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 \([OH^-]\).
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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.
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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.