Find pH of mixture

Question

There is a case in which 0.025 litres of a solution containing 2.0M of HCl is combined with a 0.040 litres of solution containing 0.25M of Mg(OH)2. Using this information, what is the pH of the resulting mixture?

Answer 1

To find the pH, we want to find the final concentration of H⁺ ions, [H⁺], or the concentration of OH^-, [OH^-] that is in excess following the reaction. To do this, we first look at the correctly balanced equation for the reaction:

2HCl + Mg(OH)₂ ==> MgCl₂ + 2H₂O ... balanced equation

Now we find moles HCl and moles Mg(OH)₂ present:

0.025 L x 2.0 mol/L = 0.05 moles HCl

0.04 L x 0.25 mol/L = 0.01 moles Mg(OH)₂

Since it takes 2 moles HCl for each 1 mol Mg(OH)₂, the HCl will be present in excess b/c there is more than twice as much HCl as Mg(OH)₂

Moles HCl used up = 0.01 mol Mg(OH)₂ x 2 mol HCl/mol Mg(OH)₂ = 0.02 moles HCl used up

Moles HCl left over = 0.05 mol - 0.02 mol = 0.03 moles HCl left over.

Now find the final volume: 0.025 L + 0.040 L = 0.065 L

Final [HCl] = 0.03 mol/0.065 L = 0.462 M

pH = -log [H⁺] = -log 0.462

pH = 0.34