Exponential Functions

Question

If egg yolks have a pH of 6.4 then what is the pH of egg whites of they are 63 times more alkaline?

Answer 1

There are two ways to solve this. The more math intensive, and the less math intensive way. I'll explain both so that people who attempted the second can also walk through the steps.

The more math intensive way would first convert the pH to a concentration of H+ ions. In water the H+ and OH- ions are always in the balance of {H+]{OH-}=kw. So in a 63 times more alkaline (or basic) solution you would need to divide the H+ concentration by 63. You could also arrive at this number by determining the original OH- concentration and multiplying that by 63. Then taking the new value and determining the H+ concentration. If you cancel terms you'll find it ends up the same.

I prefer a more direct way. There is an equation pH = pKa + log(base/acid). We can adapt this for our use as we have a pKa, and we have the base/acid ratio.

So that makes the equation pH = 6.4 + log (63/1)

log 63 = 1.8 to the correct number of sig figs in the question.

So pH = 6.4 + 1.8

Or pH = 8.2