Question

The Henry’s law constant for CO2 dissolved in dichloromethane (DCM) at 25 °C is 153 bar.

a) If the vapor pressure of dichloromethane at this temperature is 56.6 kPa, what is the solubility of CO2 if the total pressure is 1 bar?


b) 100 mole/s of a mixture 17 mole% CO and the rest DCM is fed to a Flash unit operating at 25 °C and 1 bar. Determine the molar flow rates of the exiting vapor and liquid streams and their compositions.

Answer 1

Part a|
Given :

Henry's Law Constant (k) = 153 bar = 15300 kPa (Using 1 bar is approximately equal to 100 kPa)

Vapor Pressure of DCM (P_DCM) = 56.6 kPa

Total Pressure (P_Total) = 1 bar = 100 kPa

To determine : Solubility of CO₂

Now, P_{Total =} P_DCM + P_CO2

P_CO2 = P_Total - P_DCM

P_CO2 = 100 - 56.6 = 43.4 kPa

Using Henry's Law => k*x = Partial of CO₂ = P_CO2

Putting Values:

x = 2.8366*10^-3

Thus solubility of CO₂ is 2.8366*10^-3 mol/mol CO₂.   

Part b|

Given :

Feed flowrate (F) = 100 mol/s

Mole Fraction of CO in feed (x_f,CO2) = 0.17 ; Mole Fraction of DCM in feed (x_f,DCM) = 1-0.17 = 0.83

T = 25 °C ; P_total = 1 bar = 100 kPa = 10⁵ kPa

To Determine: Exiting liquid (L) and vapor (V) flow rates.

Now, using overall mole balance:

F= L+V => 100 = L + V => V = 100 - L----------------------- (1)

NOTE: x_{L,CO2 and}  y_v,CO2 are mole fractions of CO₂ in liquid and vapor streams respectively. Similarly x_{L,DCM and}  y_v,DCM are mole fractions of DCM in liquid and vapor streams respectively.

Using Henry's Law:

y_v,CO2 = k*x_L,CO2

y_v,CO2 =153*x_L,CO2 ----------------------------(2)

For DMC, vapor pressure (P_DMC) at T = 25°C is 56.6 kPa.

Thus, y_{v,DCM =} (P_DMC / P_total) = 56.6/100 = 0.566 --------------------------(3)

Now, y_v,DCM + y_v,CO2 = 1

y_{v,CO2 =} 1- y_v,DCM

From equation (3)

y_v,CO2 = 1 - 0.566 = 0.434 -------------------------------(4)

From equation (2)

y_v,CO2 =153*x_L,CO2

x_L,CO2 = (y_v,CO2/153)

Putting the value of y_v,CO2 from equation (4)

x_L,CO2 = (0.434/153) = 2.8366*10^-3 --------------------------(5)

Applying component mole balance for CO₂:

F*x_f,CO2 = L*x_{L,CO2 +} V*y_v,CO2

From equations (1), (4) and (5)

From equation (1)

Now, from equation (5)

x_L,CO2 = 2.8366*10^-3

Thus, x_L,DCM = 1 - x_L,CO2 = 1 - 2.8366*10^-3 = 0.9971634

Thus, the compositions are:

x_L,CO2 = 2.8366*10^-3

x_L,DCM = 0.9971634

y_v,CO2 = 0.434

y_v,DCM = 0.566