The reaction of bromine with methane is represented by the following chemical equation: Br2 + CH4 -> — Physical Chemistry Chemistry Question
Br2 + CH4 reaction mechanism
The reaction of bromine with methane is represented by the following chemical equation:
Br2 + CH4 → CH3Br + HBr
The proposed mechanism for this reaction is as follows:
Br2 + M -(k1)-> 2 Br + M (1) initiation
Br + CH4 -(k2)-> CH3 + HBr (2) propagation
Br2 + CH3 -(k3)-> CH3Br + Br (3) propagation
HBr + CH3 -(k4)-> CH4 + Br (4) propagation
2 Br + M -(k5)-> Br2 (5) termination
M stands for some molecular species. k3 and k4 are of the same order of magnitude.
In the proposed mechanism of this reaction some very unstable species are involved, such as the radicals CH3 and Br. These very active species react as soon as they are formed, so their concentrations are very small compared to the other species. Shortly after the beginning of the reaction their concentrations remain approximately constant, so: d[CH3]/dt = 0 and d[Br]/dt = 0. This is called the “steady state” condition or approximation for the CH3 and Br radicals.
Find the expression for the rate of formation of CH3Br as a function of the concentration of the stable species that are involved in the reaction and the reaction rate constants, k1, k2, k3, k4, and k5.
The rate law you found may be simplified when we consider the reaction progress. The three expressions below refer to the form of the rate law at the start, the steady state condition of the CH3 and Br radicals and near the end of the reaction:
(I) v = ( k2 * (k1/k5)^(1/2) * [Br2]^(1/2) * [CH4] ) / ( 1 + k4[HBr] / k3[Br2] )
(II) v' = k2 * (k1/k5)^(1/2) * [Br2]^(1/2) * [CH4]
(III) v'' = ( k2 * k3 * (k1/k5)^(1/2) * [Br2]^(3/2) * [CH4] ) / ( k4 * [HBr] )
Model Answer
The rate of formation of CH3Br is given by the equation:
d[CH3Br]/dt = v = k3[CH3][Br2] (1)
The “steady state approximation” for CH3 and Br are given by the equation:
d[CH3]/dt = k2[Br][CH4] - k3[CH3][Br2] - k4[CH3][HBr] = 0 (2)
d[Br]/dt = 2 k1[Br2][M] - k2[Br][CH4] + k3[CH3][Br2] + k4[CH3][HBr] - 2 k5[Br]^2[M] = 0 (3)
From equation (2):
[CH3]_st = k2[Br][CH4] / (k3[Br2] + k4[HBr]) (4)
From equations (2) and (3):
2 k1[Br2][M] - 2 k5[Br]^2[M] = 0
[Br]_st = (k1/k5)^(1/2) * [Br2]^(1/2) (5)
By combining equations (1), (4) and (5) the expression for the rate of the formation of CH3Br as a function of the concentrations of the stable species that are involved in the reaction is given by equation (6):
v = ( k2 * (k1/k5)^(1/2) * [Br2]^(1/2) * [CH4] ) / ( 1 + k4[HBr] / k3[Br2] ) (6)
Enter a numeral (I, II, III) next to each stage of the reaction to indicate which expression corresponds to which stage.
Start of the reaction _______
Steady state condition _______
Near the end of the reaction _______
Model Answer
Start of the reaction: II
Steady state condition: I
Near to the end of the reaction: III
State the assumptions you need to make at each stage in order to simplify the rate law.
Model Answer
Start of the reaction: [Br2] >> [HBr] and, since k3 ~ k4:
k3[Br2] >> k4[HBr], so k4[HBr] / k3[Br2] << 1
Steady state condition: ---
Near to the end of the reaction: [Br2] << [HBr] and, since k3 ~ k4:
k3[Br2] << k4[HBr], so k4[HBr] / k3[Br2] >> 1