	ext{mol} \cdot 	ext{K}}$$, and $$T_1 = 190$$ 	ext{K}$$, what is T_2$?

Accepted Answer

$$T_2 = 210$$ 	ext{K}$$

Question 4

Solve the quadratic equation $$6x^2 + 19x - 7 = 0$ for x$.

Accepted Answer

$$x = 1/3 or$$ $$x = -7/2$$

Question 5

Solve for $$z in $$the equation $$z^2 - 16z + 61 = 2z - 20$.

Accepted Answer

$$z = 9$$

Question 6

A reaction has $$\Delta G^\circ = -53.5 \ \frac{	ext{kJ}}{	ext{mol}} at$$ $$305.1 \ 	ext{K}. $$What is the equilibrium constant $$K$$ for this reaction? Use $$\Delta G^\circ = -RT \ln K$$ and $$R = 8.314 \ \frac{	ext{J}}{	ext{mol} \cdot 	ext{K}}.$$

Accepted Answer

$$K \approx 2.5 	imes 10^9$

Question 7

If the rate constant $$k$$ for a reaction increases by a factor of 10 when the temperature is raised from $$300 \ 	ext{K} to$$ $$310 \ 	ext{K}$$, what is the activation energy $$E_a$$? Use the Arrhenius equation: $$\ln \left( \frac{k_2$}{k_1$} ight) = -\frac{E_a}{R} \left( \frac{1}{T_2$} - \frac{1}{T_1$} ight).$$

Accepted Answer

$$E_a \approx 53.1 \ \frac{	ext{kJ}}{	ext{mol}}$$

Question 8

A chemical reaction at $$T = 305.1 \ 	ext{K}$$ has $$Q = 0.0523$$ and $$K = 2.5 	imes 10^9$. Is the reaction at equilibrium, and in which direction will it proceed?

Accepted Answer

The reaction is not at equilibrium and will proceed forward to form more products.

Question 9

If $$\Delta G$$ for a reaction is negative, what does this indicate about the spontaneity of the reaction under standard conditions?

Accepted Answer

The reaction is spontaneous under standard conditions.

Question 10

A student is asked to calculate the change in free energy for a reaction using $$\Delta G = \Delta G^\circ + RT \ln Q. If$$ $$\Delta G^\circ = -40 \ \frac{	ext{kJ}}{	ext{mol}}$$, $$R = 8.314 \ \frac{	ext{J}}{	ext{mol} \cdot 	ext{K}}$$, $$T = 298 \ 	ext{K}$$, and $$Q = 10$$, what is $$\Delta G$$?

Accepted Answer

$$\Delta G = -33.1 \ \frac{	ext{kJ}}{	ext{mol}}$$

Question 11

Which of the following best describes the effect of increasing temperature on the equilibrium constant $$K$$ for an endothermic reaction?

Accepted Answer

$$K$$ increases as temperature increases.

Question 12

A reaction has $$\Delta G^\circ = 0. $$What can be said about the equilibrium constant $$K at $$this temperature?

Accepted Answer

$$K = 1$$

Question 13

If $$\Delta G$$ for a reaction is positive, which of the following is true?

Accepted Answer

The reaction is nonspontaneous under the given conditions.

Question 14

A reaction mixture initially contains only reactants. As the reaction proceeds, $$Q$$ increases. What happens to $$\Delta G as$$ $$Q$$ approaches $$K$$?

Accepted Answer

$$\Delta G$$ approaches zero.

Question 15

A reaction at $$T = 298 \ 	ext{K}$$ has $$\Delta G^\circ = -30 \ \frac{	ext{kJ}}{	ext{mol}}. $$What is the value of $$K$$? Use $$R = 8.314 \ \frac{	ext{J}}{	ext{mol} \cdot 	ext{K}}.$$

Accepted Answer

$$K \approx 1.6 	imes 10^5$

Thermodynamics and Chemical Equilibrium: Key Concepts and Calculations

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