What is the pH of this new solution?

[TT0]

Homework Statement

Equal volumes of two solutions of hydrochloric acid are mixed. One solution has a pH 1 while the other pH 5. The pH of the solution obtained is?

A) Less than 1

B) Between 1 and 2

C) 3

D) Between 4 and 5

E) More than 5

Homework Equations

-log[H+] = pH
10^-pH = [H+]

The Attempt at a Solution

let v = volume of solution 1 added

number of mol of H+ in solution with pH 1:
10^-1 * v

number of mol of H+ in solution with pH 5:
10^-5 * v

molarity of H+ in new solution
$$\frac {10^{-1} * v + 10^{-5} *v} {2v}$$

therefore $$pH = -log(\frac {10^{-1} + 10^{-5}}{2})$$

Hence pH = 1.300

Answer is B.

Is this correct?

 

[MexChemE]

Yes, nicely done.

 

[TT0]

Sweet, cheers!