(A) The rate law for the reaction is given by $V_f = k[A]_0^x$,where $x$ is the order of the reaction with respect to $A$.Taking the logarithm on both

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(A) The rate law for the reaction is given by $V_f = k[A]_0^x$,where $x$ is the order of the reaction with respect to $A$.Taking the logarithm on both sides,we get $\log V_f = \log k + x \log [A]_0$.This is in the form of a straight-line equation $y = mx + c$,where the slope $m = x$.From the graph,we can calculate the slope using two points: $(6, 7)$ and $(12, 11)$.Slope $x = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 - 7}{12 - 6} = \frac{4}{6} = \frac{2}{3}$.Therefore,the order of the reaction with respect to $A$ is $\frac{2}{3}$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

For the reaction $A + B \rightarrow C$,experiments were performed in the presence of a large amount of $B$ to measure the initial reaction rate $(V_f)$ as a function of the initial concentration of $A ([A]_0)$. The data from the experiments are plotted as shown below. The order of the reaction with respect to $A$ is $.....$

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A
$\frac{2}{3}$
B
$3$
C
$1$
D
$\frac{3}{2}$

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$(b)$ Hence or otherwise,show that every positive rational number can be expressed in the form $\frac{a}{10^b(10^c-1)}$ for some natural numbers $a, b, c$.

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