Question

For the reaction:

2A + B → A₂B

the rate = k[A][B]² with k = 2.0 × 10⁻⁶ mol⁻² L² s⁻¹. Calculate the initial rate of the reaction when [A] = 0.1 mol L⁻¹, [B] = 0.2 mol L⁻¹. Calculate the rate of reaction after [A] is reduced to 0.06 mol L⁻¹.

Answer 1

The initial rate of the reaction is

Rate = k [A][B]²

= (2.0 × 10⁻⁶ mol⁻² L² s⁻¹) (0.1 mol L⁻¹) (0.2 mol L⁻¹)²

= 8.0 × 10⁻⁹ mol⁻² L² s⁻¹

When [A] is reduced from 0.1 mol L⁻¹ to 0.06 mol⁻¹, the concentration of A reacted = (0.1 − 0.06) mol L⁻¹ = 0.04 mol L⁻¹

Therefore, concentration of B reacted = 0.02 mol L⁻¹

Then, concentration of B available, [B] = (0.2 − 0.02) mol L⁻¹

= 0.18 mol L⁻¹

After [A] is reduced to 0.06 mol L⁻¹, the rate of the reaction is given by,

Rate = k [A][B]²

= (2.0 × 10⁻⁶ mol⁻² L² s⁻¹) (0.06 mol L⁻¹) (0.18 mol L⁻¹)²

= 3.89 mol L⁻¹ s⁻¹