Question

A 10.0-mL sample of an HCl solution has a pH of 2.000. What volume of water must be added to change the pH to 4.000?

Short answer

A 10.0-mL sample of an HCl solution with pH of 2.000 can be converted to a solution of pH to 4.000 by adding 990 mL of water.

Step-by-step solution

Calculating [H+] Concentration of HCl

pH of the given acid is 2.

${\text{[H}}^{\text{+}}]={10}^{\text{-pH}}={10}^{\text{-2}}$

Calculating Volume of Solution

N₁V₁=N₂V₂

$\begin{array}{l}{\text{N}}_{\text{1}}{\text{V}}_{\text{1}}{\text{=10}}^{\text{-2}}\text{×10\hspace{0.17em}mL=0.1}\\ {\text{N}}_{\text{2}}{\text{V}}_2{\text{=10}}^{\text{-4}}{\text{×V}}_{\text{2}}\\ {\text{10}}^{\text{-4}}{\text{×V}}_{\text{2}}\text{=0.1}\end{array}$

${\text{V}}_{\text{2}}=\frac{0.1}{{10}^{-4}}={10}^3\mathrm{mL}=1L$

Calculation of Volume of Water 

$\text{Water\hspace{0.17em}needs\hspace{0.17em}to\hspace{0.17em}be\hspace{0.17em}added\hspace{0.17em}=}1000-10mL=990mL$