Mass Transfer Question

Question

Predict the diffusion coefficient for nitrogen through a mixture containing 50% hydrogen, 30% ammonia, 15% nitrogen, and 5% water at 25°C and 1 atm. This was my thought process on which equation to start with but do I assume I'm dealing with water and ammonia in a gas phase? Would this even be a correct equation to use?.

Assumptions: Stagnant mixture

$$D_{AM} = \frac {1-x_A}{\sum_{i=1}^n \frac{x_i}{D_{Ai}}} = \frac{1-x_A}{\frac{x_B}{D_{AB}}+\frac{x_C}{D_{AC}}+\frac{x_D}{D_{AD}}}$$ $A=\text{N}_2$

$B=\text{H}_2$

$C=\text{NH}_3$

$D=\text{H}_2\text{O}$

Answer 1

One thing to keep in mind for mass transfer is to stay consistent when using x's and y's. You identified that this must be in the gas phase at STP, yet the equation you used has x's which represent the mole fraction of components in liquid phase. Mixing up these can get you in trouble later on with multiphase systems. Here is the equation for the effective diffusion coefficient of gas A with respect to the total gas mixture. Further explanation can be found here.

$$D'_{A} = \frac {1-y_A}{\sum_{i=1}^n \frac{y_i}{D_{Ai}}} = \frac{1-y_A}{\frac{y_B}{D_{AB}}+\frac{y_C}{D_{AC}}+\frac{y_D}{D_{AD}}}$$ $A=\text{N}_2$

$B=\text{H}_2$

$C=\text{NH}_3$

$D=\text{H}_2\text{O}$

Your textbook might be a little different, but I don't like adding subscripts to denote mixtures. I noticed your equation has $D_{AM}$. I changed this to D prime of component A, $D'_A$.