Answer to Question #138493 in Physical Chemistry for Aashuu

Question

Using the following data, which is the correct rate law of the sample reaction?
A + 5B + 6C → 3D + 3E
Experiment [A] (M) [B] (M) [C] (M)
Initial Rate
(M/s)
1 0.35 0.35 0.35 8x10-4
2 0.70 0.35 0.35 3.2x10-3
3 0.70 0.70 0.35 6.4x10-3
4 0.70 0.35 0.70 3.2x10-3

Answer 1

Ans.

For this given reaction, A + 5B + 6C → 3D + 3E

The rate law may be R = k[A]^a[B]^b[C]^c

R₂ = 3.2 x 10^-3 (M/S)  when [A] = 0.70 M, [B] = 0.35 M, [C] = 0.35 M

R₃ = 6.4 x 10^-3 (M/S) when [A] = 0.70 M, [B] = 0.70 M, [C] = 0.35 M

3.2 x 10^-3  = k[0.70]^a[0.35]^b[0.35]^c       (i)

6.4 x 10^-3  = k[0.70]^a[0.70]^b[0.35]^c   (ii)

Dividing equation ii by equation i

(0.70/0.35)^b = 2 ; b = 1

R₂ = 3.2 x 10^-3 (M/S)  when [A] = 0.70 M, [B] = 0.35 M, [C] = 0.35 M

R₄ = 3.2 x 10^-3 (M/S) when [A] = 0.70 M, [B] = 0.35 M, [C] = 0.70 M

3.2 x 10^-3  = k[0.70]^a[0.35]^b[0.35]^c       (i)

6.4 x 10^-3  = k[0.70]^a[0.35]^b[0.70]^c   (iii)

Dividing equation iii by equation i

(0.70/0.35)^c = 1 ; c = 0

R₁ = 8 x 10^-4 (M/S)  when [A] = 0.35 M, [B] = 0.35 M, [C] = 0.35 M

R₂ = 3.2 x 10^-3 (M/S)  when [A] = 0.70 M, [B] = 0.35 M, [C] = 0.35 M

3.2 x 10^-3  = k[0.70]^a[0.35]^b[0.35]^c       (i)

8 x 10^-4  = k[0.35]^a[0.35]^b[0.35]^c   (iv)

Dividing equation i by equation iv

(0.70/0.35)^a = 4 ; a = 2

So the rate law for this reaction is R = k[A]²[B]¹[C]⁰ (where k is rate constant) (Ans.)