The hydrogenation of butane to butane on certain catalysts is believed to procee
ID: 499772 • Letter: T
Question
The hydrogenation of butane to butane on certain catalysts is believed to proceed according to the sequence of elementary reactions: C_4 H_8 + S_1 doubleheadarrow C_4 H_8 middot S_1 H_2 + S_2 doubleheadarrow H_2 middot S_2 H_2 middot S_2 + C_4 H_8 middot S_1 doubleheadarrow C_4 H_10 middot S_1 + S_2 C_4 H_10 middot S_1 doubleheadarrow C_4 H_10 + S_1 In the above mechanism, S1 and S2 are two distinctly different types of sites. Only H_2 adsorbs on S_2; both C_4 H_8 and C_4 H_10 adsorb on S_1 but H_2 does not. Assume that Step 3 is the rate-limiting step. Derive a rate equation for the rate of disappearance of butane. Consider the overall reaction to be reversible.Explanation / Answer
All the reactions are reversible, hence there will be a forward as well as backward rate constants.kn is forward rate constant and kn' is backward rate constant for all the analysis used.
From reaction 1:
R1 = k1[C4H8][S1] - k1'[C4H8S1]
This is not the rate limiting step, hence this occurs fast. Therefore, R1 = 0. Hence,
k1[C4H8][S1] = k1'[C4H8S1]'
[C4H8S1] = k1[C4H8][S1] /k1' = K1[C4H8][S1] ...........[1]
Reaction - 2:
R2 = k2[H2][S2] - k2'[H2S2]
This is not rate limitng step, hence
k2[H2][S2] = k2'[H2S2]
[H2S2] = k2[H2][S2] /k2' = K2[H2][S2] ............[2]
From reaction 4:
R4 = k4[C4H10S1] - k4'[C4H10][S1]
This is not rate limitng, hence
k4[C4H10S1] = k4'[C4H10][S1]
[C4H10S1] = k4'[C4H10][S1] /k4 = K4[C4H10][S1] ............[3]
Reaction-3:
R3 = k3[H2S2][C4H8S1] - k3'[C4H10S1] [S2]
from [1], [2], [3] substitute in reaction [3]
R3 = k3K2[H2][S2] *K1[C4H8][S1] - k3'K4[C4H10][S1] [S2]
Hence, the rate expression will be:
R3 = R = k3K2K1[H2][C4H8][S1][S2] - k3'K4[C4H10][S1] [S2]
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