# A 100.0-mL sample of 1.00 M HCl is titrated with 1.00 M NaOH. What is the pH of the solution after 100.0 mL of NaOH have been added to the acid?

Jun 30, 2016

$\text{pH} = 7$

#### Explanation:

This titration involves hydrochloric acid, $\text{HCl}$, a strong acid, and sodium hydroxide, $\text{NaOH}$, a strong base, so right from the start you should expect to have a neutral solution at equivalence point.

In other words, when the solution contains enough strong base to neutralize all the acid, its pH should be equal to that of pure water.

Hydrochloric acid will ionize completely in aqueous solution to produce hydronium cations, ${\text{H"_3"O}}^{+}$

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

Similarly, sodium hydroxide will ionize completely in aqueous solution to produce hydroxide anions, ${\text{OH}}^{-}$

${\text{NaOH"_ ((aq)) -> "Na"_ ((aq))^(+) + "OH}}_{\left(a q\right)}^{-}$

When these two solutions are mixed, the hydronium cations and the hydroxide anions will neutralize each other to produce water

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

As you can see, it takes equal numbers of moles of hydronium cations and hydroxide anions to have a complete neutralization.

In your case, you have $\text{100.0 mL}$ of $\text{1.0 M}$ hydrochloric acid solution. You're titrating this with $\text{100.0 mL}$ of $\text{1.0 M}$ sodium hydroxide solution.

Since both solution have the same volume and the same concentration, it follows that they also have the same number of moles of hydronium cations and hydroxide anions.

Therefore, mixing these two solutions will result in a complete neutralization.

As a result, the pH of the solution will be equal to that of water, which at room temperature is $7$.