# How to calculate the pH value of 0.0001 M "HCl" ?

Sep 5, 2016

$\text{pH} = 4.0$

#### Explanation:

Hydrochloric acid, $\text{HCl}$, is a strong acid, which means that it dissociates completely in aqueous solution to produce hydronium cations, ${\text{H"_3"O}}^{+}$, and chloride anions, ${\text{Cl}}^{-}$.

In order to calculate the pH of this solution, you need to know the concentration of hydronium cations.

The dissociation of the acid will produce

${\text{HCl"_ ((aq)) + "H"_ 2 "O" _ ((l)) -> "H"_ 3"O"_ ((aq)) + "Cl}}_{\left(a q\right)}^{-}$

Here every mole of hydrochloric acid added to the solution will produce one mole of hydronium cations. In your case, you have

["HCl"] = "0.0001 M" = 10^(-4)"M"

This means that the concentration of hydronium cations is

["H"_3"O"^(+)] = 10^(-4)"M"

Plug this into the equation for pH

color(purple)(bar(ul(|color(white)(a/a)color(black)("pH" = - log(["H"_3"O"^(+)]))color(white)(a/a)|)))

to find the pH of the solution

$\text{pH} = - \log \left({10}^{- 4}\right) = - \left(- 4\right) \cdot \log \left(10\right) = 4.0$

The answer is rounded to one decimal place because you have one significant figure for the concentraiton of the solution.