Chemists and engineers must be able to predict the changes in chemical concentration in a reaction. A model used for many singlereactant 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

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

 

and the solution for a third-order reaction (n = 3) is

Time t (min) …………… C (mol of reactant/L)

5 …………………………………… 0.3575

10 ………………………………….. 0.3010

15 ………………………………….. 0.2505

20 ………………………………….. 0.2095

25 ………………………………….. 0.1800

30 ………………………………….. 0.1500

35 ………………………………….. 0.1245

40 ………………………………….. 0.1070

45 ………………………………….. 0.0865

The preceding data describe a certain reaction. By examining the residuals, determine whether this is a first-order , second-order, or third-order reaction, and estimate the value of the rate constant k.

1 1 + kt C(0) C(t)