A weak monobasic acid has a concentration of 0.20\text{ mol dm}^{-3} in aqueous solution. … — JAMB UTME

A weak monobasic acid has a concentration of $0.20\text{ mol dm}^{-3}$ in aqueous solution. At equilibrium, the hydrogen ion concentration, $[H^+]$ , is measured to be $1.0 \times 10^{-3}\text{ mol dm}^{-3}$ . What is the percentage degree of ionization of the acid in this solution?

Answer: 0.5 %

Answer

The percentage degree of ionization of the weak acid is 0.5%.

The percentage degree of ionization measures the fraction of acid molecules that ionize in water, expressed as a percentage. By substituting

[H^+] = 1.0 \times 10^{-3}\text{ mol dm}^{-3}

and initial concentration

C = 0.20\text{ mol dm}^{-3}

into

\text{Percentage ionization} = \left(\frac{[H^+]}{C}\right) \times 100\%

, we obtain

\left(\frac{0.001}{0.20}\right) \times 100\% = 0.5\%

Step-by-Step Solution

Identify the relationship between degree of ionization (\alpha), hydrogen ion concentration (

[H^+]

), and initial acid concentration (

C

\alpha = \frac{[H^+]}{C}

For a weak monobasic acid ionizing according to

HA \rightleftharpoons H^+ + A^-

, the concentration of ionized hydrogen ions equals

\alpha C

Calculate the fractional degree of ionization (\alpha).

\alpha = \frac{1.0 \times 10^{-3}\text{ mol dm}^{-3}}{0.20\text{ mol dm}^{-3}} = 0.005

Dividing the equilibrium hydrogen ion concentration by the initial acid concentration gives the fraction of acid molecules that ionized.

Convert the fractional degree of ionization into a percentage.

\text{Percentage ionization} = 0.005 \times 100\% = 0.5\%

Multiplying the decimal fraction by 100 converts the degree of ionization into percentage form.

Key Concept

Degree of Ionization of Weak Acids

Estimated Time:1m 30s

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