# Diffusion model using gas pressure decay

Hi,

This isn't a homework problem - this is to help with the design of an experiment. I know the questions below are probably fairly simple physics questions, but I've got lost in laws and units! Please help me out.

The experiment

A cylinder 20cm long and 2cm wide is filled with 6cm of liquid so that there is 14cm for gas available above the liquid. From the top, the cylinder is filled with helium until the gas pressure is 100 bars. Then the cylinder is sealed. The pressure in the cylinder drops with time, which in a closed system is assumed to result from diffusion of the gas into the liquid.

So...

The problem

1) If I know the solubility of helium in the liquid at atmospheric pressure, how can I arrive at the solubility at high pressure? If it's using henry's law (as far as I've got) then how do I get the henry's constant for a liquid?

2) If I know D, the diffusion rate, of helium in this liquid, how can I calculate the theoretical amount of helium (mol) in the liquid with time?

3) How can I arrive at a modelled diffusion gradient across the 6cm of liquid at the end of the experiment? Let's say the experiment lasts 12 hours.

Thanks so much for your help,
QforK

## Answers and Replies

Chestermiller
Mentor
The Henry's law constant for most gases is available in the literature. The concentration in the liquid at the interface is equal to the pressure in the gas times the Henry's law constant. Below the interface, you have a transient diffusion problem analogous mathematically to the transient conduction heat transfer problem for a bar.