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## 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?