Question

How many moles of HCl(g) must be added to 1.0 L of 2.0 M NaOH to achieve a pH of 0.00? (Neglect any volume changes.)

Short answer

Moles of HCl is 4 mol/L.

Step-by-step solution

[H+] Calculation  

As the pH of the resulting solution is said to be zero, so [H⁺] concentration

$\begin{array}{l}{\text{[H}}^{\text{+}}{\text{]=10}}^{\text{-pH}}\\ {\text{[H}}^{\text{+}}{\text{]=10}}^{\text{-0}}\\ {\text{[H}}^{\text{+}}\text{]=1}\end{array}$

Calculating Concentration

$\begin{array}{l}\text{ForAcid-BaseMixture:}\\ {\text{N}}_{\text{1}}{\text{-N}}_{\text{2}}={\text{N}}_{\text{3}}{\text{V}}_{\text{3}}\\ {\text{N}}_{\text{1}}\text{-2}=\text{2}\\ {\text{N}}_{\text{1}}\text{=2+2=4}\end{array}$

So moles of HCl is 4 mol/L.