For the reaction:
2A + B → A2B the rate = k[A][B]2 with k = 2.0 x 10-6 mol-2L2s-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.
The initial rate of the reaction is
Rate = k[A][B]2
= (2.0 × 10-6 mol-2L2s-1) (0.1 mol L-1) (0.2 mol L-1)2
= 8.0 × 10-9 mol-2L2s-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-2L2s-1) (0.06 mol L-1) (0.18 mol L-1)2
= 3.89 mol L-1 s-1