Calculate the pH of the solution that results from the addition of 0.040 moles of HNO3 to a buffer?

Question

made by combining
0.500 L of 0.380 M HC3H5O2 ( Ka = 1.30 x 10-5 )
and 0.500 L of 0.380 M NaC3H5O2

An explanation on how the answer was derived would be greatly appreciated!!

Answer 1

The moles, and molarities, of each of these substances are the same, which is very fortunate.

If you look at [H+] = Ka x [acid]/[base], you will see that, if the acid and base have the same concentrations, they will cancel out. So [H+] = Ka, and pH = pKa.

So take the negative log of Ka, and that's your answer.