I am having a hard time understanding how to calculate pH. my textbook states that that pH =-log[H^+].

Question

I have two questions that asks:

What is the H^+ concentration in an acid with of pH 4.6? Express your answer as a power of 10.

What is the H^+ concentration in a base with a pH of 12.2. Express your answer as a power of 10.

Please help.
I tried log on my calculator and got 0.662757832 and 1.86359831 respectively.
if these are the correct answers for both these problems how do i express these to the power of ten.
If both of these answers are incorrect can someone please help me to understand how to solve these problems.

Thanking you in advance

Answer 1

You asked parts of this yesterday and Bob Pursley answered.
pH = -log(H^+)
or (H^+) = 10^-pH
So pH = 12.2 means (H^+) = 10^-12.2
and pH = 4.6 means (H^+) = 10^-4.6 and I've written them this way because that's the question and we're told to express them this way. By the way, when the pH scale was developed that is the original way it was done. Now, if you want the (H^+) in what I consider more conventional form, then
pH = -log(H^+)
12.2 = -log(H^+)
-12.2 = log(H^+)
antilog -12.2 = antilog log(H^+)
antilog -12.2 = (H^+)
and (H^+) = 6.31E-13
But there is another way to do it and your prof is trying to lead you in that direction. If (H^+) = 10^-pH, then punch in 10 on your calculator, hit the y^x button, and type in -12.2. You will get 6.31E-13 but not how much less trouble it is to get it than I went through the pH = -log(H^+) bit I did above and it gets away from all that antilog stuff.

For pH 4.60, (H^+) = 2.52E-5 following the above steps for 12.2.
Also note here that 10^-4.6 gives 2.52E-5 directly without any of that fuss above. Hope this help.s