Question

Consider a carbonated drink in a bottle at 37°C and 126 kPa. It is assumed that the gas space above the liquid consists of a saturated mixture of CO₂ and water vapor.

Given:

The saturation pressure of water at 37°C is 6.33 kPa. Henry's constant for CO₂ dissolved in water at 37°C (310 K) is H = 2170 bar. Molar masses of CO₂ and water are 44 and 18 kg/kmol, respectively. Treating the drink as water, determine the mole fraction of the water vapor in the CO₂ gas.

The mole fraction of water vapor in the CO₂ gas is __________ %. (Correct to two decimal places.)

Answer 1

It is assumed that CO2 is saturated with water vapor and hence partial pressure of water vapor= vapor pressure= 6.33 Kpa

Mole fraction of water vapor in the gas phase= partial pressure of water vapor/total pressure = 6.33Kpa/126Kpa=0.050

partial pressure of CO2= total pressure- partial pressure of water vapor= 126-6.33= 119.67 Kpa

hence mole fraction of CO2 in the liquid = partial pressure of CO2 in the gas phase/ Henrys constant = 119.67/2170=0.055

mole fraction of water in the liquid phase =1-0.055=0.945