Question

For the chemical reaction A + 2B $\to$ C, rate of the reaction is increased by 2.82 times when the concentration of A is doubled and increased by 9 times when the concentration of B was tripled. What is the order with respect to B, A, and the total order ?

• A. 3/2, 2; 7/2
• B. 2,3/2; 7/2
• C. 5/2, 2; 9/2
• D. 2, 5/2; 9/2

Answer 1

The correct option is B 2,3/2; 7/2

The rate of the reaction is given by the expression $r=k\left[A{]}^m\right[B{]}^n$
The rate of the reaction is increased by 2.82 times when the concentration of A is doubled
$r^{\prime }=2.82r=k{2}^m\left[A{]}^m\right[B{]}^n$
$2.82r=2^m\left(k\right[A{]}^m\left[B{]}^n\right)=2^{m}r$
$2^m=2.82$
$mlog2=log2.82$
$m=1.5$
Thus, the order w.r.t A is 1.5
The rate of the reaction is increased by 9 times when the concentration of B was tripled.
$r"=9r=k\left[A{]}^m{3}^n\right[B{]}^n=3^n\left(k\right[A{]}^m\left[B{]}^n\right)=3^{n}r$
$3^n=9=m^2$
$m=2$
Thus, the order w.r.t B is 2.
The overall order is $m+n=2+1.5=3.5$