Polyolefins such as polyethylene undergo slow degradation when placed in air. Degradation occurs by reactions with atmospheric oxygen that lead to the formation of carbonyl groups (groups containing oxygen), gradual chain scission (reduction in molecular weight), and loss of strength. The concentration of carbonyl groups can be monitored with

time using the absorbance of the infrared spectroscopy peak at 1741 cm⁻¹. In the table below, carbonyl absorbance at 1741 cm−1 versus time data for the oxidation of a 200 μm thick low density polyethylene (LDPE) film at 373 K are tabulated.

(a) The kinetics for this reaction obey a power-law expression of the form

in which A is the absorbance, t represents time, and K₇ and K₈ are constants. Using data in the above table, determine values for K₇ and K₈.

(b) Compute the amount of time required for an absorbance of 0.20.