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For the reaction: 2 A+B \rightarrow A_{2} B is k[A][B]^{2} with k=2.0 \times 10^{-6} \mathrm{~mol}^{-2} L^{2} \mathrm{~s}^{-1}. Calculate the initial rate of the reaction when [\mathrm{A}]=0.1 \mathrm{~mol} \mathrm{~L}^{-1},[\mathrm{~B}]=0.2 \mathrm{~mol} \mathrm{~L}^{-1} . Calculate the rate of reaction after [A] is reduced to 0.06 \mathrm{~mol} \mathrm{~L}^{-1}
Chemistry | Previous Year Question Papers
For the reaction: 2 A+B \rightarrow A_{2} B is k[A][B]^{2} with k=2.0 \times 10^{-6} \mathrm{~mol}^{-2} L^{2} \mathrm{~s}^{-1}. Calculate the initial rate of the reaction when [\mathrm{A}]=0.1 \mathrm{~mol} \mathrm{~L}^{-1},[\mathrm{~B}]=0.2 \mathrm{~mol} \mathrm{~L}^{-1} . Calculate the rate of reaction after [A] is reduced to 0.06 \mathrm{~mol} \mathrm{~L}^{-1}

Solution:
The initial rate of reaction is

    \[\begin{array}{l} \text { Rate }=k[A][B]^{2} \\ =\left(2.0 \times 10^{-6} \mathrm{~mol}^{-2} L^{2} s^{-1}\right)\left(0.1 \mathrm{~mol} L^{-1}\right)\left(0.2 \mathrm{~mol} L^{-1}\right)^{2} \\ =8.0 \times 10^{-9} \mathrm{~mol}^{-2} L^{2} \mathrm{~s}^{-1} \end{array}\]

When [\mathrm{A}] is reduced from 0.1 \mathrm{~mol} L^{-1} to 0.06 \mathrm{~mol} L^{-1}, the concentration of A reacted =
(0.1-0.06) mol L^{-1}=0.04 mol L^{-1}
Therefore, concentration of B reacted =\frac{1}{2} \times 0.04 \mathrm{~mol} L^{-1}=0.02 \mathrm{~mol} L^{-1}
Then, concentration of B available, [B]=(0.2-0.02) \mathrm{mol} L^{-1}=0.18 \mathrm{~mol} L^{-1}
After [A] is reduced to 0.06 \mathrm{~mol} L^{-1}, the rate of the reaction is given by,

    \[\begin{array}{l} \text { Rate }=k[A][B]^{2} \\ =\left(2.0 \times 10^{-6} \mathrm{~mol}^{-2} L^{2} s^{-1}\right)\left(0.06 \text { molL }^{-1}\right)\left(0.18 \mathrm{~mol} L^{-1}\right)^{2} \\ =3.89 \times 10^{-9} \mathrm{~mol} L^{-1} s^{-1} \end{array}\]

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