The reaction between $A$ and $B$ is first order with respect to $A$ and zero order with respect to $B$. Fill in the blanks in the following table:
Experiment
$[ A ] / mol\, ^{-1}$
$[ B ] / mol\, ^{-1}$
Initial rate $/$ $mol$ $L^{-1}$ $min$ $^{-1}$
$I$
$0.1$
$0.1$
$2.0 \times 10^{-2}$
$II$
-
$0.2$
$4.0 \times 10^{-2}$
$III$
$0.4$
$0.4$
-
$IV$
-
$0.2$
$2.0 \times 10^{-2}$
The reaction between $A$ and $B$ is first order with respect to $A$ and zero order with respect to $B$. Fill in the blanks in the following table:
| Experiment | $[ A ] / mol\, ^{-1}$ | $[ B ] / mol\, ^{-1}$ | Initial rate $/$ $mol$ $L^{-1}$ $min$ $^{-1}$ |
| $I$ | $0.1$ | $0.1$ | $2.0 \times 10^{-2}$ |
| $II$ | - | $0.2$ | $4.0 \times 10^{-2}$ |
| $III$ | $0.4$ | $0.4$ | - |
| $IV$ | - | $0.2$ | $2.0 \times 10^{-2}$ |
The given reaction is of the first order with respect to $A$ and of zero order with respect to $B$.
Therefore, the rate of the reaction is given by,
Rate $=k[ A ]^{1}[ B ]^{0}$
$\Rightarrow$ Rate $=k[ A ]$
From experiment $I$, we obtain
$2.0 \times 10^{-2} \,mol\, L ^{-1} \,min ^{-1}= k \left(0.1 \,mol\, L ^{-1}\right)$
$\Rightarrow k=0.2 \,min ^{-1}$
From experiment $II$, we obtain
$4.0 \times 10^{-2}\, mol\, L ^{-1}\, min ^{-1}=0.2\, min ^{-1}[ A ]$
$\Rightarrow[A]=0.2 \,mol \,L ^{-1}$
From experiment $III$, we obtain Rate
$=0.2 \,min ^{-1} \times 0.4 \,mol\, L ^{-1}$
$=0.08 \,mol \,L ^{-1} \,min ^{-1}$
From experiment $IV$, we obtain
$2.0 \times 10^{-2}\, mol\, L ^{-1} \,min ^{-1}=0.2 \,min ^{-1}[ A ]$
$\Rightarrow[A]=0.1 \,mol \,L ^{-1}$
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