GATE 2026 CH – Question 36
K value is defined as the ratio of mole fraction of a component in the vapor phase to that in the liquid phase. The K values of propane and iso-butane at 293 K are given in the table.
| Pressure (kPa) | K propane | K iso-butane |
|---|---|---|
| 1100 | 1.8 | 0.85 |
| 1200 | 1.6 | 0.75 |
| 1300 | 1.4 | 0.65 |
| 1400 | 1.25 | 0.5 |
| 1500 | 1.1 | 0.45 |
Which one of the following is closest to the bubble point pressure (in kPa) of an equimolar mixture of propane and iso-butane at 293 K?
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Correct answer: (C) 1310
Explanation
At the bubble point $\sum K_i x_i = 1$. With $x = 0.5$ for both, $K_{propane} + K_{butane} = 2$. The sum of the K values is 2.65, 2.35, 2.05 and 1.75 at 1100, 1200, 1300 and 1400 kPa. The sum of 2 lies between 1300 and 1400 kPa, close to 1300: by interpolation $P = 1300 + 100 \times \frac{0.05}{0.30} \approx 1317$ kPa. The closest option is 1310.