Question

For the reaction, \[\ce{2A + B + C -> A2B + C}\], the rate law has been determined to be

Rate = k[A][B]².

If the value of k is 2.0 × 10⁻⁶ mol⁻² L² s⁻¹ for the reaction, determine the initial rate of the reaction with [A] = 0.2 mol L⁻¹, [B] = 0.1 mol L⁻¹ and [C] = 0.5 mol L⁻¹.

Answer 1

Given:

k = 2.0 × 10⁻⁶ mol⁻² L s⁻¹

[A] = 0.2 mol L⁻¹

[B] = 0.1 mol L⁻¹

[C] = 0.5 mol L⁻¹ (but not in the rate law, so it's irrelevant here)

Rate = k [A] [B]²

= 2.0 × 10⁻⁶ × (0.2) × (0.1)²

= 2.0 × 10⁻⁶ × 0.2 × 0.01

= 2.0 × 10⁻⁶ × 0.002

= 4.0 × 10⁻⁹ mol L⁻¹ s⁻¹

∴ The initial rate of the reaction is 4.0 × 10⁻⁹ mol L⁻¹ s⁻¹.