Question

Consider the following reaction. 2 A + B −→ P A table of initial rates with initial concentrations of A and B is given below. [A]o (M) [B]o (M) rate M s 0.2 0.1 1.2 × 10−5 0.4 0.1 2.4 × 10−5 0.4 0.2 9.2 × 10−5 0.1 0.1 6.0 × 10−6 What is the rate expression? (a) r = k[A] [B]2 (b) r = k[A] [B] (c) r = k[A]2 [B] (d) r = k[A]2 [B]2

Answer 1

Let the rate is, r = k[A]^x [B]^y

[A]⁰                       [B]⁰                       r

0.2                        0.1                        1.2*10^-5                    (i)

0.4                        0.1                        2.4*10^-5                    (ii)

0.4                        0.2                        9.2*10^-5               (iii)

0.1                        0.1                        6.0*10^-6                    (iv)

from, (i)

r =1.2*10^-5= k[A]^x [B]^y = k[0.2]^x [0.1]^y........1

from, (ii)

r =2.4*10^-5= k[A]^x [B]^y = k[0.4]^x [0.1]^y............2

deviding 2 by 1 we get,

2^x = 2

so, x = 1

from, (iii)

r =9.2*10^-5= k[A]^x [B]^y = k[0.4]^x [0.2]^y............3

deviding 3 by 2 we get,

2^y = 3.8 = 4 (almost)

so, y = 2

the rate is, r= k[A]^x [B]^y = k[A] [B]²