Question

(Note: The rate law only depends on the concentration of NO2.) Consider the reaction NO2(g) + CO(g) → NO(g) + CO2(g). The rate law is rate = k[NO2]2. This table shows the data obtained by observing the reaction. What is the value for the rate constant, k (with units)? A: 2.08 × 10-4 s-1 B: -2.08 × 10-4 M-1 s-1 C: 2.08 × 10-4 M-1 s-1 D: -2.08 × 10-4 s-1

Answer 1

This problem is providing us with the rate law for the reaction between nitrogen dioxide and carbon monoxide to produce nitrogen monoxide and carbon dioxide. Thus, the required rate constant turns out to be C: 2.08 × 10-4 M-1 s-1 as show below:

Chemical kinetics

In chemistry, chemical kinetics is used to study the changes in the amount of a substance that undergoes consumption or production in a chemical reaction with respect to the time.

In this case, considering the attached picture wherein the data is presented, one can write the following version of the rate law:

$\frac{d[NO_2]}{dt}=-k[NO_2]^2$

Which can be integrated by parts:

$\int{\frac{1}{[NO_2]^2 } } \, d[NO_2]=-k\int{}\, dt\\\\\frac{1}{[NO_2]}=kt$

Which resembles y=mx+b; this means we need to prepare a 1/[NO₂] vs t graph with a trendline, task that can be done on Excel as shown on the second attached file.

Hence, we see the trendline as y = 0.000208x + 1.977, where the slope, 0.000208, is equal to k (rate constant) and with the appropriate units, it will be:

C: 2.08 × 10-4 M-1 s-1

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