# Homework Help: Compare the recombination rates for 2-body and 3-body reactions (i.e. forming O2)

1. Oct 30, 2012

### buzz3

1. The problem statement, all variables and given/known data

Assume that recombination of atoms proceeds at the gas-kinetic rate of collisions. Compare the recombination rates for a 2-body and 3-body reaction, such as in the formation of O2.
(hint: you may want to use production rate equations and calculate the number density of molecules needed for equal rates Kr2 = Kr3)

2. Relevant equations
(1) 2-body recombination: O + O = O2 + hv
(2) 3-body recombination: O + O + M = O2 + M (M is an atmospheric molecule that absorbs excess energy)

gas-kinetic rate of collsions: Kgk = sig*vo ; where sig is collisional cross section and vo is mean thermal velocity (sqrt(2kT/m), where k is boltzmann's constant, T is temp, and m is particle mass)

The 2-body reaction rate (Kr2) is then Kgk with the above assumption.
The 3-body reaction rate Kr3 = 2*R/vo * Kgk2

I think the rate equations would be: (1) d[O2]/dt = [O]^2*Kgk ;
(2) d[O2]/dt = [O]^2*[M]*Kr3

If I set Kgk = Kr3, I end up with 2*sig*R = 1 ...which I can't make sense of

If I equate the rate equations (assuming I derived them correctly), I get 2*sig*R*[M] = 1

Neither way do I see a way to get at the number density. I expect that I would use the ideal gas law in some way if I could figure out how it would work into these relationships...

for example, PV = nkT...so n/V would be number density (N); N = P/kT

I'm totally lost here, any nudge in the right direction would be greatly appreciated

3. The attempt at a solution
oh, my attempt is shown above
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution