Question

For a reaction A + B → products, the following data were collected. Experiment Number Initial Concentration of A (M) Initial Concentration of B (M) Observed Initial Rate (M/s) 1 3.40 4.16 1.82 ✕ 10−4 2 4.59 4.16 3.32 ✕ 10−4 3 3.40 5.46 1.82 ✕ 10−4 Calculate the rate constant for this reaction.

Answer 1

Rate constant k = 1.57*10⁻⁵ s⁻¹

Step-by-step explanation:

Given reaction:

`A\rightarrow B`

Expt [A] M [B] M Rate [M/s]

1 3.40 4.16 1.82*10^-4

2 4.59 4.16 3.32*10^-4

3. 3.40 5.46 1.82*10^-4

`Rate = k[A]^(x)[B]^(y)`

where k = rate constant

x and y are the orders wrt to A and B

To find x:

Divide rate of expt 2 by expt 1

`(3.32*10^(-4) )/(1.82*10^(-4) ) =([4.59]^(x) [4.16]^(y) )/([3.40]^(x) [4.16]^(y) )\\\\x =2`

To find y:

Divide rate of expt 3 by expt 1

`(1.82*10^(-4) )/(1.82*10^(-4) ) =([3.40]^(x) [5.46]^(y) )/([3.40]^(x) [4.16]^(y) )\\\\y =0`

Therefore: x = 2, y = 0

`Rate = k[A]^(2)[B]^(0)`

To find k

Use rate for expt 1:

`k = (Rate1)/([A]^(2) ) =(1.82*10^(-4)M/s )/([3.40]^(2) ) =1.57*10^(-5) s-1`