Question

How would you prepare 1600 mL of a pH = 1.50 solution using concentrated (12 M) HCl?

Short answer

To prepare 1600 mL of a pH = 1.50 solution using concentrated (12 M) HCl take 4.2 mL of the given HCl solution and add water till the solution becomes 1600 mL in volume.

Step-by-step solution

Concentration of [H+] ion Calculation

[H⁺] ion concentration in solution with pH= 1.5 can be calculated as,

$$\begin{gathered} {\text{pH = - log[H}}^{\text{+}}\text{]} \\ {\text{[H}}^{\text{+}}\text{]=}{\text{10}}^{\text{- pH}}={10}^{-1.5}=0.0316 \end{gathered}$$

Calculation ofVolume of HCl Required

For strong acid like HCl

${\text{[H}}^{\text{+}}\text{]=}[\text{HCl]}\text{= 12M}$

As,

$$\begin{gathered} {\text{M}}_{\text{1}}{\text{V}}_{\text{1}}\text{=}{\text{M}}_{\text{2}}{\text{V}}_{\text{2}} \\ \text{12M}\times {\text{V}}_{\text{1}}\text{= 0.0316}\times \text{1600 mL} \\ {\text{V}}_{\text{1}}\text{=}\frac{\text{0.0316}\times \text{1600 mL}}{12}=4.2\text{mL} \end{gathered}$$

Thus, we need to take 4.2 mL of HCl solution and add water till the solution becomes 1600 mL in volume.