pH of Weak Acid | H3O+ concentration

Weak acid partially dissociate in the water to its ions. Therfore their acidic strength 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 .


Weak acid definition

When anion of acid is not stable in the water, that acid is called as a weak acid. That anion reacts with a H2O molecule and takes a proton.


Dissociation of weak acid

As previously mentioned, weak acid dissociate partially to its H3O+ and related anion.

weak acid dissociation to H3O+ and anion

H3O+ concentration and pH

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. That solution pH is 4.


If there are two solution, one is a weak acid and other one is a strong acid. If both of them 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

Examples of H3O+ concentration, pH and weak acid concentration

CH3COOH concentration and H3O+ are listed below. Then you can understand that H3O+ concentration is very less. Later in this tutorial, we do few examples to calculate H3O+ concentration and pH of weak acid.



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

weak acid dissociation equilibrium expression
  • Ka = Equilibrium Constant
  • [HA(aq)] = Equilibrium concentration of acid
  • [A-(aq)] = Equilibrium concentration of anion
  • [H3O+(aq)] = Equilibrium concentration of hydronium ion

Ka depends on the acid and the temperature. When concentrations are taken in mol dm-3 units, Ka also has the mol dm-3 units.

Ka value is different for CH3COOH acid and HCOOH acid. Also Ka is different for 200C and 300C for HCOOH acid.

When Ka and weak acid concentration are given, H3O+ concentration and pH can be found easily making some assumption. These assumptions are explained in the examples.


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

Ka of CH3COOH(aq) = 1.8 * 10-5 mol dm-3


Solution

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


Assumptions made in the calculations

  • Dissociation of water is negligible when it comparing with weak acid dissociation. Therefore we can assume, H3O+(aq) is given by weak acid dissociation. And also pH of the solution totally depends on the weak acid.
  • After gaining the equilibrium, weak acid concentration is same as the initial weak acid concentration because dissociated amount (concentration) is very small comparing with initial amount (initial concentration).


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.

CH3COOH dissociation and equilibrium concentrations

Substitute equilibrium concentrations to equilibrium expression

equilibrium expression for CH3COOH

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.

assumptions made in weak acid equilibrium expresssion

Calculate pH of CH3COOH solution

Substitute calculated H3O+ concentration to the pH equation.

pH of CH3COOH weak acid

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