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.

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?

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

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?

From the following equilibrium constant expression, write a balanced chemical equation for the gas-phase reaction. Does $K_{\mathrm{c}}=K_P$ for this reaction?

$$K_{\mathrm{c}}=\frac{\left[\mathrm{NH}_3\right]^2\left[\mathrm{H}_2 \mathrm{O}\right]^4}{\left[\mathrm{NO}_2\right]^2\left[\mathrm{H}_2\right]^7}$$

Write $K_{\mathrm{c}}$ and $K_P$ for the decomposition of dinitrogen pentoxide:

$$2 \mathrm{N}_2 \mathrm{O}_5(g) \rightleftharpoons 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)$$

Consider the equilibrium $\mathrm{X} \rightleftharpoons \mathrm{Y}$, where the forward reaction rate constant is greater than the reverse reaction rate constant. Which of the following is true about the equilibrium constant? (a) $K_{\mathrm{c}}>1$, (b) $K_{\mathrm{c}}<1$, (c) $K_{\mathrm{c}}=1$.

Define equilibrium. Give 2 examples of a dynamic equilibrium.

In this exercise, simplify the following.

$$\left(1.8 \times 10^{-3}\right) \times\left(2 \times 10^5\right)$$

Add or subtract. Write your answer in scientific notation.

$$6.2 \times 10 ^ { 5 } - 2.6 \times 10 ^ { 4 } - 1.9 \times 10 ^ { 2 }$$

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Which of the numbers below are correctly written in scientific notation? For each that is not, rewrite it correctly. a.

$$4.51 \times 10 ^ { - 2 }$$

, b.

$$0.789 \times 10 ^ { 5 }$$

, c.

$$31.5 \times 10 ^ { 2 }$$

, d.

$$3.008 \times 10 ^ { - 8 }$$

Show that the vector $\mathbf{b}=\mathbf{a}_{1} \times \mathbf{a}_{2} \times \cdots \times \mathbf{a}_{n-1}$ is orthogonal to $\mathbf{a}_{1}, \dots, \mathbf{a}_{n-1}$.