3. Consider the following proposed mechanism for the reaction A P ki. k.I k4 k3.

Question

3. Consider the following proposed mechanism for the reaction A P ki. k.I k4 k3.k. kr. k. a) Write a differential equation for the rate of formation ofB. b) The formation of B from A and C is fast to equilibrium with equilibrium constants Ki kl/k.1, K2 k2/k-2, and K3 k3/k.3. Also, k4 is smaller that the other k's. Write a differential equation for the formation of P in terms of concentration of A, equilibrium constants, and k4. c) Write an expression, containing no derivatives, for the concentration of P as a function of time. At zero time, [A A0] and [B], [C], [P] 0

Explanation / Answer

a) rate of formation of B = d[B]/dt = rate of apperance of B - rate of disapperance of B

or, rate of formation of B = {k1[A] - k-1[B]} + {-k4[B]} + {k-2[C] - k2[C]}

or, rate of formation of B = = {k1[A] + k-2[C]} - {k-1[B] + k4[B] - k2[C]}

b) Rate of formation of P = d[P]/dt = k4[B] ................(1)

Now, K1 = k1/k-1 = [B]/[A]

or, [B] = K1[A]..............(2)

Also, K2 = k2/k-2 = [C]/[B]

or, [B] = K2/[C]....................(3)

Also, K3 = k3/k-3 = [C]/[A]

or, [C] = K3[A]........(4)

From (3) & (4) we get

[B] = K2/{K3[A]}.............(5)

Comparing (2) & (5) we get

K2/{K3[A]} = K1[A]

or, [A]2 = K2/{K1*K3}

or, [A] = sqrt[K2/{K1*K3}].............(6)

Now, rate of formation of P = d[P]/dt = k4[B] = k4*{K2/{K3[A]}} = k4*{K1[A]

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