Question

The results given in the below table were obtained during kinetic studies of the following reaction:

$2A + B \longrightarrow C+D$ [JEE (Main) 2020]

Experiment	$[A]/molL^{-1}$	$[B]/molL^{-1}$	Initial rate/$molL^{-1}$ $min^{-1}$
I	0.1	0.1	$6.00 \times 10^{-3}$
II	0.1	0.2	$2.40 \times 10^{-2}$
III	0.2	0.1	$1.20 \times 10^{-2}$
IV	X	0.2	$7.20 \times 10^{-2}$
V	0.3	Y	$2.88 \times 10^{-1}$

Answer 1

X=0.30, Y=0.40

Answer 2

The problem involves determining the rate law and then using it to find unknown concentrations.

1. Determine reaction orders: By comparing experiments where one reactant's concentration is kept constant while the other varies, the order of reaction with respect to each reactant is found.

   • Comparing Exp I and II (constant [A]), doubling [B] quadruples the rate, indicating second order with respect to B ($b=2$).
   • Comparing Exp I and III (constant [B]), doubling [A] doubles the rate, indicating first order with respect to A ($a=1$).

2. Write rate law: Combine the orders to get the overall rate law: Rate $= k[A][B]^2$.

3. Calculate rate constant (k): Substitute data from any experiment (e.g., Exp I) into the rate law to find the value of $k$.

4. Calculate X and Y: Use the determined rate law and the calculated $k$ value, along with the data from Experiments IV and V, to solve for the unknown concentrations X and Y.