Ammonia gas dissolves in water according to the following equation:

$$\mathrm{NH}_3(g)+\mathrm{H}_2 \mathrm{O}(l) \rightleftarrows \mathrm{NH}_4^{+}(a q)+\mathrm{OH}^{-}(a q)+\text { energy; } K=1.8 \times 10^{-5}$$

______________a. Is aqueous ammonia an acid or a base?

______________b. Is the equation given above an example of hydrolysis?

______________c. For the given value of $K$, does the equilibrium favor the forward or reverse reaction?

What is the proper form of the equilibrium constant expression for the equation:

$$\ce{N2(g) + O2(g)<=>2NO(g)}$$

a. What information is provided by the standard reduction potential of a given half-cell? b. What does the relative value of the reduction potential of a given half-reaction indicate about its oxidation-reduction tendency?

Consider the following equilibrium for which

$$\Delta H < 0$$

$$2 \mathrm { SO } _ { 2 } ( g ) + \mathrm { O } _ { 2 } ( g ) \rightleftharpoons 2 \mathrm { SO } _ { 3 } ( g )$$

How will each of the following changes affect an equilibrium mixture of the three gases: the volume of the reaction vessel is doubled.

Consider the following equilibrium equation: $\mathrm{CH}_3 \mathrm{OH}(\mathrm{g})+101 \mathrm{~kJ} \rightleftarrows \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_2(\mathrm{~g})$.

________a. Increasing $[\mathrm{CO}]$ will

(a) increase $\left[\mathrm{H}_2\right]$.

(c) not change $\left[\mathrm{H}_2\right]$.

(b) decrease $\left[\mathrm{H}_2\right]$.

(d) cause $\left[\mathrm{H}_2\right]$ to fluctuate.

________b. Raising the temperature will cause the equilibrium of the system to

(a) favor the reverse reaction.

(c) shift back and forth.

(b) favor the forward reaction.

(d) remain as it was before.

________c. Raising the temperature will

(a) increase the value of $K$.

(b) decrease the value of $K$.

(c) not change the value of $K$.

(d) make the value of $K$ fluctuate.

a. Write the appropriate chemical equilibrium expression for each of the following equations. Include the value of $K$.

(1) $\mathrm{N}_2 \mathrm{O}_4(\mathrm{~g}) \rightleftarrows 2 \mathrm{NO}_2(\mathrm{~g})$

$$K=0.1$$

(2) $\mathrm{NH}_4 \mathrm{OH}(a q) \rightleftarrows \mathrm{NH}_4^{+}(a q)+\mathrm{OH}^{-}(a q) \quad K-2 \times 10^{-5}$

(3) $\mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{HI}(\mathrm{g})$

$$K=54.0$$

(4) $2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftarrows 2 \mathrm{SO}_3(\mathrm{~g})$

$$K-1.8 \times 10^{-2}$$

____________b. Which of the four systems in part a proceeds furthest forward before equilibrium is established?

____________c. Which system contains mostly reactants at equilibrium?

_________Addition of the salt of a weak acid to a solution of the weak acid

(a) lowers the concentration of the nonionized acid and the concentration of the $\mathrm{H}_3 \mathrm{O}^{+}$ion.

(b) lowers the concentration of the nonionized acid and raises the concentration of the $\mathrm{H}_3 \mathrm{O}^{+}$ion.

(c) raises the concentration of the nonionized acid and the concentration of the $\mathrm{H}_3 \mathrm{O}^{+}$ion.

(d) raises the concentration of the nonionized acid and lowers the concentration of the $\mathrm{H}_3 \mathrm{O}^{+}$ion.

Silver carbonate, $\mathrm{Ag}_2 \mathrm{CO}_3$, makes a saturated solution with $K_{sp}$ =10^{-11}$.

a. Write the equilibrium expression for the dissolution of$ $\mathrm{Ag}$_2 $\mathrm{CO}$_3$.

____________b. In this system, will the foward or reverse reaction be favored if extra$ $\mathrm{Ag}$^{+}{ }^{+}$ions are added?

Consider the following equilibrium equation:

$$\mathrm{N}_2(g)+2 \mathrm{O}_2(g) \rightleftarrows 2 \mathrm{NO}_2(g) ; \Delta H=+33 \mathrm{~kJ} / \mathrm{mol}$$

At equilibrium, which reaction is favored when

______________a. some $\mathrm{N}_2$ is removed?

______________b. a catalyst is introduced?

______________c. pressure on the system increases due to a decrease in the volume?

______________d. the temperature of the system is increased?

_________ Lime juice turns litmus paper red, indicating that lime juice is

(a) acidic.

(b) basic.

(c) neutral.

(d) alkaline

Match the solution type on the right to the corresponding relationship between the ion product and the $K_{sp}$ for that solution, listed on the left.

________The ion product exceeds the $K_{s p}$. $\quad$

________The ion product equals the $K_{s p}$. $\quad$

________The ion product is less than the $K_{s p}$. $\quad$

(a) The solution is saturated; no more solid will dissolve.

(b) The solution is unsaturated; no solid is present.

(c) The solution is supersaturated; solid may form if the solution is disturbed.

Write the equilibrium expression for the following hypothetical equation:

$$3 \mathrm{~A}(a q)+\mathrm{B}(a q) \rightleftarrows 2 \mathrm{C}(a q)+3 \mathrm{D}(a q)$$

Suppose A, B, and X are $n \times n$ matrices with A, X, and A-AX invertible, and suppose $(A-A X)^{-1}=X^{-1} B$. a. Explain why B is invertible. B. Solve the equation for X. If you need to invert a matrix, explain why that matrix is invertible.

Explain how to solve a matrix equation.