## Q. 18.2

Calculating $[H_3O^+]$ or $[OH^−]$ in Aqueous Solution

Problem A research chemist adds a measured amount of HCl gas to pure water at 25°C and obtains a solution with $[H_3O^+] = 3.0×10^{−4} M$. Calculate $[OH^−]$. Is the solution neutral, acidic, or basic?

## Verified Solution

Plan We use the known value of $K_w$ at 25°C $(1.0×10^{−14})$ and the given $[H_3O^+] (3.0×10^{−4} M)$ to solve for $[OH^−]$. Then we compare $[H_3O^+]$ with $[OH^−]$ to determine whether the solution is acidic, basic, or neutral (see Figure 18.3).
Solution Calculating $[OH^−]$:
$[OH^−] = \frac{K_w }{[H_3O^+]} = \frac{1.0×10^{−14}}{3.0×10^{−4}} = 3.3×10^{−11} M$
Because $[H_3O^+] > [OH^−]$, the solution is acidic.
Check It makes sense that adding an acid to water results in an acidic solution.
Also, since $[H_3O^+]$ is greater than $10^{−7}$ M, $[OH^−]$ must be less than $10^{−7}$ M to give a constant $K_w$.