I have a kinetic theory/Brownian motion/difussion problem that I need
to solve, pls take a look at the following..
consider a 1 litre closed cube/box, with side 10 cm. In the box are
two gases - A and B.
A is Nitrogen and B is Benzene. We can assume the mixture to behave as
ideal gas mixture with no interactions between the two gas molecules.
also Assume STP conditions. (Lets say total number of molecules in the
box ~ 10^22)
The mole fraction of A to B = 10^9 (1 billion) ... that is, there is 1
molecule of benzene per billon molecules of nitrogen... Or Number of
benzene molecules in the cube = 10^13
The property of the box is that it captures Benzene molecules. That is
to say, when a benzene molecule collides against the wall of the box
it sticks to the wall, or reacts with it etc, but does not rebound the
benzene molecule. It consumes benzene molecules that collide on the
How much time does it take for the population of Benzene molecules to
reduce by an order of magnitude ... that is from 10^13 (initially) to
10^12 molecules ?
How long does it take (as a statistical function in time) for all the
benzene molecules to stick to the walls of the box ? ie as a function
of time - the concentration of benzene molecules remaining after 10
milli seconds , 1 second, 1000 seconds so on...
How do I approach this problem ? I am unable to get a clear idea..
I am sure this is a standard problem solved as an example in the
fileds of brownian motion / kinetic theory / reaction kinetics etc..
but cannot find it in any of these texts.. any one has any idea where
to find this problem discussed ?
many thanks in advance guys..
Clarification of Question by
16 Dec 2005 11:39 PST
Taishar : )
thanks for your attempt at analysis.. the way you are considering, and
I too initially, in first principle is highly involving in math - pure
Brownian motion kind of stochastic analysis.. i asked my friends and
found that the diffusion approach to solving this problem, with apt
boundary conditions, is easier
the approach i am taking now is solving the ficks second law PDE by
separation of variables... i think i got a good start from their
imputs.. so withdrawing this question..
and no i did not intend any one to solve this problem and give me the
solution.. It is quite time consuming to solve it rigorously, which is
what i am interested in.. i was asking for a reference, in way of text
book or publication etc where a similar one is solved.. and this is a
standard problem in chem engg.. so for such a reference I placed 10
$... and no this is not a take home exam.. encountered it and need to
solve it to analyze an aspect as part of my research (phd)... thanks
again for your comments though..
kottekoe - mean free path under ideal gas approximation is infinite.. ?