organic chemistry

Question

Hg + H2 → 2H + Hg k1

H + C2H4 → C2H5 k2

C2H5 + H2 → C2H6 + H k3

H + H → H2 k4

Assuming that the intermediates H and C2H5 attain a steady state, determine the rate of formation of the product C2H6

Answer 1

If you add all these up, you get H₂ + C₂H₄ → C₂H₆ We are told that C₂H₅ and H intermediates are in equilibrium, which means their forward and backward rates are equal.

First, rate of C₂H₆ production (from (3)) r = k₃[C₂H₅][H₂] (i)

Second, equil of C₂H₅: k₂[H][C₂H₄] = k₃[C₂H₅][H₂] = r from eqn (i) (removed C₂H₅) (ii)

Third equil of H: 2k₁[H₂] + k₃[C₂H₅][H₂] = k₂[H][C₂H₄] + 2k₄[H]² Middle two expressions cancel from (ii)

so k₁[H₂] = k₄[H]² (iii)

Using (iii), substitute for [H] in (ii) and you get the full rate equation in terms of the two reactants, C₂H₄ and H₂