Kinetics Questions - see picture attached! Thank you in advance Phosgene, CI_2 C

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Kinetics Questions - see picture attached! Thank you in advance

Phosgene, CI_2 CO, is used to produce polycarbonate polymers that are molded to make eye-glass lenses, DVDs, food containers... Industrially, phosgene is produced from CO and Cl_2 gases. CO(g) + Cl_2(g) COCl_2(g) rate = k[CO][Cl_2]^3/2 The reaction is exothermic. A proposed mechanism for the formation of phosgene is: Cl_2 doubleheadarrow 2 Cl (fast, equilibrium constant K_1 = k_1/k_1) Cl + CO doubleheadarrow ClCO (fast, equilibrium constant K_2 = k_2/k_2) ClCO + Cl_2 rightarrow Cl_2 CO+Cl (slow, rate constant for forward reaction k_3) Write down the equilibrium expressions for the two equilibria. Write down the rate expression (rate of formation of Cl_2 CO) for the third step. Use the equilibrium expressions to eliminate the concentrations of intermediates from the rate law. Relate the rate constant k, in the overall rate law, to the rate constant k_3 and the equilibrium constants K_1 and K_2 (or use k_1, k_1, k_2, k_2 if you prefer).

Explanation / Answer

For the given reaction mechanism,

i. Equilibrium expression for,

First step, K1 = [Cl]^2/[Cl2]

Second step, K2 = [ClCO]/[Cl][CO]

ii. Rate expression for third step,

rate = d[Cl2CO]/dt = k3[ClCO][Cl2]

iii. From equations, Cl and ClCO are intermedites

For [Cl],

[Cl] = k1[Cl2]^1/2 ...(1)

For [ClCO],

[ClCO] = k2[Cl][CO] ....(2)

Substitute (1) in (2)

[ClCO] = k1^1/2.K2[Cl2]^1/2.[CO] ---(3)

From rate determining slow step,

rate = k3[ClCO][Cl2]

Substitute (3) in above equation,

rate = k1^1/2.K2.K3.[CO][Cl2]^3/2

with,

K = K1^3/2.K2.K3

rate = K[CO][Cl2]^3/2

Is overall rate law

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