# Reaction involve henry's law constant

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### Yip Li

Dec 6, 2023, 6:35:47 PM12/6/23
to COPASI User Forum
I want to model a system involves gas partitioning to water and i can only find their Henry's law constant instead of the forward and backward rate constant. Can henry's law constant still be used in copasi ?

### Pedro Mendes

Dec 8, 2023, 8:17:26 AM12/8/23
Hi,

You can still model a reaction where you only have the equilibrium
constant but not the explicit values of the forward and backward rate
constants.

the normal mass action rate law is

v = k_on * [S] - k_off * [P]

knowing that K_eq = k_on / k_off and so also

k_off = k_on / K_eq

you can rewrite the rate law as:

v = k_on * [S] - k_on / K_eq * [P]

if you know K_eq, then you can speculate on a value for k_on and use
this rate law. What should k_on be? It depends; if you know this
reaction is faster than the rest of your system, then you can just use a
value of k_on that is much higher than the other k values of other
reactions. If it is slower than you can make it slower. The only thing
that the k_on value affects is the rate at which the process happens,
but since you are using a known K_eq the proportion of [S] and [P] at
equilibrium would be the correct one.

Now, you mentioned Henry's law, and this has many forms. I suspect that
you are referring to the dimensionless version? (the ratio of the two
concentrations at equilibrium) In that case the Henry's constant is the
same as I used above as K_eq. If you are using a different Henry
constant, eg using the gas pressure, then the above does not apply...

Pedro
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