Question

An experiment on the vapor-liquid equilibrium for the methanol (1) + dimethyl carbonate (2) system at 337.35 K provides the following information:

x₁ = 0.0, y₁ = 0.0 and P = 41.02 kPa

x₁ = 0.20, y₁ = 0.51 and P = 68.23 kPa

x₁ = 1.0, y₁ = 1.0 and P = 99.91 kPa

Use this information to estimate the system pressure and vapor-phase mole fraction when x₁ = 0.8. Use the 1-parameter Margules equation.

Answer 1

Given:

x₁ = 0.0, y₁ = 0.0 and P = 41.02 kPa

x₁ = 0.20, y₁ = 0.51 and P = 68.23 kPa

x₁ = 1.0, y₁ = 1.0 and P = 99.91 kPa

T= 337.35 K

Use of a modified Raoult's Law approach is the 1-parameter Margules equation,

Raoult’s law relates the composition of the vapor and liquid phases that are in equilibrium with each other through the vapor pressure and the total system pressure. The two major assumptions of Raoult’s Law are:

• The vapor phase behaves as an ideal gas.

• The liquid phase behaves as an ideal solution.

NOTE: Raoult’s may not be applied for systems where the vapor and liquid phases are not in equilibrium with each other. Raoult’s law is:

p_i = y_iP = x_ip_{i*         -}-----------> eqn 1

where yi is the mole fraction of component i in the gas phase, xi is the mole fraction of component i in the liquid phase, pi* is the vapor pressure of component i, P is the total system pressure and pi is the partial pressure of component i.

Since the total system pressure P is equal to the sum of the partial pressures pi, we can derive the following expression:

P = x1p1* + x2p2* + ... + xnpn*     ------>eqn 2

Combining equations 1 and 2 gives the following useful expression:

y1P/p1* + y2P/p2* + ... + ynP/pn* = 1   ----------> eqn 3

A simple rearrangement of equation 3 yields,

      ----------------> eqn 4

With these equations, it is possible to perform a variety of calculations, which are listed in the table below.

Dimethyl carbonate,

Dimethyl carbonate is an organic compound with the formula OC(OCH₃)₂. It is a colourless, flammable liquid. It is classified as a carbonate ester.

Density: 1.07 g/cm³

Boiling point: 90 °C

Molar mass: 90.08 g/mol

Formula: C₃H₆O₃

Pressure composition data,

Pressure-composition diagram,

Liquid phase(circles), vapor phase(diamonds). Solid lines serve only as a guide to the eye.