Calculate [H3O^+] for each pH value using the formula [H3O^+] = 10^-pH.

For $\text{pH}=5$:

$$[\text{H}_3\text{O}^+] = 10^{-5} \text{ M}$$

For $\text{pH}=8$:

$$[\text{H}_3\text{O}^+] = 10^{-8} \text{ M}$$

Since $10^{-5} > 10^{-8}$, the solution with $\text{pH}=5$ has a higher $[\text{H}_3\text{O}^+]$ concentration.
Answer: The solution with $\text{pH}=5$ has a higher $[\text{H}_3\text{O}^+]$ concentration.

2. Which solution has the higher $\text{OH}^-$ concentration?

For $\text{pH}=5$:

$$\text{pOH} = 14 - 5 = 9$$

For $\text{pH}=8$:

$$\text{pOH} = 14 - 8 = 6$$

For $\text{pOH}=9$:

$$[\text{OH}^-] = 10^{-9} \text{ M}$$

For $\text{pOH}=6$:

$$[\text{OH}^-] = 10^{-6} \text{ M}$$

Since $10^{-6} > 10^{-9}$, the solution with $\text{pH}=8$ has a higher $[\text{OH}^-]$ concentration.
Answer: The solution with $\text{pH}=8$ has a higher $[\text{OH}^-]$ concentration.

3. Give the $\text{pH}$ and $\text{pOH}$ for each solution with the following concentrations:

a) $[\text{H}_3\text{O}^+] = 1.0 \times 10^{-3}$

$$\text{pOH} = 14 - 3.0 = 11.0$$

Answer: $\boxed{\text{pH} = 3.0, \text{pOH} = 11.0}$

b) $[\text{OH}^-] = 1.0 \times 10^{-9} \text{ M}$

$$\text{pH} = 14 - 9.0 = 5.0$$

Answer: $\boxed{\text{pH} = 5.0, \text{pOH} = 9.0}$

4. Give the hydroxide ion concentrations of solutions with the following values of $\text{pH}$:

a) $\text{pH } 13.0$

$$[\text{OH}^-] = 10^{-1.0} \text{ M} = 0.1 \text{ M}$$

Answer: $\boxed{[\text{OH}^-] = 0.1 \text{ M}}$

b) $\text{pH } 3.0$

$$[\text{OH}^-] = 10^{-11.0} \text{ M}$$

Answer: $\boxed{[\text{OH}^-] = 10^{-11.0} \text{ M}}$

c) $\text{pH } 8.0$

$$[\text{OH}^-] = 10^{-6.0} \text{ M}$$

Answer: $\boxed{[\text{OH}^-] = 10^{-6.0} \text{ M}}$

5. Which of the solutions is most acidic? Which is most basic? (Referring to the solutions from part 4: $\text{pH } 13.0$, $\text{pH } 3.0$, $\text{pH } 8.0$)

• Acidity increases as $\text{pH}$ decreases. The lowest $\text{pH}$ among 13.0, 3.0, and 8.0 is 3.0.
• Basicity increases as $\text{pH}$ increases. The highest $\text{pH}$ among 13.0, 3.0, and 8.0 is 13.0. Answer: The solution with $\text{pH}=3.0$ is most acidic. The solution with $\text{pH}=13.0$ is most basic.