Answer
The pH of that solution is equal to 12.60
Work Step by Step
1. Write the $K_w$ expression for the water equilibrium. Then substitute the value for $[OH^-]$, and solve for $[H_3O^+]$:
$[OH^-] * [H_3O^+] = Kw = 10^{-14}$
$ 4.0 \times 10^{- 2} * [H_3O^+] = 10^{-14}$
$[H_3O^+] = \frac{10^{-14}}{ 4.0 \times 10^{- 2}}$
$[H_3O^+] = 2.5 \times 10^{- 13}M$
2. Calculate the pH Value
$pH = -log[H_3O^+]$
$pH = -log( 2.5 \times 10^{- 13})$
$pH = 12.60206$
3. Determine the right number of significant figures.
The $[H_3O^+]$ had 2 significant figures: $2.5 \times 10^{-13}$.
So, there must be only 2 numbers on the right of the decimal point of the pH.
- Round the number to 2 decimal places:
$pH = 12.60$
