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.

Answer 1

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.