8. (3 points)Phosgene, COCl2 is formed from the reaction of carbon monoxide and

Question

8. (3 points)Phosgene, COCl2 is formed from the reaction of carbon monoxide and chlorine gas. Determine the rate law after an initial buildup period has passed, assuming the following mechanism is correct:

8. (3 points)Phosgene, COCl2 is formed from the reaction of carbon monoxide and chlorine gas. Determine the rate law after an initial buildup period has passed, assuming the following mechanism is correct: Cl 2 Cl (rate constants ki and k CI CO COCI (rate constants k2 and k2 COC C12 COC 2 Cl (rate constant k State any assumptions you make. Your rate law may include rate constants k ki', k2, k2', and k3 and reactant concentration. It should not include any intermediates.

Explanation / Answer

The key to solve such problems is formation of rate expression and the eliminating the intermediates with each step.

For step 1 reaction , the rate law would be R1 = k1[Cl2] - k1'[Cl]2

here k1 is the forward rate constant and k1' is the backward rate constant.

For step 2: R2 = k2[Cl][CO] - k2'[COCl]

here k2is the forward rate constant and k2' is the backward rate constant.

For step 3: R3 = k3[COCl][Cl2]

k3 is the rate constant for step 3 (reaction is irreversible)

Now,

Step 1 contains intermediates, and is not rate determining. Considering Step 1 as fast equilibrium step,

R1 = 0

k1[Cl2] = k1'[Cl]2

Thus, the intermediate [Cl]2 = k1 [Cl2]/k1' = K1[Cl2]

where K1 = k1/k1'

[Cl] = (K1 [Cl2])1/2

Substitute this value of [Cl] into step 2 to eliminate intermediate [Cl]

R2 = k2[Cl][CO] - k2'[COCl]

hence, R2 = k2(K1[Cl2])1/2 [CO]- k2'[COCl]

Since it contains intermediate [COCl], it is not rate determining step. Now, let's look at step 3

R3 = k3[COCl][Cl2]
We need to eliminate [COCl] from here, hence considering R2 as fast equilibrium

R2 = 0

k2(K1[Cl2])1/2 [CO]= k2'[COCl]

[COCl] = k2 [CO](K1[Cl2])1/2 / k2'

[COCl] = K2[CO]((K1[Cl2])1/2 ) where K2 = k2/k2'

Now, substitute this in R3 to get the final rate expression:

R3 = k3[COCl][Cl2]
R3 = k3K2[CO]((K1[Cl2])1/2 ) [Cl2]

R3 = K[CO][Cl2]3/2

where K = k3K2K11/2

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