CHE 120 – Mass Transfer
Name ________________________
Exam 1
April 22, 2022
1. (12 pts) Consider a binary mixture of hydrogen (H2, M = 2) and carbon dioxide (CO2, M = 44). The
total mass concentration of the mixture is 1.8 kg/m3 and the mass fraction of H2 is 0.06. What is
the molar concentration of H2 in mol/m3 (also written as gmole/m3)?
Questions 2 through 5 are all for a dilute mixture of air (M = 29, yA = 0.003) in ethanol (C2H5OH, M =
46, yB = 0.997) at 1.9 atm pressure and 298 K temperature.
2. (8 pts) Using the simplest approach possible, calculate the gas phase binary diffusion coefficient of
the air in ethanol gas.
3. (14 pts) For that same gas mixture, calculate the effective diffusion coefficient of the air inside a
pore with a diameter of 35 nm.
4. (14 pts) Using the simplest approach possible, calculate the liquid phase diffusion coefficient of the
dissolved air in liquid ethanol. The viscosity of ethanol at that temperature is 1.090 cP (= 1.090 x
10-3 Pa∙s).
5. (14 pts) For that same liquid mixture, calculate the effective diffusion coefficient of the air inside a
pore with a diameter of 1.5 nm. You can approximate the diameter of the dissolved air molecules
as being the same as their Lennard-Jones molecular diameter.
6. (8 pts) Which of the forms of the flux equation is appropriate for a system in which the flux of A is
equal and opposite to the flux of B (such as for an isomerization reaction of A  B)?
𝑎𝑎. 𝐍𝐍𝐴𝐴 = −𝑐𝑐𝐷𝐷𝐴𝐴𝐴𝐴 ∇𝑦𝑦𝐴𝐴 + 𝑦𝑦𝐴𝐴 (2𝐍𝐍𝐴𝐴 )
𝑏𝑏. 𝐍𝐍𝐴𝐴 = −𝑐𝑐𝐷𝐷𝐴𝐴𝐴𝐴 ∇𝑦𝑦𝐴𝐴
𝑐𝑐. 𝐍𝐍𝐴𝐴 = −𝑐𝑐𝐷𝐷𝐴𝐴𝐴𝐴 ∇𝑦𝑦𝐴𝐴 + 𝑦𝑦𝐴𝐴 𝐍𝐍𝐴𝐴
𝑑𝑑. 𝐍𝐍𝐴𝐴 = −
𝑐𝑐𝐷𝐷𝐴𝐴𝐴𝐴 ∇𝑦𝑦𝐴𝐴
+ 𝑦𝑦𝐴𝐴 𝐍𝐍𝐴𝐴
1 − 𝑦𝑦𝐴𝐴
7. (8 pts) Which of the following boundary conditions is appropriate for the equilibrium at a nonreactive liquid/solid interface?
𝑎𝑎. 𝑁𝑁𝐴𝐴 = −𝑘𝑘𝑠𝑠 𝑐𝑐𝐴𝐴𝐴𝐴
𝑏𝑏. 𝑐𝑐𝐴𝐴,𝑠𝑠 = 0
𝑐𝑐. 𝑐𝑐𝐴𝐴𝐴𝐴 = 𝑐𝑐𝐴𝐴∗
𝑑𝑑. 𝑝𝑝𝐴𝐴𝐴𝐴 = 𝑥𝑥𝐴𝐴 𝑃𝑃𝐴𝐴
8. (22 pts) For one of the examples we went through in class, we reached the simplified continuity
equation for component A in a binary gas mixture:
1 𝜕𝜕
𝜕𝜕𝑁𝑁𝐴𝐴,𝑧𝑧
�𝑟𝑟𝑁𝑁𝐴𝐴,𝑟𝑟 � +
=0
𝑟𝑟 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
For the cylindrical coordinates that were most appropriate for the problem geometry. We then
found simplified flux expressions for the r- and z- directions:
𝑁𝑁𝐴𝐴,𝑟𝑟 = −𝑐𝑐𝐷𝐷𝐴𝐴𝐴𝐴
𝜕𝜕𝑦𝑦𝐴𝐴
𝜕𝜕𝜕𝜕
and 𝑁𝑁𝐴𝐴,𝑧𝑧 = −𝑐𝑐𝐷𝐷𝐴𝐴𝐴𝐴
𝜕𝜕𝑦𝑦𝐴𝐴
𝜕𝜕𝜕𝜕
Combine those equations to provide the most simplified form of the general differential equation
in terms of the gas phase mole fraction, yA, for a system in which pressure is constant and
i)
(10 pts) Temperature is not constant
ii)
(12 pts) Temperature is constant