Question

Calculate the equilibrium concentration of H3O in the solution if the initial concentration of C6H5COOH is 0.056 M . Express your answer using two significant figures.

Answer 1

1.9 × 10⁻³ M

Step-by-step explanation:

Step 1: Write the acid ionization of benzoic acid

C₆H₅COOH(aq) + H₂O(l) ⇄ C₆H₅COO⁻(aq) + H₃O⁺(aq)

Step 2: Calculate the acid ionization constant (Ka) of benzoic acid

The pKa of benzoic acid is 4.20

pKa = -log Ka

Ka = antilog -pKa = antilog -4.20 = 6.31 × 10⁻⁵

Step 3: Calculate the equilibrium concentration of the hydronium ion

Considering that the initial concentration of the benzoic acid is Ca = 0.056 M, we can calculate the equilibrium concentration of the hydronium ion using the following expression.

[H₃O⁺] = √(Ca × Ka) = √(0.056 × 6.31 × 10⁻⁵) = 1.9 × 10⁻³ M