# 4.4 Practice Problems

1. Label each species in the reactions below as acid, base, conjugate base, or conjugate acid:

$$
\begin{align*}
\ce{
H2SO4 + 2 NH3 &-> 2 NH4+ + SO4^2-\\
HCl + NO2- &-> HNO2 + Cl-\\
HF + NH3 &<=> F- + NH4+\\
CH3COO- + H2O &<=> CH3COOH + OH-
}
\end{align*}
$$

2. Calculate $[\ce{OH-}]$  in a $\pu{1.4e-3 M}$  $\ce{HCl}$ solution at $\pu{25 ^\circ C}$.

3. Calculate $[\ce{H3O+}]$ in a solution for which $[\ce{OH-}] = \pu{0.25 M}$ at $\pu{25 ^\circ C}$.

4. Calculate the concentration of the strong acid, $\ce{HBr}$, in a solution at $\pu{25 ^\circ C}$ that has a $p\ce{H}$ of 
	1. $0.12$
	2. $2.46$
	3. $6.27$

5. A sample of acid rain collected from a pond was shown to have a $p\ce{H} = 4.65$. What concentration of $\ce{HNO3}$ is this $p\ce{H}$ equivalent to?

6. Calculate the concentration of $\ce{HCl}$ in a solution at $\pu{25 ^\circ C}$ that has $p\ce{H} =$ 
	1. $4.95$
	2. $3.45$
	3. $2.78$

7. An aqueous solution of a strong base has $p\ce{H} = 8.15$ at $\pu{25 ^\circ C}$. Calculate the original concentration of the base in the solution if the base is 
	1. $\ce{NaOH}$
	2. $\ce{Ba(OH)2}$

8. Calculate the $p\ce{H}$ of an aqueous solution at $\pu{25 ^\circ C}$ that is $\pu{0.095 M}$ in hydrocyanic acid ($\ce{HCN}$). ($K_a = \pu{4.9e-10}$)

9. Calculate the equilibrium $p\ce{H}$ of $\pu{0.0075 M}$ $\ce{HClO}$ (hypochlorous acid, the main ingredient of bleach) solution at $\pu{25 ^\circ C}$. This equilibrium reaction is

$$\ce{
HClO (aq) + H2O (l) <=> H3O+ (aq) + ClO- (aq) \qquad $K_a= \pu{3.5e-8}$
}$$

10. The $p\ce{H}$ of an aqueous acid solution is $\pu{6.20}$ at $\pu{25 ^\circ C}$. Calculate $K_a$ for this acid if the initial acid concentration is $\pu{0.010 M}$. Assume the acid to be a weak monoprotic acid.

11. Using the acetic acid equilibrium reaction as shown below, determine the $p\ce{H}$ and percent ionization for acetic acid ($\ce{CH3COOH}$) solutions at $\pu{25 ^\circ C}$ with concentrations :
	1. $\pu{0.15 M}$
	2. $\pu{0.015 M}$
	3. $\pu{0.0015 M}$

$$\ce{
CH3COOH (aq) <=> H+ (aq) + CH3COO- (aq) \qquad $K_a = \pu{1.8e-5}$
}$$

12. In the following dissociation reaction of $\ce{H4SiO4 (aq)}$, calculate the relative abundance of $\ce{H4SiO4 (aq)}$ to $\ce{H3SiO4- (aq)}$ at $p\ce{H} = 8.2$ at $\pu{25 ^\circ C}$.

$$\ce{
H4SiO4 (aq) <=> H3SiO4- (aq) + H+ (aq) \qquad $K_a = 10^{-9.83}$
}$$

13. Solve the following problems that are related to the carbonate system:
	1. In a natural water whose $p\ce{H} = 4$ at $\pu{25 ^\circ C}$, calculate the relative activity of (a) $\ce{H2CO3^* (aq)}$ to $\ce{HCO3- (aq)}$ and (b) $\ce{HCO3- (aq)}$ to $\ce{CO3^2- (aq)}$.
	2. Determine the $p\ce{H}$ at which (a) $[\ce{H2CO3^* (aq)}] = [\ce{HCO3- (aq)}]$ and (b) $[\ce{HCO3- (aq)}] = [\ce{CO3^2- (aq)}]$.
	3. A groundwater sample has $p\ce{H} = 6.84$ and $[\ce{HCO3- (aq)}] = \pu{460 mg L−1}$. Calculate $P_\ce{CO2 (g)}$ at $\pu{25 ^\circ C}$. Assume that activity equals concentration.
	4. Calculate  $p\ce{H}$ of rainwater in equilibrium with atmospheric $\ce{CO2}$.
	5. Calculate the concentration of each carbonate species in solution at $\pu{25 ^\circ C}$ when $\ce{C}_T = \pu{e-3 mol L-1}$ and $p\ce{H} = 5.7$. Explain if your answer is reasonable.
	6. Calculate the acidity and alkalinity of this system at $\ce{C}_T = \pu{e-3 mol L-1}$ and $p\ce{H} = 5.7$.

14. Solve the following problems that are related to the silicate system:
	1. In a natural water whose  $p\ce{H} = 7$ at $\pu{25 ^\circ C}$, calculate the relative abundance of $\ce{H4SiO4 (aq)}$ to $\ce{H3SiO4- (aq)}$.
	2. Determine the $p\ce{H}$ at which (a) $[\ce{H4SiO4 (aq)}] = [\ce{H3SiO4- (aq)}]$ and (b) $[\ce{H3SiO4- (aq)}] = [\ce{H2SiO4^2- (aq)}]$.
	3. A river water sample has a $p\ce{H}$ of 6.5 and $\ce{Si}_T = \pu{10.5 mg L−1}$. Calculate each silica species concentration in this water sample. Note: Use the same method as that used for the carbonate system.

15. Calculate the concentration of $\ce{OH-}$ in solution if $\pu{0.1 mol}$ of $\ce{NH3}$ is dissolved in $\pu{1 L}$ of pure water at $\pu{25 ^\circ C}$. ($K_b = \pu{10^{-4.7}}$)

16. What is the original molarity of an aqueous solution of ammonia ($\ce{NH3}$) whose $p\ce{H}$ is $11.22$ at $\pu{25 ^\circ C}$?

17. $\ce{Zn(OH)2 (s)}$ is an amphoteric hydroxide. Write balanced ionic equations to show its reaction with 
	1. $\ce{HCl}$
	2. $\ce{NaOH}$ (note: the product is $\ce{Zn(OH)4^2- (aq)}$).

18. $\ce{Cu(OH)2 (s)}$ is an amphoteric compound and dissolves according to the shown after the question. Answer the following questions and assume that the water temperature is $\pu{25 ^\circ C}$.
	1. Excess copper hydroxide is added to a beaker of water, i.e., solid copper hydroxide is present in the water. The solution $p\ce{H}$ is adjusted to $10$ using a base. Calculate $[\ce{Cu(OH)3- (aq)}]$ in the solution at equilibrium. 
	2. A strong acid is added to the solution until the $p\ce{H}$ is reduced to $4$. Will the amount of $\ce{Cu(OH)3- (aq)}$ in the beaker increase or decrease? Explain. At this $p\ce{H}$, calculate $[\ce{Cu(OH)3- (aq)}]$ in the solution. 

$$\ce{
Cu(OH)2 (s) + OH- (aq) <=> Cu(OH)3- (aq) \qquad $K_a = 10^{-2.9}$
}$$

19. Calculate the $p\ce{H}$ of a buffer system made up of $\pu{0.15 M}$ $\ce{NH3}$ and $\pu{0.35 M}$ $\ce{NH4Cl}$. $pK_a= 9.26$ for $\ce{NH4+}/\ce{NH3}$.

20. What is the $p\ce{H}$ of the buffer that is made up of  $\pu{0.10 M}$ of $\ce{Na2HPO4}$ and $\pu{0.15 M}$ of  $\ce{KH2PO4}$? $pK_a$'s for the dissociation of the weak acid, $\ce{H3PO4}$ are $2.15$, $7.20$, and $12.35$.

21. If $\pu{0.10 M}$ $\ce{NaOH}$ is added to a buffer solution containing $\pu{1 M}$ each of $\ce{CH3COOH}$ and $\ce{CH3COONa}$, determine the final solution $p\ce{H}$.

22. The $p\ce{H}$ of a bicarbonate-carbonic acid buffer is $8.0$. Calculate the ratio of the concentration of carbonic acid ($\ce{H2CO3}$) to that of the bicarbonate ion ($\ce{HCO3-}$).

23. In a natural water sample that is in equilibrium with atmospheric $\ce{CO2}$ and an initial $p\ce{H}$ of $6.35$, determine the change in $p\ce{H}$ upon the addition of a strong acid at the following concentrations: (Note: The activity of $\ce{CO3^2-}$ is negligible.)
	1. $\pu{e-3 mol}$
	2. $\pu{e-4 mol}$
	3. $\pu{e-5 mol}$

24. A water sample from the Rio Grande River in Texas has $[\ce{Ca^2+}] = \pu{109 mg L-1}$ and $[\ce{SO4^2-}] = \pu{238 mg L-1}$ in addition to other ions. Is this water under-, over-, or saturated with respect to gypsum ($K_{s0} = 10^{-4.6}$)?