Consider the test tube partially filled with a volatile liquid shown below.
A mass balance on A in the gas phase gives
Using the quasi-sate assumption that the concentration at each point z changes very slowly with time,
Then
Integrating WA = Number which is independent of distance, z, but is a function of time, t
WA = f(t)
For diffusion of A through a stagnant gas
WB = 0
at z = 0 yA = yA2 = 0
z = zo
= L
where PV = vapor pressure and PT = total pressure
Since NA is independent of z under the quasi-steady assumption, the above differential equation can be integrated to give
Then
For constant temperature and pressure, C = total concentration = a
constant =
. Only the distance between the top of the capillary and the gas-liquid
interface is varying.
Overall balance on the entire system
Initial conditions: t = 0 , L = Lo
Integrating
Rearranging:
The height of the gas-liquid interface, L, can easily be measured with a cathetometer. A plot at t/L–Lo vs. (L–Lo) should yield a straight line of slope S from which the diffusivity can be calculated from the equation
