How can the concentration of hydronium ions be calculated for a weak acid?

The concentration of hydronium ions in a solution of a weak acid can be determined using the formula [H₃O⁺] = √(Ka x [HA]). This equation is derived from the equilibrium expression for weak acids, where Ka is the acid dissociation constant and [HA] is the initial concentration of the weak acid.

In the context of weak acids, only a small portion of the acid dissociates into its ions. If we let [H₃O⁺] represent the concentration of hydronium ions produced upon the dissociation of the weak acid HA, the dissociation can be represented as:

HA ⇌ H₃O⁺ + A⁻

Applying the equilibrium constant expression, we have:

Ka = [H₃O⁺][A⁻] / [HA]

In the case of weak acids, because the degree of dissociation is small compared to the initial concentration of the acid, it is reasonable to assume that [HA] at equilibrium is approximately equal to the initial concentration, minus the concentration of dissociated acid. However, when solving for [H₃O⁺], it simplifies to √(Ka x [HA]), allowing us to calculate the hydron