Chemists and engineers must be able to predict the changes in chemical concentration in a reaction. A model used for many single-reactant processes is

Rate of change of concentration = -kCⁿ

where C is the chemical concentration and k is the rate constant. The order of the reaction is the value of the exponent n. Solution methods for differential equations (which are discussed in Chapter 9) can show that the solution for a first-order reaction (n = 1) is

C(t) = C(0)e^-kt

and the solution for a second-order reaction (n = 2) is

 

The following data (from Brown, 1994) describes the gas-phase decomposition of nitrogen dioxide at 300°C.

Time t (s) …….. C(mol NO2 /L)

0 ………………….. 0.0100

50 ………………… 0.0079

100 ………………… 0.0065

200 ………………… 0.0048

300 ………………… 0.0038

Determine whether this is a first-order or second-order reaction, and estimate the value of the rate constant k.