Question

Question #bd6c1

Answer 1

I usually don't follow this rule, although I admit I should, but pH and pOH values should take into account the number of sig figs given for the concentration of `H^(+)` and `OH""^(-)`, respectively.

However, there's a little trick to remember. For pH and pOH values, only the digits after the decimal count as being significant.

In your example, you have `[H^(+)] = 8.25 * 10^(-9)`. This number has 3 significant figures, 8, 2, and 5. If you take the negative log you should get

`pH_"sol" = -log([H^(+)]) = -log(8.25 * 10^(-9)) = 8.08355`

You would be tempted to say that, rounded to three sig figs, the answer should be

`pH_"sol" = 8.08` `->` you'd be wrong!

You need to take 3 sig figs after the decimal, so the answer becomes

`pH_"sol" = 8.084` `->` the three sig figs are 0, 8, and 4.

Another example. If you have `[H^(+)] = "0.1 M"`, you'd be tempted to say that the pH is

`pH_"sol" = -log(0.1) = 1` `->` with one sig fig.

But again, you'd be wrong because you actually need to have 1 dig fig after the decimal, like this

`pH_"sol" = -log(0.1) = 1.0` `->` one sig fig, which is 0.

This is just a result of how sig figs are calculated for logs and antilogs. Read more about that here (towards the bottom of the page)

http://web.campbell.edu/faculty/fetterman/Significant%20Figures.htm

and here

http://www.chemteam.info/AcidBase/pH&sig-figs.html