Q: Given the following standard entropies: $$\text{C}_2\text{H}_2(g): 200.9\ \text{J/mol}\cdot\text{K}$$, $$\text{H}_2(g): 130.6\ \text{J/mol}\cdot\text{K}$$, $$\text{C}_2\text{H}_6(g): 229.5\ \text{J/mol}\cdot\text{K}$$, calculate $$\Delta S^\circ$$ for the reaction $$\text{C}_2\text{H}_2(g) + 2\text{H}_2(g) \rightarrow \text{C}_2\text{H}_6(g).$$

$$\Delta S^\circ = 229.5 - [200.9 + 261.2] = -232.6\ \text{J/mol}\cdot\text{K}$$

Q: The entropy of a system with $$W = 2.0 \times 10$$^{17}$$ microstates is given by S = k_B$$ \ln W$$. What is the entropy in J/K? (k_B = 1.38$$ \times $$10^{-23}$$\ \text{J/K}$$)

$$S = 1.38 \times 10$$^{-23}$$ \ln(2.0 \times 10$$^{17}$$) = 5.4 \times 10$$^{-22}$$\ \text{J/K}$$

Q: For the isothermal compression of 5 mol of Kr gas from 5.5 L to 4.0 L, what is the change in entropy ($$\Delta S) of $$the gas? ($$R = 8.314\ \text{J/mol}\cdot\text{K})$$

$$\Delta S = nR \ln \left( \frac{V_f}{V_i} \right) = 5 \times 8.314 \ln \left( \frac{4.0}{5.5} \right) = -6.1\ \text{J/K}$$

Q: Given the following standard Gibbs free energies of formation: $$\text{Al}_2\text{O}_3(s): -1582.3\ \text{kJ/mol}$$, $$\text{Fe}_2\text{O}_3(s): -743.5\ \text{kJ/mol}$$, $$\text{Al}(s): 0$$, $$\text{Fe}(s): 0$$, calculate $$\Delta G$$ for the reaction $$\text{Al}_2\text{O}_3(s) + 2\text{Fe}(s) \rightarrow \text{Fe}_2\text{O}_3(s) + 2\text{Al}(s).$$

$$\Delta G = [(-743.5) + 2 \times 0] - [(-1582.3) + 2 \times 0] = 838.8\ \text{kJ}$$

Q: Which of the following reactions is spontaneous at standard conditions based on the given $$\Delta G$$ values?

$$2\text{H}_2\text{O}_2(aq) \rightarrow \text{O}_2(g) + 2\text{H}_2\text{O}(l);\ \Delta G = -211\ \text{kJ}$$

Q: The rate law for a reaction is $$\text{Rate} = k[\text{H}_2\text{O}_2][\text{Fe}^{2+}]. $$What is the order with respect to $$\text{H}_2\text{O}_2$$, $$\text{Fe}^{2+}$$, and the overall order?

First order in $$\text{H}_2\text{O}_2$$, first order in $$\text{Fe}^{2+}$$, second order overall.

Q: For the reaction $$2\text{NO}_2(g) \rightarrow 2\text{NO}(g) + \text{O}_2(g)$$, which of the following correctly expresses the rate in terms of the disappearance of $$\text{NO}_2$$ and the appearance of $$\text{O}_2$$?

$$\text{Rate} = -\frac{1}{2} \frac{d[\text{NO}_2]}{dt} = \frac{d[\text{O}_2]}{dt}$$

Question 1

Which of the following best describes entropy ($$S) in $$thermodynamics?

Accepted Answer

A measure of the disorder or number of possible microstates ($$W) $$available to a system.

Question 2

For the reaction $$2 	ext{C}_2	ext{H}_2(g) + 3 	ext{O}_2(g) ightarrow 4 	ext{CO}(g) + 2	ext{H}_2	ext{O}(g)$$, predict the sign of $$\Delta S^\circ$$ and explain why.

Accepted Answer

$$\Delta S^\circ is $$positive because the number of gas molecules increases.

Question 3

Given the following standard entropies: $$	ext{C}_2	ext{H}_2(g): 200.9\ 	ext{J/mol}\cdot	ext{K}$$, $$	ext{H}_2(g): 130.6\ 	ext{J/mol}\cdot	ext{K}$$, $$	ext{C}_2	ext{H}_6(g): 229.5\ 	ext{J/mol}\cdot	ext{K}$$, calculate $$\Delta S^\circ$$ for the reaction $$	ext{C}_2	ext{H}_2(g) + 2	ext{H}_2(g) ightarrow 	ext{C}_2	ext{H}_6(g).$$

Accepted Answer

$$\Delta S^\circ = 229.5 - [200.9 + 261.2] = -232.6\ 	ext{J/mol}\cdot	ext{K}$$

Question 4

A reaction has $$\Delta H = -200\ 	ext{kJ}$$ and $$\Delta S = -400\ 	ext{J/K}. At $$what temperature (in K) does the reaction become non-spontaneous?

Accepted Answer

$$T = \frac{\Delta H}{\Delta S} = \frac{-200,000}{-400} = 500\ 	ext{K}$$

Question 5

The entropy of a system with $$W = 2.0 	imes 10$$^{17}$$ microstates is given by S = k_B$$ \ln W$$. What is the entropy in J/K? (k_B = 1.38$$ 	imes $$10^{-23}$$\ 	ext{J/K}$$)

Accepted Answer

$$S = 1.38 	imes 10$$^{-23}$$ \ln(2.0 	imes 10$$^{17}$$) = 5.4 	imes 10$$^{-22}$$\ 	ext{J/K}$$

Question 6

For the isothermal compression of 5 mol of Kr gas from 5.5 L to 4.0 L, what is the change in entropy ($$\Delta S) of $$the gas? ($$R = 8.314\ 	ext{J/mol}\cdot	ext{K})$$

Accepted Answer

$$\Delta S = nR \ln \left( \frac{V_f}{V_i} ight) = 5 	imes 8.314 \ln \left( \frac{4.0}{5.5} ight) = -6.1\ 	ext{J/K}$$

Question 7

Given the following standard Gibbs free energies of formation: $$	ext{Al}_2	ext{O}_3(s): -1582.3\ 	ext{kJ/mol}$$, $$	ext{Fe}_2	ext{O}_3(s): -743.5\ 	ext{kJ/mol}$$, $$	ext{Al}(s): 0$$, $$	ext{Fe}(s): 0$$, calculate $$\Delta G$$ for the reaction $$	ext{Al}_2	ext{O}_3(s) + 2	ext{Fe}(s) ightarrow 	ext{Fe}_2	ext{O}_3(s) + 2	ext{Al}(s).$$

Accepted Answer

$$\Delta G = [(-743.5) + 2 	imes 0] - [(-1582.3) + 2 	imes 0] = 838.8\ 	ext{kJ}$$

Question 8

Which of the following reactions is spontaneous at standard conditions based on the given $$\Delta G$$ values?

Accepted Answer

$$2	ext{H}_2	ext{O}_2(aq) ightarrow 	ext{O}_2(g) + 2	ext{H}_2	ext{O}(l);\ \Delta G = -211\ 	ext{kJ}$$

Question 9

The rate law for a reaction is $$	ext{Rate} = k[	ext{H}_2	ext{O}_2][	ext{Fe}^{2+}]. $$What is the order with respect to $$	ext{H}_2	ext{O}_2$$, $$	ext{Fe}^{2+}$$, and the overall order?

Accepted Answer

First order in $$	ext{H}_2	ext{O}_2$$, first order in $$	ext{Fe}^{2+}$$, second order overall.

Question 10

For the reaction $$2	ext{NO}_2(g) ightarrow 2	ext{NO}(g) + 	ext{O}_2(g)$$, which of the following correctly expresses the rate in terms of the disappearance of $$	ext{NO}_2$$ and the appearance of $$	ext{O}_2$$?

Accepted Answer

$$	ext{Rate} = -\frac{1}{2} \frac{d[	ext{NO}_2]}{dt} = \frac{d[	ext{O}_2]}{dt}$$

Question 11

In a reaction, the concentration of $$	ext{Fe}^{3+}$$ decreases from $$0.03586\ 	ext{M} to$$ $$0.02638\ 	ext{M} in$$ $$4.00$$ min. What is the average rate of disappearance of $$	ext{FeCl}_3 in$$ $$	ext{M/min}$$?

Accepted Answer

$$	ext{Rate} = \frac{0.03586 - 0.02638}{4.00} = 2.37 	imes 10$$^{-3}$$\ 	ext{M/min}$$

Question 12

A reaction $$aA ightarrow$$ products is second order with $$k = 0.225\ 	ext{M}^{-1}	ext{s}^{-1}. If$$ $$[A]_0 = 0.293\ 	ext{M}$$, what is $$[A]$$ after $$35.4 s$$?

Accepted Answer

$$[A] = \frac{1}{k t + 1/[A]_0} = \frac{1}{0.225 	imes 35.4 + 1/0.293} = 0.073\ 	ext{M}$$

Question 13

The rate constant for a reaction increases from $$1.4 	imes 10$$^{-4}$$\ 	ext{s}^{-1} at$$ $$35^\circ	ext{C} to$$ $$5.0 	imes 10$$^{-4}$$\ 	ext{s}^{-1} at$$ $$45^\circ	ext{C}. $$What is the activation energy ($$E_a) in kJ/$$mol? ($$R = 8.314\ 	ext{J/mol}\cdot	ext{K})$$

Accepted Answer

$$E_a = \frac{R \ln(k_2$/k_1$)}{(1/T_1$)-(1/T_2$)} = \frac{8.314 \ln(5.0 	imes 10$$^{-4}$$/1.4 	imes 10$$^{-4}$$)}{(1/308)-(1/318)} = 47\ 	ext{kJ/mol}$$

Question 14

The rate of a reaction triples when the temperature increases from $$25^\circ	ext{C} to$$ $$35^\circ	ext{C}. $$What is the activation energy ($$E_a) in kJ/$$mol? ($$R = 8.314\ 	ext{J/mol}\cdot	ext{K})$$

Accepted Answer

$$E_a = \frac{R \ln(3)}{(1/298)-(1/308)} = 79.6\ 	ext{kJ/mol}$$

Question 15

For a reaction with the rate law $$	ext{Rate} = k[	ext{I}^-][	ext{ClO}^-]$$, doubling the concentration of $$	ext{I}^-$$ while keeping $$[	ext{ClO}^-]$$ constant will have what effect on the rate?

Accepted Answer

The rate will double.

Question 16

A first-order reaction has a rate constant $$k = 0.693\ 	ext{min}^{-1}. $$What is the half-life ($$t_{1/2}) of $$the reaction?

Accepted Answer

$$t_{1/2} = \frac{0.693}{k} = 1.0\ 	ext{min}$$

Question 17

For a second-order reaction with $$k = 0.625\ 	ext{M}^{-1}	ext{s}^{-1}$$, how long would it take for a $$1.0\ 	ext{M}$$ reactant to be reduced to $$1.22 	imes 10$$^{-3}$$\ 	ext{M}$$?

Accepted Answer

$$t = \frac{1}{k} \left( \frac{1}{[A]_t} - \frac{1}{[A]_0} ight ) = \frac{1}{0.625} \left( \frac{1}{1.22 	imes 10$$^{-3}$$} - 1 ight ) = 1300\ 	ext{s}$$

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