Analytical Chemistry
posted by James .
The question:
The pH of a solution is defined as
pH = log[H3O+].
If the pH of a solution is 3.72(+/ 0.03), what is the [H3O+] and its absolute standard deviation?
Answer: How would I carry this out? I know to find the hydronium concentration wouldn't i just take e^3.72? How do I do it the way they are asking for?

H3O+= e^pH+error
= e^pH * e^+error
=e^3.72 * e^+.03 
pH = log(H3O^+)
3.72(+/0.03) = log(H3O^+)
So the answer is antilog 3.72 (+/ ?) = 0.0001905 +/ ?.
The formula for handling antilogs (10^pH) is (s/y)= 2.303 x (abs std dev) = (s/y) = 2.303 x (0.03)
(s/y) = 0.0691
s = 0.0691 x 0.0001905 = 0.000013
answer is
0.0001905 +/0.000013 which I would round to 0.00019 +/0.00001
Check my work, especially for typos 
I believe (H3O^+) = 10^pH