Chemical Kinetics / Rate Question -- Error in Textbook Question/Answer?

Question

I am reading Kaplan's General Chemistry MCAT Review 2018-2019, and think that one of its chemical kinetic questions is wrong. (Or perhaps I am simply missing something). I have attached an image of the question, which is easier than typing out as it includes the standard table of concentrations at different trials.

The answer reads: "In the first two trials, the concentration of $\ce{XH4}$ is held constant while the concentration of $\ce{O2}$ is multiplied by 4, and the rate of the reaction also increases by a factor of approximately 4..." It ultimately comes up with a rate of $k\ce{[XH4]^2[O2]}$

Am I completely missing something? My first question is, is the book's answer right? If it is not, is the problem solvable (i.e. does the table make any sense at all)? I've tried to come up with rates using the table and encountered the following issues. Please let me know if I am right in approaching the question in this way:

1. If you try to find the rate with respect to $\ce{XH4}$ using trials 1 and 3, I believe you get an order of 3. However, if you try to find the same rate using trials 1 and 4, you get 4. This isn't normal, right? Maybe an example of a mixed order reaction? Or just a mess up?

2. How do we interpret the data from trials 3 and 4? The concentration of neither reactant changes and yet the rate doubled. If we ever see something like this in a table, does it suggest that the reaction is 0 order? Or can we not make that leap? And is it even possible to have this data alongside the other data in the table?

3. It seems to me that, based on Trials 1 and 2, the rate is 0 order with respect to $\ce{[O2]}$. Is that a correct interpretation?

Thank you so much!

Answer 1

The exercise is absurd. None of the proposed answers can be right, as for any answer A,B,C,D the rate is a function of the concentrations [XH4],[O2] but the table suggests that the rate is constant over time, e.g. 2.0$~$M/min for entry 1. Thus:

$$ R = 2.0~\text{M/min} = \text{constant} \cdot [\mathrm{XH_4}]^0 \cdot [\mathrm{O_2}]^0 $$ and is therefore a zeroth order kinetics.

I assume that the initial rate $R_0$ or a rate at some point $R_{t>0}$ is meant, and the question just heavily confuses things. So from here on, let's assume that $R$ means some rate at some point in time.

But even then, it is not possible to answer the question. This is because entries 3 and 4 have the same domain ([XH4] and [O2]) but a different codomain (different rates R). This means that there is no function mapping from the concentration of the reactants to the rate of the reaction.

However, there obviously is such a functional relation for all answers A,B,C,D.

Therefore, the question is absurd. It is probably meant to be that [O2] is 2.0 in entry 4.