Question

The hydronium ion concentration (in mol dm\(^{-3}\)) in \(0.3\ M\) solution of a weak acid is approximately \([K_a=3\times10^{-5}]\):

• A. \(3\times10^{-5}\)
• B. \(3\times10^{-2}\)
• C. \(3\times10^{-3}\)
• D. \(3\times10^{-1}\)

Hint:

For a weak acid, \[ [H_3O^+]\approx\sqrt{K_aC} \] This approximation is valid when the degree of ionization is small. It provides a quick way to calculate the hydronium ion concentration without solving the complete equilibrium equation.

Answer 1

The Correct Option is C

Step 1: Weak acid approximation.
For a weak acid of concentration C, [H₃O⁺] ≈ √(Ka C), with Ka = 3 × 10⁻⁵ and C = 0.3.

Step 2: Plugging in the numbers.
[H₃O⁺] = √[(3 × 10⁻⁵)(0.3)] = √[(3 × 10⁻⁵)(3 × 10⁻¹)] = √(9 × 10⁻⁶).

Step 3: Simplifying.
√(9 × 10⁻⁶) = √9 × √(10⁻⁶) = 3 × 10⁻³.

Step 4: Confirming against options.
The computed [H₃O⁺] = 3 × 10⁻³ mol dm⁻³ matches option (3).

Step 5: Final statement.
Therefore, the hydronium ion concentration is 3 × 10⁻³ mol dm⁻³.