For the reaction, 2A + B > $A _{ 2 }B$;
: The rate = k [A] [${{B}^{2}}$] with
k= 2.0x ${{10}^{-6}}$${{mol}^{-2}}$ ${{L}^{2}}$ ${{s}^{-1}}$. Calculate the initial rate of reaction when [A] = 0.1mol${{L}^{-1}}$
[B] =0.2 mol ${{L}^{-1}}$. Calculate the rate of reaction after [A] is reduced to 0.06 mol ${{L}^{-1}}$.
(i) Case I Initial rate = k [A] ${{B}^{2}}$
= 2.0 x ${{10}^{-6}}$ ${{mol}^{-2}}$${{L}^{2}}$${{s}^{-1}}$) x (0.1 mol ${{L}^{-1}}$) x (0.2 x mol ${{L}^{-1}}$)
=8.0 x ${{10}^{-9}}$mol ${{L}^{-1}}$${{s}^{-1}}$
(ii) Case II Concentration of A at a particular time = 0.06 mol ${{L}^{-1}}$
Amount of A reacted = (0.1 - 0.06) = 0.04 mol ${{L}^{-1}}$
Amount of B reacted = 1/2 x 0.04 mol ${{L}^{-1}}$ = 0.02 mol ${{L}^{-1}}$
Concentration of B at a particular time = (0.2 - 0.02) mol ${{L}^{-1}}$= 0.18 mol ${{L}^{-1}}$
Rate = k [A] [${{B}^{2}}$] =
(2.0 x ${{10}^{-6}}$ ${{mol}^{-2}}$${{L}^{2}}$${{s}^{-1}}$) x
(0.06 mol ${{L}^{-1}}$) x
(0.18mol${{L}^{-1}}$=
3.89x${{10}^{-9}}$mol${{L}^{-1}}$${{s}^{-1}}$