2) Calculate the molar volume of a gas mixture containing 40 mole % NH3, 30% CO2 and 30 mole % C2H4, at a pressure of 300 atm and a temperature of 200°C, using the methods described below: (i) (ii) (iii) (iv) Ideal gas law Amagat's law and the rule of corresponding states Kay's rule and the rule of corresponding states Van der Waals equation of state and averaged constants

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# Calculation of Molar Volume for a Gas Mixture

**Problem Statement:**
Calculate the molar volume of a gas mixture containing:
- 40 mole % NH₃
- 30 mole % CO₂
- 30 mole % C₂H₄

Given:
- Pressure: 300 atm
- Temperature: 200°C

Methods to be used:
1. Ideal gas law
2. Amagat’s law and the rule of corresponding states
3. Kay’s rule and the rule of corresponding states
4. Van der Waals equation of state and averaged constants

**Table of Constants:**

| Gas   | a \((\text{atm} \cdot \text{cm}^6/\text{mol}^2)\) | b \((\text{cm}^3/\text{mole})\) | \(P_c (\text{atm})\) | \(T_c (°\text{K})\) |
|-------|--------------------------------------------|----------------------------|----------------------|--------------------|
| NH₃   | \(4.19 \times 10^6\)                      | 37.3                       | 111.3                | 405.5              |
| CO₂   | \(3.60 \times 10^6\)                      | 42.8                       | 72.9                 | 304.2              |
| C₂H₄  | \(4.48 \times 10^6\)                      | 57.2                       | 50.5                 | 283.1              |

**Additional Notes:**
- In part (iv), use the Newton-Raphson scheme to find the molar volume using the Van der Waals equation.
Transcribed Image Text:# Calculation of Molar Volume for a Gas Mixture **Problem Statement:** Calculate the molar volume of a gas mixture containing: - 40 mole % NH₃ - 30 mole % CO₂ - 30 mole % C₂H₄ Given: - Pressure: 300 atm - Temperature: 200°C Methods to be used: 1. Ideal gas law 2. Amagat’s law and the rule of corresponding states 3. Kay’s rule and the rule of corresponding states 4. Van der Waals equation of state and averaged constants **Table of Constants:** | Gas | a \((\text{atm} \cdot \text{cm}^6/\text{mol}^2)\) | b \((\text{cm}^3/\text{mole})\) | \(P_c (\text{atm})\) | \(T_c (°\text{K})\) | |-------|--------------------------------------------|----------------------------|----------------------|--------------------| | NH₃ | \(4.19 \times 10^6\) | 37.3 | 111.3 | 405.5 | | CO₂ | \(3.60 \times 10^6\) | 42.8 | 72.9 | 304.2 | | C₂H₄ | \(4.48 \times 10^6\) | 57.2 | 50.5 | 283.1 | **Additional Notes:** - In part (iv), use the Newton-Raphson scheme to find the molar volume using the Van der Waals equation.
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