Question

3. The rate laws that we looked at in this course all had integers as exponents. For instance, we looked at first-order and second-order rate laws of the form rate = k[A]¹ and rate = k[A]². Your textbook also pointed out rate laws of higher order, such as rate = k[A][B]², which is first-order in A, second-order in B, and third-order overall. But the exponents in rate laws aren’t always integers, and they aren’t even always positive. In biochemistry, for example, there are many enzymatic reactions that are inhibited (or, slowed down) by other molecules; if you’ve taken a biology or physiology class, you may have talked about allosteric enzymes, feed-back inhibition, and competitive and uncompetitive inhibition.

The table below shows values for initial rates as a function of the concentrations of three reactants A, B and C. Which of the rate laws is most consistent with the data? Show your calculations, or explain your reasoning. Determine the value of k.

These are the possible rate laws. The data is consistent with one of them.

               Rate = k[A]¹[B]^1.5[C]^-1                                                   Rate = k[A]^1.5[B]^1.0[C]^-1

               Rate = k[A]¹[B]^0.5[C]^-1                                                   Rate = k[A]^0.5[B]^1.5[C]^-1

                    Rate = k[A]^0.5[B]^1.5[C]¹                                                  Rate = k[A]^1.5[B]^0.5[C]¹

This is the data:

Rate	[A]	[B]	[C]
0.0245	0.100	0.100	0.010
0.0294	0.120	0.100	0.010
0.0386	0.120	0.120	0.010
0.0155	0.120	0.120	0.025