pH Calculations - Acids

The hydronium ion concentration, [H₃O⁺], can be used to determine the pH of a solution:

pH = ^- log [H₃O⁺]

For example:

The pH of a solution with a hydronium ion concentration of 8.2 × 10^-5 mol L^-1 will be 4.09 (acidic)

The pH of a solution with a hydronium ion concentration of 5.9 × 10^-9 mol L^-1 will be 8.23 (basic/alkaline)

pH of a Strong Acid

Recall that our strong acids are:

• HCl
• HNO₃
• H₂SO₄

The pH of the first two is simply the concentration of the acid, because they fully dissociate to form one hydronium ion per acid molecule:

HCl + H₂O → H₃O⁺ + Cl^-

Therefore, if we had 0.150 mol L^-1 of HCl, the pH will be 0.82 (yes, they can be lower than 1.0)

Sulfuric acid is diprotic, donating two hydrogen ions when it dissociates:

H₂SO₄ + 2H₂O → 2H₃O⁺ + SO₄^2-

Therefore, if we had 0.150 mol L^-1 of HCl, the pH will be 0.52, not 0.82 (like HCl was).

pH of a Weak Acid/Acidic Salts

Because these partially dissociate, we need to be given the hydronium ion concentration to calculate its pH. This is the process shown at the top of this blog post.

Finding [H₃O⁺] from pH

If we know the pH, we can very easily calculate the hydronium ion concentration:

[H₃O⁺] = 10 ^-pH

For example:

The hydronium ion concentration of a solution with a pH of 4.77 is 1.70 × 10^-5 mol L^-1.

The hydronium ion concentration of a solution with a pH of 8.50 is 3.16 × 10^-9 mol L^-1.