Question

Using the reaction mechanism given below write a rate expression for the reaction shown.

Reaction: COCl2(g) + Cl2(g) → CO(g) + 2 Cl2 (g)

Mechanism: Step 1 Cl2 (g) ↔ 2 Cl (g) fast

Step 2 Cl (g) +COCl2 (g) → COCl (g) + Cl2 (g) slow

Step 3 COCl (g) + Cl (g) ↔ CO (g) + Cl2 (g) fast

rate = ?

Answer 1

For step-1, Cl₂(g)-----> 2Cl(g),

K1 = [Cl]²/[Cl₂]. ...........(I)

For step-2, 2Cl(g) + COCl₂ (g)-----------> COCl(g) + Cl₂(g),

K2 = [COCl][Cl₂] / [COCl₂][Cl]² .....................(II)

For step-3, COCl(g) + Cl(g) ----------> CO (g) + Cl₂ (g) .

K3 = [CO][Cl₂] / [COCl][Cl]. ...........................(III)

For the overall reaction, COCl₂ (g) + Cl₂ (g) -------------> CO(g) + 2Cl₂(g),

K = [CO][Cl₂]² / [Cl₂][COCl₂]

So, K = [CO][Cl₂] / [COCl₂] ................(A)

Let us have eq.(I) x eq.(II) x eq.(III)

K = K1 x K2 x K3

Hence the rate (K) = K1 x K2 x K3.