Question

A solution with a pH of 10 is 100 times more basic than a solution with pH 8. Why?

Answer 1

Because the `pH` scale is logarithmic.

Explanation:

`pH=-log_10[H_3O^+]` by definition.

And thus, if `pH=10`, `[H_3O^+]=10^(-10)*mol*L^-1`, (i.e. `pH=-log_10(10^(-10))=-(-10)=10`

And if `pH=8`, `[H_3O^+]=10^(-8)*mol*L^-1`, which is one hundred times more concentrated than the first instance, as required. In other words, if the `DeltapH=2`, there is a `10^2`, i.e. one hundredfold difference in `[H_3O^+]`.

Do not be intimidated by the `log` function. When we write `log_ab=c`, we ask to what power we raise the base `a` to get `c`. Here, `a^c=b`. And thus `log_(10)10=1,`, `log_(10)100=2,` `log_(10)10^(-1)=-1`. And `log_(10)1=0`.

I acknowledge that I have hit you with a lot of facts. But back in the day A level students routinely used log tables before the advent of electronic calculators. If you can get your head round the logarithmic function you will get it.