Question 10.5.3: Calculate pressure using the ideal gas law and the van der W......
Calculate pressure using the ideal gas law and the van der Waals equation.
A 1.78-mol sample of ammonia gas is maintained in a 2.50-L container at 302 K. Calculate the pressure of the gas using both the ideal gas law and the van der Waals equation (van der Waals constants are listed in Table 10.5.1).
| Table 10.5.1 Van der Waals Constants | ||
| Gas | a (L²·atm/mol²) | b (L/mol) |
| H_{2} | 0.244 | 0.0266 |
| He | 0.034 | 0.0237 |
| N_{2} | 1.39 | 0.0391 |
| NH_{3} | 4.17 | 0.0371 |
| CO_{2} | 3.59 | 0.0427 |
| CH_{4} | 2.25 | 0.0428 |
You are asked to calculate the pressure of a gas sample assuming ideal and nonideal behavior.
You are given the identity, amount, volume, and temperature of the gas.
First use the ideal gas law to calculate the pressure in the flask.
P = \frac{nRT}{V} = \frac{\left(1.78\text{ mol}\right) \left(0.082057\text{ L} \cdot \text{atm/k} \cdot \text{mol}\right) }{2.50\text{ L}} = 17.6 atm
Compare this pressure with that calculated using the van der Waals equation.
\left(P_{measured}+\frac{n^{2}a}{V_{measured}^{2} } \right) \left(V-nb\right) = nRT
P_{measured} = 16.0 atm
The actual pressure in the container is about 10% less than that calculated using the ideal gas law.