# What is the pH of a solution made by mixing 100.0 mL of 0.10 M HNO_3, 50.0 mL of 0.20 M HCl and 100.0 mL of water? Assume that the volumes are additive.

Apr 23, 2017

$\text{pH} = 1.10$

#### Explanation:

First thing first, calculate the total volume of the resulting solution

${V}_{\text{total" = "100.0 mL + 50.0 mL + 100.0 mL}}$

${V}_{\text{total" = "250.0 mL}}$

Now, you are dealing with two strong acids that ionize completely in aqueous solution. Both nitric acid and hydrochloric acid produce hydronium cations in $1 : 1$ mole ratios, so you know that

$\left[{\text{H"_ 3"O"^(+)]_ ("coming from HNO"_ 3) = ["HNO}}_{3}\right]$

$\left[\text{H"_ 3"O"^(+)]_ ("coming from HCl") = ["HCl}\right]$

As you know, molarity is defined as the number of moles of solute present in ${10}^{3}$ $\text{mL}$ of solution. For the nitric acid solution, you have

${\text{100.0 mL" = (10^3color(white)(.)"mL")/color(blue)(10) => n_( "H"_3"O"^(+)) = "0.10 moles"/color(blue)(10) = "0.010 moles H"_3"O}}^{+}$

For hydrochloric acid, you have

${\text{50.0 mL"= (10^3color(white)(.)"mL")/color(blue)(20) implies n_ ("H"_ 3"O"^(+)) = "0.20 moles"/color(blue)(20) = "0.010 moles H"_3"O}}^{+}$

The total number of moles of hydronium cations delivered by the two acids in the resulting solution will be

n_ ("H"_ 3"O"^(+)) = "0.010 moles + 0.010 moles"

n_ ("H"_ 3"O"^(+)) = "0.020 moles"

The concentration of the hydronium cations in the resulting solution will be

["H"_3"O"^(+)] = "0.020 moles"/(250.0 * 10^(-3)"L") = "0.080 M"

As you know, you have

color(blue)(ul(color(black)("pH" = - log(["H"_3"O"^(+)]))))

This will give you

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{pH} = - \log \left(0.080\right) = 1.10}}}$

The answer is rounded to two decimal places, the number of sig figs you have for the molarities of the two acids.

As a fun fact, a mixture of nitric acid and hydrochloric acid is called aqua regia. Ideally, aqua regia contains nitric acid and hydrochloric acid in a $1 : 3$ mole ratio, not in a $1 : 1$ mole ratio like you have here.