Consider this three-step mechanism for a reaction:
Cl₂ (g) k₁⇌k₂ 2 Cl (g) Fast
Cl (g) + CHCl₃ (g) →k₃ HCl (g) + CCl₃ (g) Slow
Cl (g) + CCl₃ (g) →k₄ CCl₄ (g) Fast
c. What is the predicted rate law?

Question

Consider this three-step mechanism for a reaction:

Cl₂ (g) k₁⇌k₂ 2 Cl (g) Fast

Cl (g) + CHCl₃ (g) →k₃ HCl (g) + CCl₃ (g) Slow

Cl (g) + CCl₃ (g) →k₄ CCl₄ (g) Fast

c. What is the predicted rate law?

Accepted Answer

Welcome back everyone to another video, consider this three step mechanism for a reaction part C. What is the predicted rate law? We given our mechanism, it consists of three steps and we're going to break it down. First of all, we have to recall that the slow step of the mechanism is the ray determining step or R DS. So we're going to use a shorthand notation and state that this is the way determining step and we begin writing the rate law as rate equals. Now, we noticed that the rate constant is K three. So we're going to include K three and multiply it by the concentration of the species we have in our reaction, raised the power of their stom meric efficiency because this is a mechanism. So we have chlorine and trichloromethane CC three. OK. Now, this would be pretty simple. But what we have to notice is that laine is actually an intermediate because in the first step, it is produced and then it is consumed in the second step. And the third step, right, we're producing two moles of chlorine and then consuming two moles of chlorine, which is essentially tells us that it is an intermediate and we cannot have an intermediate in our rate expression. However, CCL three is not an intermediate because we don't have it anywhere else other than in the second step of the mechanism. So our goal is to just express a concentration of chlorine in terms of something which is not an intermediate. And we can use the first step for that purpose because we have an equilibrium, we can say that the rate of the forward reaction which is K one multiplied by the concentration of the atomic fluorine must be equal to the rate of the reverse reaction that is K two multiplied by the concentration of chlorine to the power of two. And from here, we can easily show that the concentration of chlorine is simply K one divided by K two multiplied by the concentration of diatomic chlorine, right. We also have to take square root of that. And mathematically, we can also separate our rate constants as a square root B, square root of K one divided by K two multiplied by the concentration of chlorine, the power of one half, which is the same thing as square root. And now we can plug it in back. So the rate law becomes, first of all, we have K three, then we have square root of K one divided by K two. Then we have the concentration of chlorine, the power of one half. And now we finish it with the concentration of trichloromethane CHCL three. Finally, what we usually do is just combine our weight constants into a single weight constant. So the expression looks better and we can say that the final answer would be weight equals K. So we combine all of them into a single K multiplied by the concentration of chlorine is the power of one half multiplied by the concentration of trichloromethane. That'll be our final answer. We can label it just to make sure we understand where it is and conclude the video. Thank you for watching.

Consider this three-step mechanism for a reaction:
Cl₂ (g) k₁⇌k₂ 2 Cl (g) Fast
Cl (g) + CHCl₃ (g) →k₃ HCl (g) + CCl₃ (g) Slow
Cl (g) + CCl₃ (g) →k₄ CCl₄ (g) Fast
c. What is the predicted rate law?

Verified Solution

Key Concepts

Reaction Mechanism

Rate Law

Elementary Steps

Consider this three-step mechanism for a reaction:Cl2 (g) k1⇌k2 2 Cl (g) FastCl (g) + CHCl3 (g) →k3 HCl (g) + CCl3 (g) SlowCl (g) + CCl3 (g) →k4 CCl4 (g) Fastc. What is the predicted rate law?

Verified Solution

Key Concepts

Reaction Mechanism

Rate Law

Elementary Steps

Consider this three-step mechanism for a reaction:
Cl₂ (g) k₁⇌k₂ 2 Cl (g) Fast
Cl (g) + CHCl₃ (g) →k₃ HCl (g) + CCl₃ (g) Slow
Cl (g) + CCl₃ (g) →k₄ CCl₄ (g) Fast
c. What is the predicted rate law?