The article “Copper Oxide Mounted on Activated Carbon as Catalyst for Wet Air Oxidation of Aqueous Phenol. 1.

Kinetic and Mechanistic Approaches” (P. Alvarez, D. McLurgh, and P. Plucinski, Industrial Engineering and Chemistry Research, 2002: 2147–2152) reports the results of experiments to describe the mechanism of the catalytic wet air oxidation of aqueous phenol. In one set of experiments, the initial oxidation rate (in kilograms of phenol per kilogram of catalyst per hour) and the oxygen concentration (in mol/m3) were measured. The results (read from a graph) are presented in the following table.
Rate (y) 0.44 0.49 0.60 0.64 0.72 O2 concentration (x) 3.84 4.76 6.08 7.06 8.28

a. It is known that x and y are related by an equation of the form y = kxr , where r is the oxygen reaction order. Make appropriate transformations to express this as a linear equation.

b. Estimate the values of k and r by computing the least-squares line.

c. Based on these data, is it plausible that the oxygen reaction order is equal to 0.5? Explain.