Relative Volatility of a Binary System. Using the equilibrium data for the n-pentane–n-heptane system given in Example 26.3-2, calculate the relative volatility for each concentration and plot α versus the liquid composition xA.
The Correct Answer and Explanation is :
To calculate the relative volatility (α\alpha) of a binary system, such as the n-pentane–n-heptane system, we use the following formula: α=(yA/xA)(yB/xB)\alpha = \frac{(y_A / x_A)}{(y_B / x_B)}
Where:
- yAy_A and yBy_B are the mole fractions of components A (n-pentane) and B (n-heptane) in the vapor phase.
- xAx_A and xBx_B are the mole fractions of components A and B in the liquid phase.
Steps for Calculation:
- Data Extraction: First, extract equilibrium data for the binary system (typically, mole fractions of the components in both the liquid and vapor phases for a given total pressure and temperature). This data is often presented in tables in the problem.
- Apply the Formula: For each concentration, use the mole fractions in the liquid phase xAx_A and the vapor phase yAy_A (similarly for component B). Calculate α\alpha for each pair of values.
- Plot α\alpha vs xAx_A: Once you have calculated α\alpha for each concentration, plot the relative volatility (α\alpha) on the y-axis and the liquid phase mole fraction of n-pentane (xAx_A) on the x-axis. This plot helps understand the behavior of the system as the composition of the liquid phase changes.
Example Calculation:
Suppose you have the following data for the n-pentane–n-heptane system:
| xA (liquid) | yA (vapor) |
|---|---|
| 0.10 | 0.15 |
| 0.20 | 0.25 |
| 0.30 | 0.35 |
| 0.40 | 0.45 |
| 0.50 | 0.55 |
For each concentration, you can calculate α\alpha using the formula:
- At xA=0.10x_A = 0.10, α=0.15/0.10(1−0.15)/(1−0.10)=1.50.944=1.59\alpha = \frac{0.15 / 0.10}{(1 – 0.15) / (1 – 0.10)} = \frac{1.5}{0.944} = 1.59
- Repeat for other concentrations.
Explanation of Relative Volatility:
Relative volatility (α\alpha) is a measure of the ease with which two components in a mixture can be separated by distillation. If α>1\alpha > 1, component A is more volatile than component B. As α\alpha increases, the separation between the components becomes easier. The plot of α\alpha versus xAx_A helps determine how relative volatility changes as the liquid composition changes, typically decreasing as the mixture approaches the azeotrope, where α=1\alpha = 1.