Applications of Raoult's Law in Distillation

Understanding Raoult’s Law in Distillation

Raoult’s Law is a fundamental principle in chemistry that describes how the vapor pressure of a solvent in a solution is affected by the presence of solutes. In distillation, this law is crucial for predicting how different components will behave under heat, guiding the separation of mixtures. Below are three practical examples that demonstrate the application of Raoult’s Law in distillation.

Example 1: Distillation of an Ethanol-Water Mixture

In the beverage industry, the distillation of ethanol from fermented mixtures is a common application. Ethanol and water form a mixture where Raoult’s Law helps in understanding the vapor pressures involved. The goal is to obtain high-purity ethanol.

In this example, consider a mixture containing 40% ethanol and 60% water by volume. The vapor pressures of pure ethanol and pure water at a given temperature (e.g., 78°C) are approximately 0.59 atm and 0.31 atm, respectively. According to Raoult’s Law:

• The partial pressure of ethanol (
  P_E
  ) = mole fraction of ethanol in the liquid phase × vapor pressure of pure ethanol

• The partial pressure of water (
  P_W
  ) = mole fraction of water in the liquid phase × vapor pressure of pure water

First, we calculate the mole fractions:

• Mole fraction of ethanol (
  X_E
  ) = 0.40

• Mole fraction of water (
  X_W
  ) = 0.60

Then, the partial pressures are:

• P_E = 0.40 × 0.59 atm = 0.236 atm

• P_W = 0.60 × 0.31 atm = 0.186 atm

The total vapor pressure (
P_T
) can be calculated as:

• 
  P_T = P_E + P_W = 0.236 atm + 0.186 atm = 0.422 atm

This information can guide the distillation process, allowing operators to optimize conditions for maximum ethanol recovery.

Notes:

• With increased distillation stages, the purity of ethanol can achieve over 95%.
• Adjusting temperature and pressure can enhance separation efficiency.

Example 2: Separation of Benzene and Toluene

In petrochemical industries, the separation of benzene and toluene is essential for producing various chemical products. Both substances are non-ideal solutions, and Raoult’s Law helps predict their behavior during distillation.

Consider a mixture containing 30% benzene and 70% toluene. The vapor pressures of pure benzene and pure toluene at 80°C are approximately 0.9 atm and 0.3 atm, respectively. Applying Raoult’s Law:

• Mole fractions:

  • X_B = 0.30

  • X_T = 0.70

Calculating the partial pressures:

• P_B = X_B × P^0_B = 0.30 × 0.9 atm = 0.27 atm

• P_T = X_T × P^0_T = 0.70 × 0.3 atm = 0.21 atm

Total vapor pressure:

• 
  P_T = P_B + P_T = 0.27 atm + 0.21 atm = 0.48 atm

This information allows for optimizing the distillation column operating conditions to maximize the separation of benzene, which has a lower boiling point compared to toluene.

Notes:

• The distillation efficiency can be enhanced by using fractional distillation techniques.
• The presence of azeotropes may complicate the separation process.

Example 3: Purification of Acetic Acid

In the production of acetic acid, distillation is used to purify the product from water and other byproducts. Raoult’s Law serves as a basis for understanding the vapor-liquid equilibrium in the distillation tower.

Consider a feed mixture containing 50% acetic acid and 50% water. At 100°C, the vapor pressures are approximately 0.6 atm for acetic acid and 0.4 atm for water. Using Raoult’s Law:

• Mole fractions:

  • X_A = 0.50

  • X_W = 0.50

Calculating the partial pressures:

• P_A = X_A × P^0_A = 0.50 × 0.6 atm = 0.30 atm

• P_W = X_W × P^0_W = 0.50 × 0.4 atm = 0.20 atm

Total vapor pressure:

• 
  P_T = P_A + P_W = 0.30 atm + 0.20 atm = 0.50 atm

This data assists in determining the necessary reflux ratio to achieve the desired purity level of acetic acid in the distillate.

Notes:

• The purity of acetic acid can be increased through multiple distillation stages.
• Monitoring the temperature and pressure closely is critical for achieving optimal results.