Question

Using Raoult's law for water and Henry's law for nitrogen, calculate the pressure and gas-phase composition (mole fractions) in a system containing a liquid that is 1.200 mole% N₂ and 98.80 mole% water in equilibrium with nitrogen gas and water vapor at 50.0°C.

The Henry's law constant for nitrogen in water is recommended by NIST to be well represented by

k_H = 0.000625 exp[1300 (1/T – 1/298.15)] mol N₂ / (kg H₂O bar), where T is measured in Kelvin

a) Estimate the Henry's law constant H [atm/(mole fraction N₂)] for nitrogen in water at T = 50.0°C.
b) Estimate the nitrogen pressure in the gas phase using Henry's law.
c) Estimate the vapor pressure of water using the Antoine equation.
d) Estimate the total pressure using Raoult's law and Henry's law.
e) Estimate the mole fraction of H₂O in the gas phase.

Answer 1

It's a N2/water equilibrium system at 50 C where N2 is 1.2 mole % and 98.8 mole % in liquid state.

According to Henry Law,

K = 0.000625 exp[1300 (1/T – 1/298.15)] ( mole of N2 / mole H2O)(1/bar)

At t = 50 C or T = 323 K

Substitute value of T in above equation we get

K_H = 0.0004469 ( mole N2 /kg water ) (1/bar)

K_H = 0.0004469*(18/1000)(1/0.9869) mole fraction of N2/ atm

= 8.15097 X 10^(-6) mole fraction of N2 / atm

K^'_H = 12.268 X 10^4 atm/mol fraction N2

(b) P = K_H^' x

P = 12.2684 X 10^4 * (1.2/100)

P= 1472.25 atm

(C) Antoine equation constants for water are

A= 8.07131

B= 1730.63

C = 233.426

Vapor Pressure of water Pv at 50 C

= where t is in degree Celsius and P is in torr

Substituting values of A , B , C and t = 50 C

we get vapor pressure of water = 92.29 torr or 0.121 atm