Question

For the reaction$2A+B\to A_{2}B$ rate $=k\left[A\right][B{]}^2$ with $k=2.0\times {10}^{-6}mo{l}^{-2}{L}^2{s}^{-1}$, what is the rate of the reaction when [A] is reduced to 0.060 molL^{-1} . the initial rate of reaction when $\left[A\right]=0.1mol{L}^{-1}and\left[B\right]=0.2mol{L}^{-1}is8\times {10}^{-9}mol{L}^{-1}{s}^{-1}$

Answer 1

The initial rate of the reactionis

Rate = k [A][B]2

= (2.0 × 10 - 6mol - 2L2s - 1) (0.1 mol L - 1) (0.2 mol L - 1)2

= 8.0 × 10 - 9mol - 2L2s - 1

When [A] is reduced from 0.1 mol L - 1to 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= 1/2 x 0.04 mol L-1 = 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 - 6mol - 2L2s - 1) (0.06 mol L - 1) (0.18 mol L - 1)2

= 3.89 mol L - 1s - 1