Question

For the reaction $A+B \rightarrow C+D$, doubling the concentration of both the reactants increases the reaction rate by 8 times and doubling the initial concentration of only B simply doubles the reaction rate. The rate law for the reaction is

• A. $r=k[ A ][ B ]^2$
• B. $r=k[ A ][ B ]$
• C. $r=k[ A ]^{1 / 2}[ B ]$
• D. $r=k[ A ]^2[ B ]$

Answer 1

Answer: (D)

For the reaction $A+B \longrightarrow C+D$
Rate of reaction:
$r_1=k[ A ]^x[ B ]^y \ldots \text { (i) } $
$r_2=8 r_1=k[2 A ]^x[2 B ]^y \ldots \text { (ii) } $
$r_3=2 r_1=k[ A ]^x[2 B ]^y \ldots \text { (iii) }$
Dividing equation (iii) by (i),
$\frac{2 r_1}{r_1}=\frac{k[ A ]^x[2 B ]^y}{k[ A ]^x[ B ]^y}$
$(2)^1=(2)^y$
$y=1$
Dividing equation (ii) by (i),
$\frac{8 r_1}{r_2}=\frac{k[2 A ]^x[2 B ]^y}{k[ A ]^x[ B ]^y}$
$8=(2 x)^x(2)^y$
$8=(2)^x(2)^1 $
$4=(2)^x$
$(2)^2=(2)^x$
$x=2 $
$\therefore r=k[ A ]^2[ B ]$