The Chlorination of vinyl chloride, C2H3Cl +Cl2-->C2H3Cl3, is believed to proceed by the following mechanism:
Cl2 --(k1)--> 2Cl*
Cl* + C2H3Cl --k2--> C2H3Cl2*
C2H3Cl2* + Cl2 --k3--> C2H3Cl3 + Cl*
C2H3Cl2* + C2H3Cl2* --k4--> stable species
Derive the rate law expression for the chlorination of vinyl chloride based on this mechanism.
hrtht
k3(K1/K4)^(1/2)*[Cl2]^(3/2)
To derive the rate law expression for the chlorination of vinyl chloride, we need to determine the rate-determining step in the mechanism.
Based on the mechanism provided, the second step is the slowest step or the rate-determining step. Therefore, we can write the rate law expression based on the second step as follows:
Rate = k2 * [Cl*] * [C2H3Cl]
Since the reaction is believed to be elementary, the rate constant (k2) represents the rate at which the second step occurs.
However, we know that the concentration of the Cl* radical is not included in the given equation, so we need to express it in terms of the other species using the first step. From the first step, we can see that Cl* is formed when Cl2 reacts, and the rate of Cl2 consumption is equal to the rate of Cl* formation. Therefore:
Rate(Cl*) = -k1 * [Cl2]
Since every Cl* radical produced in the first step will be consumed in the second step, we can substitute [Cl*] in the rate law expression for the second step with the rate expression for the first step:
Rate = k2 * (-k1 * [Cl2]) * [C2H3Cl]
= -k1 * k2 * [Cl2] * [C2H3Cl]
Hence, the rate law expression for the chlorination of vinyl chloride is:
Rate = -k1 * k2 * [Cl2] * [C2H3Cl]
To derive the rate law expression for the chlorination of vinyl chloride based on the given mechanism, we have to determine the rate-determining step. The rate-determining step is the slowest step in the overall reaction and determines the rate of the entire reaction.
Looking at the mechanism, we can see that the second step, Cl* + C2H3Cl --> C2H3Cl2*, involves the consumption of one molecule of C2H3Cl (vinyl chloride) and one atom of Cl* (a highly reactive chlorine atom).
Assuming this is the rate-determining step, we can write the rate law expression based on the stoichiometry of the reaction:
Rate = k * [C2H3Cl] * [Cl*]
Where:
- Rate is the rate of the reaction
- k is the rate constant
- [C2H3Cl] is the concentration of vinyl chloride
- [Cl*] is the concentration of chlorine atoms
Note that the stoichiometric coefficients in the rate law expression are determined by the balanced equation for the rate-determining step.
Since the rate expression involves the concentration of a reactive intermediate, C2H3Cl2*, we need to express it in terms of the reactants and other intermediates.
From the third step of the mechanism, we see that C2H3Cl2* is consumed by the reaction with Cl2 to produce C2H3Cl3 and Cl*. Therefore, the concentration of C2H3Cl2* can be expressed as:
[C2H3Cl2*] = k3 * [C2H3Cl2] * [Cl2]
Substituting this expression into the rate law expression, we have:
Rate = k * [C2H3Cl] * [Cl*]
= k * [C2H3Cl] * k3 * [C2H3Cl2] * [Cl2]
Simplifying this expression gives:
Rate = ktotal * [C2H3Cl] * [C2H3Cl2] * [Cl2]
Where ktotal = k * k3 is the overall rate constant.
Therefore, the rate law expression for the chlorination of vinyl chloride based on the given mechanism is:
Rate = ktotal * [C2H3Cl] * [C2H3Cl2] * [Cl2]