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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Exp
$[A]$
$[B]$
Rate
$1$
$0.012$
$0.035$
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$2$
$0.024$
$0.070$
$0.80$
$3$
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$4$
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Select the rate law for reaction $A + B \longrightarrow C$
| Exp | $[A]$ | $[B]$ | Rate |
| $1$ | $0.012$ | $0.035$ | $0.10$ |
| $2$ | $0.024$ | $0.070$ | $0.80$ |
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For the reaction between $A$ and $B$ , the initial rate of reaction $(r_0)$ was measured for different initial concentration of $A$ and $B$ as given below Order of the reaction with respect to $A$ and $B$ respectively, is $\sqrt 2 = 1.4 ,\,\sqrt 3 \times 10^{-4}$
$A/mol\,L^{-1}$
$0.2$
$0.2$
$0.4$
$B/mol\,L^{-1}$
$0.3$
$0.1$
$0.05$
$r_0/mol^{-1}s^{-1}$
$5.0\times 10^{-5}$
$5.0\times 10^{-5}$
$1.4\times 10^{-4}$
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| $B/mol\,L^{-1}$ | $0.3$ | $0.1$ | $0.05$ |
| $r_0/mol^{-1}s^{-1}$ | $5.0\times 10^{-5}$ | $5.0\times 10^{-5}$ | $1.4\times 10^{-4}$ |
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