A) \[2\]
B) \[1\]
C) \[1\frac{1}{2}\]
D) \[1\frac{1}{3}\]
Correct Answer: C
Solution :
Suppose, the rate of reaction depends upon x power of concentration of A and y power of concentration of B. Hence, \[{{r}_{1}}=k.{{[A]}^{x}}\] \[{{r}_{2}}=k{{[2A]}^{x}}\] \[\therefore \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{{{[A]}^{x}}}{{{[2A]}^{x}}}=\frac{1}{2}\] \[\therefore \] \[x=1\] Similarly \[{{r}_{1}}=k{{[B]}^{y}}\] \[{{r}_{2}}=k{{[9B]}^{y}}\] \[\therefore \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{{{[B]}^{y}}}{{{[9B]}^{y}}}=\frac{1}{3}\] \[\therefore \] \[{{\left( \frac{1}{3} \right)}^{2y}}=\frac{1}{3}\] or \[y=\frac{1}{2}\] Hence, correct rate-law for the reaction \[=k[A]{{[B]}^{1/2}}\] Hence, order of reaction \[=1+\frac{1}{2}=1\frac{1}{2}\]
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