GATE 2025 CH – Question 32
The following data is given for a ternary $ABC$ gas mixture at 12 MPa and 308 K:
| Component $i$ | A | B | C |
|---|---|---|---|
| $y_i$ | 0.55 | 0.20 | 0.25 |
| $\hat{\phi}_i$ | 0.75 | 0.80 | 0.95 |
$y_i$: mole fraction of component $i$ in the gas mixture
$\hat{\phi}_i$: fugacity coefficient of component $i$ in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is _____ MPa (rounded off to 3 decimal places).
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Correct answer: 9.624 to 9.720
Explanation
The fugacity coefficient of the mixture follows from the component values: $\ln\phi = \sum y_i\ln\hat{\phi}_i = 0.55\ln 0.75 + 0.20\ln 0.80 + 0.25\ln 0.95 = -0.15823 - 0.04463 - 0.01282 = -0.21568$, so $\phi = 0.8061$. The fugacity of the mixture is $f = \phi P = 0.8061 \times 12 = 9.672$ MPa.