chemistry
posted by Sarah on .
Methanoic acid HCO2H(aq) also known as formic acid, is partly responsible for the characterisitic itchy rash produced by the leaves of the stinging nettle plant. Calculate the pH of 0.150 mol/L methanoic acid. The Ka for methanoic acid is 1.8 x 10^4.
My Work:
Lets call Methanoic acid HL
HL> H^+ plus L^
Ka = (H+)(L)/(HL) = 1.8 x 10^4
HL > H+ plus L
I 0.150 0 0
C x +x +x
E 0.150x +x +x
Ka = (+x)(+x)/(0.150x) = 1.8 x 10^4
= (x^2) / (0.150x) = 1.8 x 10^4
Im having problems with the next step

You appear to have more trouble solving the math problem than you do the chemistry problem.
Ka = (+x)(+x)/(0.150x) = 1.8 x 10^4
= (x^2) / (0.150x) = 1.8 x 10^4
If we try the simplifying route first, we assume 0.150x  0.15 and the equation becomes
x^2/0.150 = 1.8 x 10^4
Then x^2 = 1.8 x 10^4 x 0.150 = 2.7 x 10^6
x = sqrt (2.7 x 10^6) = 0.0052 and pH = log(0.0052) = 2.28.
Now we check to see if our assumption holds. Is 0.0052 small when compared with 0.150. Yes it is for 0.1580.0052 = 0.144 so the error is only about 3.4% error. USUALLY we can make this assumption if the error is less than 5%. 
Making the assumption keeps us from solving a quadratic. However, we could solve the quadratic and the answer comes out to be 0.051 so you see that's very close to what we got with the simplifying assumption.

In rereading Q&A, I noticed I made a typo here. That should be 0.0051 and not 0.051.

Thank you! I still have to read over it but for now I beleive I got the jist of it