Category: Chemical Engineering Math
"Published in Newark, California, USA"
Two gases, HBr and CH4, have molecular weights 81 and 16, respectively. The HBr effuses through a certain small opening at the rate of 4 mL/sec. At what rate will the CH4 effuse through the same opening?
Solution:
Since the rate of flow of the gases as well as their molecular weight are involved in the problem, then we have to us the Graham's Law of Effusion and Diffusion. What is the difference between effusion and diffusion? Effusion is the process in which a gas escapes from one chamber of a vessel by passing through a very small opening or orifice while diffusion is mixing of molecules of different gases by random motion and collision until the mixture becomes homogeneous.
The rate of effusion or diffusion of a gas is inversely proportional to the square root of its density or molecular weight. The equation of Graham's Law of Effusion and Diffusion can be written as follows
or
From the given problem, therefore, the rate of effusion of CH4 through the small opening is
Category: Chemical Engineering Math
"Published in Newark, California, USA"
What pressure is required to compress 5 liters of gas at 1 atm pressure to 1 liter at a constant temperature?
Solution:
At the given problem, if the temperature is constant during the compression of a gas, then it is a principle of Boyle's Law. The volume of a gas is inversely proportional to its pressure. The equation for Boyle's Law can be written as follows
or
Therefore, the pressure of a gas after it is compressed to 1 liter is
Category: Chemical Engineering Math
"Published in Newark, California, USA"
The vapor pressures of pure benzene and toluene at 60°C are 385 and 135 Torr, respectively. Calculate (a) the partial pressures of benzene and toluene, (b) the total vapor pressure of the solution, and (c) the mole fraction of toluene in the vapor above a solution with 0.60 mole fraction toluene.
Solution:
In the given problem, if mole fraction of toluene in a solution is
then mole fraction of benzene in a solution is
The sum of the mole fractions of the components in a solution must be equal to 1. In this case, benzene and toluene are the components in a solution.
The vapor pressures of pure benzene and toluene at 60°C are
(a) By Raoult's Law, we can calculate the partial pressures of benzene and toluene in the vapor.
Partial Pressure of Benzene:
Partial Pressure of Toluene:
(b) The total vapor pressure of the solution is
(c) Since we know already the partial pressures of benzene and toluene as well as the total vapor pressure of the solution, therefore, the mole fraction of toluene in the vapor is
