For the reaction:
$2 A + B \rightarrow A _{2} B $
the rate $=k[ A ][ B ]^{2}$ with $k =2.0 \times 10^{-6} \,mol ^{-2}\, L ^{2} \,s ^{-1}$. 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 $0.06 \,mol\, L ^{-1}$
For the reaction:
$2 A + B \rightarrow A _{2} B $
the rate $=k[ A ][ B ]^{2}$ with $k =2.0 \times 10^{-6} \,mol ^{-2}\, L ^{2} \,s ^{-1}$. 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 $0.06 \,mol\, L ^{-1}$
The initial rate of the reaction is
Rate $=k[ A ][ B ]^{2}$
$=\left(2.0 \times 10^{-6}\, mol ^{-2} \,L ^{2}\, s ^{-1}\right)\left(0.1\, mol\, L ^{-1}\right)\left(0.2 \,mol\, L ^{-1}\right)^{2}$
$=8.0 \times 10^{-9}\, mol ^{-2}\, L ^{2}\, s ^{-1}$
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 $=\frac{1}{2} \times 0.04 \,mol\, L ^{-1}=0.02 \,mol\, L ^{-1}$
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 $=k[ A ][ B ]^{2}$
$=\left(2.0 \times 10^{-6}\, mol ^{-2}\, L ^{2} \,s ^{-1}\right)\left(0.06 \,mol \,L ^{-1}\right)\left(0.18 \,mol\, L ^{-1}\right)^{2}$
$=3.89 \,mol\, L ^{-1}\, s ^{-1}$
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