I've been stuck on this question for a while now, any help is appreciated

Question

Initial rate data was generated for the following balanced reaction at a temperature of 300 K.

A (g) + 2B (g) → C (g)

Experiment	[A] (M)	[B] (M)	Initial rate (M/s)
1	0.10	0.10	1.6 x 10-3
2	0.20	0.10	3.2 x 10-3
3	0.10	0.20	1.6 x 10-3

(a) Determine the rate law and identify the overall order of the reaction. Support your rate law with an explanation or calculation of the order for each reactant.

(b) Calculate the value of the rate constant, k. Include units on your answer.

(c) Determine if the following mechanism is reasonable for the rate law in part (a). Explain why or why not.

A+ B → X fast

X + Y → D slow

B + D → C + Y very fast

(d) What is the function of substance Y in the reaction? How does it accomplish its purpose?

Answer 1

I would like to add to the previous answer from @Greg S. I agree with his entire solution except for the mechanism part. I'd like to offer an alternative answer. I believe the entire 3-step equation is purported to be the mechanism (not just step a, b, or c). So, I would suggest that the proposed mechanism is reasonable for the determined rate law, and my reasoning is as follows:

We should look at the step leading up to and including the rate limiting step. This would be steps (a) and (b in the proposed mechanism

(a) A + B <=k1,k-1=> X fast

(b) X + Y <=k2=> D slow

In (a), let k1 be the rate constant for the forward reaction, and let k-1 be the rate constant for the reverse rx.

We can then write k1[A][B] = k-1[x] and solving for [x] we have [x] = k1/k-1[A][B]

In (b) we have the rate = k2[X][Y] and substituting for [X] we have...

rate = k2k1/k-1[A][B][Y]

so this can be written as rate = k'[A][B][Y] which would be in agreement with the determined rate law

Answer 2

Your first step here is to evaluate the dependence of the rate upon the initial concentrations of the reactants given in the data table.

Going from row 1 to row 2, the concentration of [A] is doubled, and the initial rate doubles. That indicates that the rate law is 1st order in [A]. Comparing Row 1 to 3, you can see that the rate does not depend at all on [B]. It is zero order in [B].

From that, you can write a rate law as:

d[A]/dt = rate= -k[A]

The rate law is first order.

Since the initial rate is given as -1.6 x 10^-3 M/s for [A] = 0.10 M, you can see that k = (1.6 x 10^-3M/s)/(0.1M).

Thus k = 1.6 x 10^-2 s^-1.

When it comes to determining the mechanism, you can immediately state that the mechanism in (c) is not correct. This is because the rate determining step is the second step, X + Y --> D. The rate law for that mechanism would be second order, being first order in both [X] and [Y]. While [X] might depend upon the initial concentration of [A], it would also depend upon the initial concentration of [B], but changes in the concentration of [B] do not affect the rate. So, there are two reasons to rule out the mechanism proposed in (c).

The answer to (d) is that, at least in the proposed mechanism for (c), Y functions as a catalyst, in that it participates in the reaction, but is not consumed.

Note that there is a general procedure that can be extrapolated from this approach to this problem: First, evaluate the data to determine how changes in the initial concentrations affect the observed rate. This helps you build the rate law. When it comes to mechanisms, always check the rate determining step. The rate law you would predict for that should correspond to the observed rate law. It is likely that you will find this information your text, or other course resources. You can also look for example problems like this online to compare the approaches and look for explanations.

Be sure that you can apply this reasoning to other problems; you should seek them out, and practice them, ideally without help, until you can do them consistently and well.