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

Question

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 $[H_3{O}^{+}]$ and $[O{H}^{-}]$.

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: $[H_3{O}^{+}]$ and $[O{H}^{-}]$ are related through the ion product of water ($K_w$): $$K_w=[H_3{O}^{+}][O{H}^{-}]=1.0\times {10}^{-14}$$ From this, if you know $[H_3{O}^{+}]$, you can find $[O{H}^{-}]$ and vice versa.

Now, let's evaluate each option:

a. $[H_3{O}^{+}]=1\times {10}^{-2}$

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

b. $[O{H}^{-}]=1\times {10}^{-2}$

$$[H_3{O}^{+}]=\frac{K_w}{[O{H}^{-}]}=\frac{1.0\times {10}^{-14}}{1.0\times {10}^{-2}}=1.0\times {10}^{-12}$$ $$pH=14-pOH=14-(-\log (1\times {10}^{-2}))=14-2=12$$ This is basic.

c. $[H_3{O}^{+}]=1\times {10}^{-7}$

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

d. $[H_3{O}^{+}]=1\times {10}^{-12}$

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

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

• b. $[O{H}^{-}]=1\times {10}^{-2}$ (pH = 12)
• d. $[H_3{O}^{+}]=1\times {10}^{-12}$ (pH = 12)

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