Question

Using the given data, determine the rate constant of this reaction. _[A]_______[B]________Rate 1) 0.260____0.270______0.0194 2) 0.260____0.540______0.0194 3) 0.520____0.270______0.0776

Answer 1

Let the rate constant be k and the rate law be [A]^x[B]^y

from the first data,

0.0194 = k[0.260]^x[0.270]^y ...(1)

from the second,

0.0194 = k[0.260]^x[0.540]^y ...(2)

from the third,

0.0776 = k[0.520]^x[0.270]^y ...(3)

Dividing eq1 from eq 2 we get,

0.0194/0.0194 = k[0.260]^x[0.540]^y / k[0.260]^x[0.270]^y

1 = [0.540/0.270]^y

1 = [2]^y

[2]⁰ = [2]^y

so, y = 0

Dividing eq 1 from eq 3, we get

0.0776/0.0194 = [0.520/0.260]^x

4 = [2]^x

[2]² = [2]^x

x = 2

so rate law is-

Rate = k[A]²

thus,

k = rate / [A]²

keeping the values from data given

k = 0.0194/0.260² = 0.287

k = 0.0776/0.520² = 0.287

thus, rate constant = 0.287M^-1sec^-1