Determination of Diffusivity

Example 17.2-1 - Determination of Diffusivity

In this example, the diffusivity of CCl₄ in oxygen is examined, according to the figure below. Liquid CCl₄ is contained in a tube in the sole presence of oxygen. The mole fraction of CCl₄ is measured at the surface of the liquid and the top of the tube, with the system at steady state.

The graphic on the right represents how the mole fractions of both components change with height z. In order to calculate the diffusivity, the only unknown is the molar flux of CCl₄. This can be calculated using the given conditions, followed by the diffusivity. The following conditions are given in the problem:

The molar density of CCl₄
The surface area of the liquid, and hence the tube
Temperature
The distance between the surface level and the top of the tube
Atmospheric pressure
Partial pressure of oxygen at both points of measurement
The volume of CCl₄ which diffuses, and the time it takes to diffuse

The problem is easily solved in Maple. First, the known values are defined and the molar flux of CCl₄ is solved. The molar flux is then plugged into the equation of diffusivity.

> restart; Example 17.2-1: Determination of Diffusivity

Begin by defining constants, such as the density, time, temperature, distance travelled by the CCl4, etc.

> MWCCl4:=1/154*gmole/g; Area:=.82*cm^2; t:=3600*10*s; rhoCCl4:=1.59*g/cm^3; R:=82.05*cm^3*atm/(gmole*K); T:=273*K; dz:=17.1*cm;p:=755/760*atm; pO2_2:=755/760*atm; pO2_1:=722/760*atm; volrate:=0.0208*cm^3;

> NCCl4:=volrate*rhoCCl4/(Area*t)*MWCCl4; Determine the molar flux of CCl4 using the volumetric evaporation rate.

> DCCl4_O2:=NCCl4*dz*R*T/(p*ln(pO2_2/pO2_1)); Determine diffusivity using equation 17.2-15a in the book.

> simplify(%);

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