What is the rate constant for the reaction 2a+b→c? (the initial rate was measured at several different reactant concentrations) [a] (m) [b] (m) initial rate (m/s) 0.05 0.05 0.035 0.10 0.05 0.14 0.20 0.10 1.12?

To find the rate constant we can write a rate expression for the following reaction:

2A + B → C

A rate expression is written as some rate constant multiplied by the concentrations of the reactants, with each concentration raised to the power of the molar coefficient. [A] has a coefficient of 2, and [B] has a coefficient of 1. Therefore, we get the following rate expression:

rate = k[A]²[B]

We are given a table of values and we can enter the three variable to solve for k.

k = (rate) / ([A]²[B])

k = (0.035) / ((0.05) ² (0.05))

k = 280

We can confirm if the value for k is correct by using another set of concentrations, along with the rate constant and solve for the rate.

rate = 280 [0.10]²[0.05]

rate = 280 (0.01) (0.05)

rate = 0.14

The value we solved for agrees with the rate provided in the table, therefore we know our value for the rate constant is correct which is k = 280.