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

The following data describe the reaction

 

Use these data to obtain a least-squares t to estimate the value of k.

Time t (h) …………… C(mol of (CH3)3 CBr/L)

0 ………………………….. 0.1039

3.15 ………………………. 0.0896

6.20 ………………………. 0.0776

10.0 ………………………. 0.0639

18.3 ………………………. 0.0353

30.8 ………………………. 0.0207

43.8 ……………………….. 0.0101

(CH3);CBr + H,O (CH3);COH + HBr