Question

which of the following could represent the pH of a strong base?

a. [H3O+]=1x10-2
b. [OH-]=1x10-2
c. [H3O+]=1x10-7
d. [H3O+]=1x10-12

Answer 1

To determine which of the options could represent the pH of a strong base, we should first recall what pH and pOH represent and the relationship between \([H_3O^+]\) and \([OH^-]\).

1. **pH Scale**: Ranges from 0 to 14. A pH less than 7 indicates an acid, a pH of 7 indicates neutrality, and a pH greater than 7 indicates a base.

2. **Relationship**: \([H_3O^+]\) and \([OH^-]\) are related through the ion product of water (\(K_w\)):
\[
K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}
\]
From this, if you know \([H_3O^+]\), you can find \([OH^-]\) and vice versa.

Now, let's evaluate each option:

a. \([H_3O^+]=1 \times 10^{-2}\)

\[
pH = -\log(1 \times 10^{-2}) = 2
\]
This is strongly acidic.

b. \([OH^-]=1 \times 10^{-2}\)

\[
[H_3O^+] = \frac{K_w}{[OH^-]} = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-2}} = 1.0 \times 10^{-12}
\]
\[
pH = 14 - pOH = 14 - (-\log(1 \times 10^{-2})) = 14 - 2 = 12
\]
This is basic.

c. \([H_3O^+]=1 \times 10^{-7}\)

\[
pH = -\log(1 \times 10^{-7}) = 7
\]
This is neutral.

d. \([H_3O^+]=1 \times 10^{-12}\)

\[
pH = -\log(1 \times 10^{-12}) = 12
\]
This is also basic.

Thus, the options that could represent the pH of a strong base are:

- **b. \([OH^-]=1 \times 10^{-2}\) (pH = 12)**
- **d. \([H_3O^+]=1 \times 10^{-12}\) (pH = 12)**

Both **b** and **d** represent the pH of a strong base.