Chapter 18

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.