Question

A 1 kg-mol bottled gas consists of the following composition at 30\(^\circ\)C. The equilibrium vapour composition of n-Butane in mol % is ____________ (rounded off to two decimal places).

Hint:

In multicomponent vapour-liquid equilibrium, lighter components dominate the vapour phase due to higher vapour pressures.

Answer 1

Correct Answer: 18

Use Raoult’s law for ideal mixtures:
\[ y_i = \frac{x_i P_i^{sat}}{\sum x_j P_j^{sat}} \]
Given mole fractions:
\[ x_{b} = 0.50,\quad x_{p} = 0.45,\quad x_{e} = 0.05 \]
Compute contribution of each component:
\[ x_b P_b = 0.50 \times 3 = 1.5 \]
\[ x_p P_p = 0.45 \times 10 = 4.5 \]
\[ x_e P_e = 0.05 \times 40 = 2.0 \]
Total:
\[ \sum x_j P_j = 1.5 + 4.5 + 2.0 = 8.0 \]
Thus the vapour-phase composition of n-Butane is:
\[ y_b = \frac{1.5}{8.0} = 0.1875 \]
Convert to mol%:
\[ y_b = 18.75% \]
Final Answer: 18.75