What is the pH of the resulting solution?

The equal volume of two HCl solutions of pH=3 and pH=5 were mixed. What is the pH of the resulting solution?

To calculate the pH of the resulting solution from the two solutions whose pH values are known. Firstly, calculate hydrogen ion concentration of both the solutions with the help of pH formula.

We know that, pH = -log[H⁺]

and Concentration = ^Moles/_Volume

Assuming that the volume of each solution is 1 L.

HCl dissociates completely into its constituent ions H⁺ and Cl^–, as it is a strong acid.

Dissociation is done as: HCl (aq) → H⁺ (aq) + Cl^– (aq)

Now,

For pH = 3

3 = -log[H⁺]

⇒ [H⁺] = 10^-3 M

For pH = 5

5 = -log[H⁺]

⇒ [H⁺] = 10^-5 M

Since the volume for each solution is assumed as 1 L.

So, Moles of H⁺ ions (for pH = 3) = Molarity * Volume = 10^-3 M * 1 L = 10^-3 mol = 0.001 mol

and Moles of H⁺ ions (for pH = 5) = Molarity * Volume = 10^-5 M * 1 L = 10^-5 mol = 0.00001 mol

Total moles of H⁺ ions = 0.001 + 0.00001 = 0.00101 mol

After mixing both the solution, total volume = 1 + 1 = 2 L

So, the concentration of H⁺ for the final mixture is-

Concentration = ^Moles/_Volume = 0.00101 mol/2 L = 0.000505 M

So, pH of the resulting solution = -log[H⁺] = -log(0.000505) = 3.296 = 3.30 (upto two decimal places)

Hence, the pH of the resulting solution is 3.30

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