Weak Acid Solutions

A weak acid, like hydrocyanic acid, is a Brønsted acid as it donates a proton to the water molecule and produces the hydronium ion. A weak acid dissociates partially in water according to its acid dissociation constant, K_a, which is 4.9 × 10⁻¹⁰ for hydrocyanic acid.

For hydrocyanic acid, the K_a is equal to the concentration of hydronium times the concentration of cyanide ions divided by the concentration of hydrocyanic acid.

The acid dissociation constant, K_a, can be used to determine the hydronium ion concentration in a weak acid solution and consequently, the pH of the solution.

The concentration of hydronium ions and the pH of a 0.15 molar solution of hydrocyanic acid can be calculated using its equilibrium expression and an ICE table.

The concentrations of hydrocyanic acid, hydronium, and cyanide initially and at equilibrium can be expressed in a table that shows the Initial, Change, and Equilibrium concentrations of each of the molecules.

To reach equilibrium, the initial concentration of the reactants decreases as the initial concentration of the products increases according to their molar ratios. This change in the concentration of the reactants and products is denoted by x.

Substituting equilibrium concentrations in the expression for the K_a yields x times x divided by 0.15 minus x.

In many weak acids, x, the amount of dissociation, is likely to be very small compared to the initial concentration of 0.15 molar. 0.15 minus x can be assumed to be approximately 0.15.

When the equation is solved, x equals 8.6 × 10⁻⁶ molar.

The approximation, 0.15 minus x equal to 0.15, is valid only if x is less than 5% of 0.15 molar. Here, x is 0.0057% of 0.15 molar and hence this approximation is valid.

Therefore, the concentration of hydronium is 8.6 × 10⁻⁶ molar. To determine the pH, take the negative log of the hydronium ion concentration. Solving this shows the pH of the 0.15 M hydrocyanic acid solution is 5.07.

The pH of a solution can be used to determine the K_a of a weak acid.

For example, acetic acid dissociates partially into hydronium ions and acetate ions when dissolved in water. The K_a for acetic acid can be expressed as the hydronium ion concentration times the acetate ion concentration divided by the concentration of acetic acid.

If the pH of a 0.20 molar acetic acid solution is 2.72, its hydronium concentration can be calculated, which is 1.9 × 10⁻³ molar.

The ICE table can be constructed from the initial and equilibrium concentrations of the acetic acid, hydronium ions, and acetate ions.

Using significant figures, 0.20 minus 1.9 × 10⁻³ is essentially equal to 0.20. By substituting the equilibrium values into the K_a expression, K_a equals 1.8 × 10⁻⁵.