Question

Part A

What is the rate law for the following mechanism in terms of the overall rate constant k?

Step1:Step2:A+BB+C⇌→CD(fast)(slow)

Express your answer in terms of k and the necessary concentrations (e.g., k*[A]^3*[D]).

Part B

Consider the reaction

2X2Y+Z2⇌2X2YZ

which has a rate law of

rate= k[X2Y][Z2]

Select a possible mechanism for the reaction.

A Step1:Step2:Step3:Z2→Z+Z           (slow)X2Y+Z→X2YZ   (fast)X2Y+Z→X2YZ   (fast)

B Step1:Step2:X2Y+Z2→X2YZ+Z   (slow)X2Y+Z→X2YZ   (fast)

C Step1:Step2:X2Y+Z2→X2YZ2   (slow)X2YZ2→X2YZ+Z   (fast)

D Step1:Step2:2X2Y⇌X4Y2   (fast)X4Y2+Z2→2X2YZ   (slow)

E Step1:2X2Y+Z2→2X2YZ   (slow)

Answer 1

The question in part A isn't correct; there are two steps given but only one product. Each step should have a production matter how insignificant. I will answer Part B.

The given reaction is

2 X₂Y + Z₂ ------> 2 X₂YZ

The overall rate constant for the reaction is given as

Rate = k*[X₂Y][Z₂]

The overall rate law shows that the reaction is first order in X₂Y. An important consideration while deriving rate laws is that we need to treat each and every step of the mechanism as an elementary reaction; i.e, two molecules collide to form the product(s).

We need to eliminate mechanism (C) since this mechanism produces an unwanted Z.

We shall eliminate mechanisms (D) and (E) because both these mechanisms must be bimolecular in X₂Y and the given reaction in unimolecular in X₂Y, i.e, the order is 1 with respect to X₂Y.

Work out the rate laws for mechanisms (A) and (B).

Mechanism A: This is a 2 step mechanism. Note that steps 2 and 3 are identical and should be treated as one step while deducing the rate law. Let k₁ and k₂ be the rate constants.

Rate of Step 1 = k₁*[Z₂]

Rate of Step 2 = k₂*[X₂Y][Z]

At equilibrium, the rates of production and consumption of Z must be equal; therefore,

k₁*[Z₂] = k₂*[X₂Y][Z]

====> [Z] = k₁/k₂*[Z₂]/[X₂Y] …..(1)

Rate of production of X₂YZ = k₂*[X₂Y][Z] = k₂*[X₂Y]*k₁/k₂*[Z₂]/[X₂Y] = k₁*[Z₂]

The above equation doesn’t comply with the supplied rate law; hence discard.

Mechanism B: Let k₁ and k₂ be the rate constants.

Rate of Step 1 = k₁*[X₂Y][Z₂]

Rate of Step 2 = k₂*[X₂Y][Z]

At equilibrium, the rates of production and consumption of Z must be equal; therefore,

k₁*[X₂Y][Z₂] = k₂*[X₂Y][Z]

====> [Z] = k₁/k₂*[Z₂] ……(2)

Rate of production of X₂YZ = k₁*[X₂Y][Z₂] + k₂[X₂Y][Z] = k₁*[X₂Y][Z₂] + k₂*[X₂Y]*k₁/k₂*[Z₂] = 2k₁*[X₂Y][Z₂] = k*[X₂Y][Z₂] where k = 2k₁.

The above rate law matches the given rate law and hence (B) is the correct answer (ans).