Question

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