Question

A gas described by van der Waals' equation:

• A. behaves similar to an ideal gas in the limit of large molar volume
• B. behaves similar to an ideal gas in the limit of large pressure
• C. is characterized by van der Waals' coefficients that are dependent on the identity of the gas, but are independent of the temperature
• D. has the pressure that is lower than the pressure exerted by the same gas behaving ideally

Answer 1

Answer: (A), (C), (D)

The correct options are
A behaves similar to an ideal gas in the limit of large molar volume
C is characterized by van der Waals' coefficients that are dependent on the identity of the gas, but are independent of the temperature
D has the pressure that is lower than the pressure exerted by the same gas behaving ideally

A) At larger molar volume, molecules will be far apart with negligible intermolecular interactions. Moreover, the volume occupied by molecules will be negligible in comparison to the molar volume. These facts lead to ideal gas behaviour.
B) In the limit of large pressure, the compressibility factor $z>1$. Hence, the gas shows deviation from ideal behavior.
C) The van der Waals constants characterize a real gas and are independent of temperature.
D) In the equation $(p+\frac{a}{V^2})(V-b)=RT$, the term $p+\frac{a}{V^2}$ corresponds to ideal gas pressure. Hence, $p_{real}<p_{ideal}$.