# Rate equation of a radical

Consider the following elementary reaction mechanism where both the forward and reverse reaction mechanism are important $$\ce{CO + O2<->[1] CO2 + O}$$ $$\ce{O + H2O<->[2] OH + OH}$$ $$\ce{CO + OH<->[3] CO2 + H}$$ $$\ce{H + O2<->[4] OH + O}$$ How many chemical rate equations are need to determine the chemical evolution of a system defined by this mechanism? Write out the rate equation for the hydroxyl radical.

This question is from the book Introduction to Combustion: Concepts and Applications by Stephen R. Turns.

My answer to the second part is $$\frac{d[\ce{OH}]}{dt}=( k_{f_2}[\ce{O}][\ce{H2O}]+k_{r_3}[\ce{CO2}][\ce{H}]+ k_{f_4}[\ce{H}][\ce{O2}] ) - (k_{r_2}[\ce{OH}][\ce{OH}]+k_{f_3}[\ce{CO}][\ce{OH}] +k_{r_4}[\ce{OH}][\ce{O}])$$

Is this correct?

$$k_f$$ is the elementary forward rate coefficient

$$k_r$$ is the elementary reverse rate coefficient

[ ] refers to concentration

• Second reaction stems from first one so it also should be present in equation, afaik. – Mithoron Nov 24 '18 at 19:31
• Hei, second reaction is included in the rate equation I wrote – F.O Nov 24 '18 at 22:43
• I meant include first. Gah, language is such a terrible tool. – Mithoron Nov 24 '18 at 22:54
• Is there a difference between the rate equation and net reaction rate ? Because What I wrote is the net reaction rate and I have been told that my answer was wrong. – F.O Nov 25 '18 at 11:00
• I would have a factor of 2 in the two terms for reaction 2 in the OH balance. – Chet Miller Nov 25 '18 at 18:34