Chemistry 112

## Using K_{a}

If an equilibrium constant is known, then the equilibrium concentrations of products and reactants can
be determined. Usually, for weak acids, this means finding the pH of the solution.

This is a standard equilibrium problem, so we follow the typical procedures.

#### Examples

Find the pH of a 0.010 M solution of hypochlorous
acid at 25 ^{o}C.

What is a reasonable answer to expect?

If this were a strong acid, the pH would be –log (0.0__10__) = 2.__00__. If this were pure water, the pH would be 7.00. Thus, our answer must lie between these values.

What is the pH of a 3.8×10^{–5} M solution of acetic acid at 25 ^{o}C. pK_{a} = 4.77

What is a reasonable answer to expect?

If this were a strong acid, the pH would be –log (__3.8__×10^{–5}) = 4.__42__. If this were pure water, the pH would be 7.00. Thus, our answer must lie between these values. Further, since K_{a} is fairly large, the final answer probably is a little closer to 4 than to 7, perhaps ~5.

### When can we make approximations?

We can decide this by comparing K_{a} to the initial concentration:

If then approximation will give less
than 5% error, which is acceptable.

If then approximation is
__not__ acceptable and the calculation must be done using the quadratic formula.