Q: For the reaction $2\mathrm{CO}(g) \rightleftharpoons \mathrm{C}(s) + \mathrm{CO}_2(g)$ at 800 K, $K_c = 4.4 \times 10^{-2}$. What is $K_p$ at this temperature? ($R = 0.08206\ \mathrm{L\ atm\ mol^{-1}\ K^{-1}}$)

$K_p = K_c (RT)^{\Delta n} = 4.4 \times 10^{-2} \times (0.08206 \times 800)^{1} = 2.9$

Q: For the reaction $\mathrm{CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)}$, if additional $CO_2(g)$ is added to the system and it is allowed to return to equilibrium, what will happen to the amount of $CaCO_3(s)$?

The amount of $CaCO_3(s)$ will increase.

Q: According to Le Châtelier’s Principle, what will happen to the equilibrium position of the reaction $\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$ if the pressure is increased by decreasing the volume?

The equilibrium will shift toward the products ($NH_3$).

Q: Which of the following is a correct statement about the effect of temperature on the equilibrium constant $K_c$ for an endothermic reaction?

$K_c$ increases as temperature increases.

Q: Which of the following best describes the effect of increasing temperature on the autoionization constant of water, $K_w$?

$K_w$ increases as temperature increases.

Q: A solution is prepared by mixing 50 mL of $0.020\ \mathrm{M}\ \mathrm{Ca(OH)_2}$ with 100 mL of $0.010\ \mathrm{M}\ \mathrm{NaOH}$. What is the final pH of the solution? (Assume complete dissociation and additive volumes.)

First, calculate total moles of $OH^-$: $0.050\ \mathrm{L} \times 0.020\ \mathrm{mol/L} \times 2 = 0.0020\ \mathrm{mol}$ from $Ca(OH)_2$ and $0.100\ \mathrm{L} \times 0.010\ \mathrm{mol/L} = 0.0010\ \mathrm{mol}$ from $NaOH$. Total $OH^-$: $0.0030\ \mathrm{mol}$ in $0.150\ \mathrm{L}$, $[OH^-] = 0.020\ \mathrm{M}$, $pOH = 1.70$, $pH = 14 - 1.70 = 12.30$.

Q: Which of the following is the correct expression for the equilibrium constant $K_c$ for the reaction $\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$?

$K_c = \dfrac{[NH_3]^2}{[N_2][H_2]^3}$

Question 1

A 1.0 mol sample of X and 2.0 mol sample of Y are placed in a 4.0 L container and allowed to reach equilibrium according to the reaction:

$\mathrm{X(aq) + 2Y(aq) \rightleftharpoons 3Z(aq)}$

At equilibrium, $[X] = 0.10\ \mathrm{M}$, $[Y] = 0.20\ \mathrm{M}$, and $[Z] = 0.30\ \mathrm{M}$. What is the value of $K_c$ for this reaction?

Accepted Answer

$K_c = \dfrac{[Z]^3}{[X][Y]^2} = \dfrac{(0.30)^3}{(0.10)(0.20)^2} = 6.75$

Question 2

For the reaction $2\mathrm{CO}(g) ightleftharpoons \mathrm{C}(s) + \mathrm{CO}_2(g)$ at 800 K, $K_c = 4.4 	imes 10^{-2}$. What is $K_p$ at this temperature? ($R = 0.08206\ \mathrm{L\ atm\ mol^{-1}\ K^{-1}}$)

Accepted Answer

$K_p = K_c (RT)^{\Delta n} = 4.4 	imes 10^{-2} 	imes (0.08206 	imes 800)^{1} = 2.9$

Question 3

Which of the following reactions would NOT shift when the concentration of all substances is doubled, i.e., the system remains at equilibrium?

Accepted Answer

$\mathrm{A(aq) + B(aq) \rightleftharpoons AB(s)}$

Question 4

Nickel(II) oxide is reduced to nickel metal by the reaction:

$\mathrm{NiO(s) + CO(g) ightleftharpoons Ni(s) + CO_2(g)}$

At 1000 K, $K_p = 6.0 	imes 10^2$. If $P_{CO} = 0.250$ atm and $P_{CO_2} = 0.803$ atm, will NiO be reduced to Ni metal?

Accepted Answer

Yes, because $Q = \dfrac{P_{CO_2}}{P_{CO}} = \dfrac{0.803}{0.250} = 3.21 < K_p$, so the reaction proceeds forward.

Question 5

For the reaction $\mathrm{CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)}$, if additional $CO_2(g)$ is added to the system and it is allowed to return to equilibrium, what will happen to the amount of $CaCO_3(s)$?

Accepted Answer

The amount of $CaCO_3(s)$ will increase.

Question 6

According to Le Châtelier’s Principle, what will happen to the equilibrium position of the reaction $\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$ if the pressure is increased by decreasing the volume?

Accepted Answer

The equilibrium will shift toward the products ($NH_3$).

Question 7

Which of the following will increase the rate at which equilibrium is reached but does NOT change the equilibrium composition for a chemical reaction?

Accepted Answer

Adding a catalyst.

Question 8

Which of the following is a correct statement about the effect of temperature on the equilibrium constant $K_c$ for an endothermic reaction?

Accepted Answer

$K_c$ increases as temperature increases.

Question 9

Which of the following is amphoteric (can act as both an acid and a base)?

Accepted Answer

$\mathrm{HCO_3^-}$

Question 10

Which of the following is a strong acid?

Accepted Answer

$\mathrm{HClO_4}$

Question 11

What is the pH of a $0.020\ \mathrm{M}$ solution of $\mathrm{HClO_4}$ (a strong acid)?

Accepted Answer

$pH = -\log(0.020) = 1.70$

Question 12

Which of the following best describes the effect of increasing temperature on the autoionization constant of water, $K_w$?

Accepted Answer

$K_w$ increases as temperature increases.

Question 13

A solution is prepared by mixing 50 mL of $0.020\ \mathrm{M}\ \mathrm{Ca(OH)_2}$ with 100 mL of $0.010\ \mathrm{M}\ \mathrm{NaOH}$. What is the final pH of the solution? (Assume complete dissociation and additive volumes.)

Accepted Answer

First, calculate total moles of $OH^-$: $0.050\ \mathrm{L} 	imes 0.020\ \mathrm{mol/L} 	imes 2 = 0.0020\ \mathrm{mol}$ from $Ca(OH)_2$ and $0.100\ \mathrm{L} 	imes 0.010\ \mathrm{mol/L} = 0.0010\ \mathrm{mol}$ from $NaOH$. Total $OH^-$: $0.0030\ \mathrm{mol}$ in $0.150\ \mathrm{L}$, $[OH^-] = 0.020\ \mathrm{M}$, $pOH = 1.70$, $pH = 14 - 1.70 = 12.30$.

Question 14

Which of the following is the correct expression for the equilibrium constant $K_c$ for the reaction $\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$?

Accepted Answer

$K_c = \dfrac{[NH_3]^2}{[N_2][H_2]^3}$

Question 15

If more $H_2$ is added to the equilibrium mixture of $\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$, what happens immediately to the rates of the forward and reverse reactions?

Accepted Answer

The rate of the forward reaction increases, while the rate of the reverse reaction remains unchanged initially.

Question 16

Which of the following compounds is insoluble in water?

Accepted Answer

$\mathrm{AgCl}$

Question 17

Which of the following best describes the effect of adding a catalyst to a reaction at equilibrium?

Accepted Answer

It increases the rate at which equilibrium is reached but does not change the equilibrium composition.

Question 18

Which of the following is the correct relationship for the autoionization constant of water at 25°C?

Accepted Answer

$K_w = [H_3O^+][OH^-] = 1.0 	imes 10^{-14}$

Question 19

A solution is prepared by mixing 50 mL of $0.020\ \mathrm{M}\ \mathrm{Ca(OH)_2}$ with 100 mL of $0.010\ \mathrm{M}\ \mathrm{HI}$ at 50°C. If $pK_w = 13.25$ at 50°C, what is the pH of the final mixture?

Accepted Answer

First, $Ca(OH)_2$ provides $0.0020$ mol $OH^-$, $HI$ provides $0.0010$ mol $H^+$. $OH^-$ in excess: $0.0010$ mol in $0.150$ L, $[OH^-] = 0.0067$ M, $pOH = -\log(0.0067) = 2.17$, $pH = 13.25 - 2.17 = 11.08$.

Chemical Equilibrium and Le Châtelier’s Principle: Concepts, Calculations, and Applications

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