Chapter 9, Problem 9.6P

(Tribology) Why you change your motor oil? One of the major reasons for engine-oil degradation is the oxidation of the motor oil. To retard the degradation process, most oils contain an antioxidant [see Ind. Eng. Chem. 26, 902 (1987)]. Without an inhibitor to oxidation present, the suggested mechanism at low temperatures is

$I_2\stackrel{k_0}{\to }\text{2}I\cdot$

$I\cdot +\text{RH}\stackrel{k_i}{\to }\text{R}\cdot \text{+H}I$

$\text{R}\cdot +{\text{O}}_{\text{2}}\stackrel{k_{p\text{l}}}{\to }{\text{RO}}_{\text{2}}^{\cdot }$

${\text{RO}}_2^{\cdot }+\text{RH}\stackrel{k_{p\text{2}}}{\to }\text{ROOH}\text{+}\text{R}$

${\text{2RO}}_2^{\cdot }\stackrel{k_t}{\to }\text{inactive}$

where I₂ is an initiator and RH is the hydrocarbon in the oil.

When an antioxidant is added to retard degradation at low temperatures, the following additional termination steps occur:

${\text{2RO}}_2^{}\cdot +\text{AH}\stackrel{k_{A1}}{\to }\text{ROOH}\text{+}\text{A}\cdot$

$\text{A}\cdot {\text{+RO}}_2^{\cdot }\stackrel{k_{A2}}{\to }\text{inactive}$

1. (a) Derive a rate law for the degradation of the motor oil in the absence of an antioxidant at low temperatures.
2. (b) Derive a rate law for the rate of degradation of the motor oil in the presence of an antioxidant for low temperatures.
3. (c) How would your answer to part (a) change if the radicals I· were produced at a constant rate in the engine and then found their way into the oil?
4. (d) Sketch a reaction pathway diagram for both high and low temperatures, with and without antioxidant.
5. (e) See the open-ended problem G.2 in Appendix G and on the CRE Web site for more on this problem.