A reaction vessel contains $\mathrm{NH}_3, \mathrm{~N}_2$, and $\mathrm{H}_2$ at equilibrium at a certain temperature. The equilibrium concentrations are $\left[\mathrm{NH}_3\right]=0.25~M,\left[\mathrm{~N}_2\right]=0.11~M$, and $\left[\mathrm{H}_2\right]=1.91~M$. Calculate the equilibrium constant $K_{\mathrm{c}}$ for the synthesis of ammonia if the reaction is represented as (a) $\mathrm{N}_2(g)+3 \mathrm{H}_2(g) \rightleftharpoons 2 \mathrm{NH}_3(g)$

Consider the following equilibrium process at $700^{\circ} \mathrm{C}$ :

$$2 \mathrm{H}_2(g)+\mathrm{S}_2(g) \rightleftharpoons 2 \mathrm{H}_2 \mathrm{~S}(g)$$

Analysis shows that there are $2.50$ moles of $\mathrm{H}_2, 1.35 \times$ $10^{-5}$ mole of $\mathrm{S}_2$, and $8.70$ moles of $\mathrm{H}_2 \mathrm{S}$ present in a $12.0-\mathrm{L}$ flask at equilibrium. Calculate the equilibrium constant $K_{\mathrm{c}}$ for the reaction.

The equilibrium constant $\left(K_{\mathrm{c}}\right)$ for the reaction

$$2 \mathrm{HCl}(g) \rightleftharpoons \mathrm{H}_2(g)+\mathrm{Cl}_2(g)$$

is $4.17 \times 10^{-34}$ at $25^{\circ} \mathrm{C}$. What is the equilibrium constant for the reaction

$$\mathrm{H}_2(g)+\mathrm{Cl}_2(g) \rightleftharpoons 2 \mathrm{HCl}(g)$$

at the same temperature?

Consider the following equilibrium system:

$$\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g) \quad \Delta H^{\circ}=58.0 \mathrm{~kJ} / \mathrm{mol}$$

(b) If the temperatures of the reacting system is changed at constant pressure, describe what a plot of $V$ versus $T$ would look like for the system.

Consider the following equilibrium system:

$$\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g) \quad \Delta H^{\circ}=58.0 \mathrm{~kJ} / \mathrm{mol}$$

(a) If the volume of the reacting system is changed at constant temperature, describe what a plot of $P$ versus $1 / V$ would look like for the system.

Iodine is sparingly soluble in water but much more so in carbon tetrachloride $\left(\mathrm{CCl}_4\right)$. The equilibrium constant, also called the partition coefficient, for the distribution of $\mathrm{I}_2$ between these two phases

$$\mathrm{I}_2(a q) \rightleftharpoons \mathrm{I}_2\left(\mathrm{CCl}_4\right)$$

is 83 at $20^{\circ} \mathrm{C}$. (c) Compare the result in (b) with a single extraction using $0.060 \mathrm{~L}$ of $\mathrm{CCl}_4$. Comment on the difference.

Iodine is sparingly soluble in water but much more so in carbon tetrachloride $\left(\mathrm{CCl}_4\right)$. The equilibrium constant, also called the partition coefficient, for the distribution of $\mathrm{I}_2$ between these two phases

$$\mathrm{I}_2(a q) \rightleftharpoons \mathrm{I}_2\left(\mathrm{CCl}_4\right)$$

is 83 at $20^{\circ} \mathrm{C}$. (b) The student now repeats the extraction of $\mathrm{I}_2$ with another $0.030 \mathrm{~L}$ of $\mathrm{CCl}_4$. Calculate the fraction of the $\mathrm{I}_2$ from the original solution that remains in the aqueous phase.

Iodine is sparingly soluble in water but much more so in carbon tetrachloride $\left(\mathrm{CCl}_4\right)$. The equilibrium constant, also called the partition coefficient, for the distribution of $\mathrm{I}_2$ between these two phases

$$\mathrm{I}_2(a q) \rightleftharpoons \mathrm{I}_2\left(\mathrm{CCl}_4\right)$$

is 83 at $20^{\circ} \mathrm{C}$. (a) A student adds $0.030 \mathrm{~L}$ of $\mathrm{CCl}_4$ to $0.200 \mathrm{~L}$ of an aqueous solution containing $0.032 \mathrm{~g}$ $\mathrm{I}_2$. The mixture is shaken and the two phases are then allowed to separate. Calculate the fraction of $\mathrm{I}_2$ remaining in the aqueous phase.

Consider the following reaction at a certain temperature

$$\mathrm{A}_2+\mathrm{B}_2 \rightleftharpoons 2 \mathrm{AB}$$

The mixing of 1 mole of $\mathrm{A}_2$ with 3 moles of $\mathrm{B}_2$ gives rise to $x$ mole of $\mathrm{AB}$ at equilibrium. The addition of 2 more moles of $\mathrm{A}_2$ produces another $x$ mole of AB. What is the equilibrium constant for the reaction?

The vapor pressures of water are $31.82 \mathrm{~mmHg}$ at $30^{\circ} \mathrm{C}$ and $92.51 \mathrm{~mmHg}$ at $50^{\circ} \mathrm{C}$. Calculate the molar heat of vaporization of water.

Use the van't Hoff equation in above Problem to derive the following expression, which relates the equilibrium constants at two different temperatures

$$\ln \frac{K_1}{K_2}=\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$$

How does this equation support the prediction based on Le Chatelier's principle about the shift in equilibrium with temperature?

Consider the equilibrium between molecular oxygen and ozone

$$3 \mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{O}_3(g) \quad \Delta H^{\circ}=284 \mathrm{~kJ} / \mathrm{mol}$$

What would be the effect of (a) increasing the pressure on the system by decreasing the volume, (b) adding $\mathrm{O}_2$ to the system, (c) decreasing the temperature, and (d) adding a catalyst?

Write the equation relating $K_{\mathrm{c}}$ and $K_P$ and define all the terms.

Define equilibrium. Give 2 examples of a dynamic equilibrium.