A mixture of ideal gases A (propane) and B (isopropanol) exist in a vapor-liquid
ID: 717944 • Letter: A
Question
A mixture of ideal gases A (propane) and B (isopropanol) exist in a vapor-liquid equilibrium in a constant temperature and pressure container. Originally, there is 1 mol A and 1 mol B. The mol fraction of A in the gas phase is 76% and 22% in the liquid phase. Gases A and B start to flow into the system at constant flow rates (at the same constant T and P). The flow rate of A is 3 mol/s. a. Calculate the flow rate of B that will fill the container within 10 minutes such that the gas mixture has the same number of moles of A in the liquid and vapor phase (nA, vapor = nA, liquid). b. Calculate the molar composition of each phase at t=0 minutes and t=10 minutes.
Explanation / Answer
A = propane
B = isopropanol
Exist in a constant temperature and pressure container
Flow Rates:
A = 3 mol/sec
Calculate:
a.) B = ?,
that will fill the container within 10 minutes such that the gas mixture
has the same number of moles of A in the liquid vapor phase.
At t = 0 minute,
Moles of A = 1 mol
Moles of B = 1 mol
Moles of A in gas phase = 76% = 0.76 mol
Moles of A in liquid phase = 22% mole = 22 mol
Moles of B in gas phase = 24% = 0.24 mol
Moles of B in liquid phase = 78% = 0.78 mole
At t = 10 minute,
Moles of A = 1 + 3*10*60 = 1801 mol
Moles of A in gas phase = moles of A in liquid phase
Moles of A in gas phase = 1801/2 = 900.5 moles
Moles of A in liquid phase = 1801/2 = 900.5 moles
At same temperature and pressure mole fractions will be same
after 10 minutes:
Moles of B in gas phase = 24%
Moles of B in liquid phase = 78%
Total moles in gas phase: Y
Y = moles of A in gas phase + moles of B in gas phase
Y = 900.5 + 0.24*Y
0.76Y = 900.5
Y = 1184.87
Moles of B in gas phase = 0.24*1184.87 = 284.37 mole
Total moles in liquid phase: X
X = moles of A in liquid phase + moles of B in liquid phase
X = 900.5 + 0.78*Y
0.22X = 900.5
X = 4093.18
Moles of B in liquid phase = 0.78*4093.18 = 3192.68 mole
Total moles of B = 3192.68 + 284.37 = 3477.05
Molar flow rate of B: F
Total moles of B = 1(initially present) + F*10*60 (after 10 minutes)
Total moles of B = 1 + 600F
3477.05 = 1 + 600F
a.) F = 3476/600 = 5.79 mol/sec Ans.
b.) Molar composition of each phase:
At t = 0 minute,
Total moles in gas phase = 1 mol
Total moles in liquid phase = 1 mol
At t = 10 minute,
Total moles in gas phase =
moles of A in gas phase + moles of B in gas phase
= 900.5 + 284.37 = 1184.87 ~ 1185 moles Ans.
Total moles in liquid phase =
moles of A in liquid phase + moles of B in liquid phase
= 900.5 + 3477.05 = 4377.55 ~ 4378 moles Ans.
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