Chemistry - Determining Rate Law and Reaction Mechanism from Method of Initial Rates

Solution 1:

Empirical rate law is:

$$\mathrm{Rate} = \frac{[\ce{A}][\ce{B}]}{[\ce{B}] + [\ce{C}]}$$

In the first block of data you can notice that $\ce{C}$ and $\ce{D}$ are not necessarily required for reaction to proceed because otherwise the rate would be zero. You can also deduce that their concentration must appear as a sum in the rate law for the same reason. The sum will appear in denominator because $\ce{C}$ slows down the overall reaction.

Next step is to guess elementary reactions. From the law's denominator sum you can conclude that intermediate will competitively react with $\ce{B}$ and $\ce{C}$.

$\ce{A ->[k1] I}$ (Probably some kind of excitation)

$\ce{I + C ->[k2] D}$

$\ce{I + B ->[k3]Product}$

Then you derive the overall rate via steady state approximation (assumption).

$$\mathrm{Rate} = \frac{k_1k_3[\ce{A}][\ce{B}]}{k_3[\ce{B}] + k_2[\ce{C}]}$$

and ${k_1}={k_2}={k_3}$

Solution 2:

I think you should consider some sequence of reactions involving mass action kinetics. The rate they give in the table must be the rate of disappearance of A (I guess). So the rate might be represented by something like $R=C_1A+C_2B+C_3C+C_4A^2+C_5B^2+C_6C^2+C_7AB+C_8BC+C_9AC$. Not all the coefficients would be positive because of reverse reactions. There is not enough data in the table to determine all the coefficients even for this set up to 2nd order. So you might have to play with the coefficients to determine the simplest version which matches the table I hope this helps and I hope it works.