The following results were obtained during kinetic studies of the reaction. 2 A + B → product…

The following results were obtained during kinetic studies of the reaction.

2A+B product
 
Experiment A in mol L-1 B  in mol L-1 Initial rate of reaction in mol L-1 min -1
I 0.10 0.20 6.93×10-3
II 0.10 0.25 6.93×10-3
III 0.20 0.30 1.386×10-2

The time (in minutes) required to consume half of A is
  1. 100
  2. 10
  3. 5
  4. 1

Solution

Let's assume x and y are the order of the reaction with respect to A and B, respectively.

From equation 1 and 2,

0.10.1x0.20.25y=6.93×10-36.93×10-3y=0

From equation 1 and 3 and put the value y=0,

0.10.2x0.20.30=6.93×10-31.386×10-2    y=0

12x=12x=1

The rate law will be R=K[A]1[B]0

Hence, the reaction is of the first order.

K=RA=6.93×10-30.1=6.93×10-2

Here t12 for the first-order reaction is given by, t12=0.693K=0.693(6.93×10-2)=10

Asked in: JEE Main 2019 (09 Jan Shift 1)

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