Calculate pH and H₃O⁺ concentration of Weak Acid

Weak acid partially dissociate to its ions in the water. Therefore their acidic strength of weak acid is not strong like strong acids. Weak acid dissociation is a reversible reaction. Le Chatelier's principle and equilibrium formula is applied to calculate concentrations of each components in the solution .

In this tutorial, we will discuss followings.

Weak acid definition

When weak acid is partially dissociated to H₃O⁺ ion and respective anion and formed anion is not stable in the water, that acid is called as a weak acid. That anion has the capability of reacting with a H₂O molecule and obtain a proton from H₂O molecule. Nitrous acid, acetic acid, formic acid are several examples for weak acids and we will teach you how to calculate pH of these weak acidic solutions in series of tutorials.

Dissociation of weak acid

As previously mentioned, weak acid dissociate partially to hydronium ions (H₃O⁺) ion and respective anion. As an example, when acetic acid (CH₃COOH) is partially dissociated in water, acetate ion (CH₃COO^-) and hydronium ion (H₃O⁺) ions.

H₃O⁺ concentration and pH value

H₃O⁺ concentration is very low when it compares with weak acid concentration. As an example, if weak acid concentration is 0.1 mol dm^-3, H₃O⁺ concentration may be 0.0001 mol dm^-3. pH of that solution is 4.

If there are two separate aqueous solutions, one is a weak acid and other one is a strong acid and both of their concentration are same, pH of weak acid is higher than strong acid.

Weak acids examples

• Formic acid (HCOOH)
• Ethanoic acid (CH₃COOH)
• Sulfurous acid (H₂CO₃)
• Carbonic acid (H₂CO₃)
• Nitrous acid (HNO₂)

Examples to calculate H₃O⁺ concentration, pH and weak acid concentration

As an example, concentrations of CH₃COOH and H₃O⁺ are listed below. Then you can understand that H₃O⁺ concentration is very less compared to the CH₃COOH concentration. Later in this tutorial, we do few example problems to calculate H₃O⁺ concentration and pH of several weak acids.

How to calculate H₃O⁺ concentration and pH

How to calculate H₃O⁺ concentration

When weak acid gained the equilibrium, we can apply equilibrium expression.

Equilibrium expression

• K_a = Equilibrium Constant
• [HA_(aq)] = Equilibrium concentration of acid
• [A^-_(aq)] = Equilibrium concentration of anion
• [H₃O⁺_(aq)] = Equilibrium concentration of hydronium ion

How to calculate pH of a weak acid

Substitute calculated H₃O⁺ concentration to the pH equation.

pH = -log₁₀[H₃O⁺_(aq)]

Example

Calculating H₃O⁺ concentration and pH of CH₃COOH acidic solution.

There is a CH₃COOH acid solution in the laboratory. Initial CH₃COOH_(aq) concentration is 1 mol dm^-3. After obtaining the equilibrium, calculate followings and mention all the assumptions you made in the calculations.

• Equilibrium [H₃O⁺_(aq)] concentration
• pH of the solution

K_a of CH₃COOH_(aq) = 1.8 * 10^-5 mol dm^-3

Solution

First look what are the data given for you. Only K_a of CH₃COOH and Initial CH₃COOH_(aq) concentration are given to solve the question.

Chemical reaction between CH₃COOH and water

Write the chemical reaction between CH₃COOH and water. Then construct a table as below and write down the three rows as initial, dissociated / formed, and equilibrium concentrations with mol dm^-3.

We take dissociated concentration as a mol dm^-3. When a amount concentration is dissociated, a amount concentrations of CH₃COO^- and H₃O⁺ are formed.

Then we know the equilibrium concentrations. We neglect water concentration because water concentrations is very larger than other components.

Substitute equilibrium concentrations to equilibrium expression

According to the assumptions we made earlier, we can assume equilibrium CH₃COOH concentration equals to the initial CH₃COOH concentration. Therefore equilibrium CH₃COOH concentration = 1.0 mol dm ^-3.

Calculate pH of CH₃COOH solution

Substitute calculated H₃O⁺ concentration to the pH equation.

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