van der Waals Equation — Prelims Questions

For a real gas, the van der Waals equation is given by $(P + a\frac{n^2}{V^2})(V - nb) = nRT$. Which of the following statements is INCORRECT regarding the constants 'a' and 'b'?

Which of the following gases would have the highest value of the van der Waals constant 'a'?

For $1,\text{mole}$ of a real gas, the van der Waals equation is $(P + a/V^2)(V - b) = RT$. If the gas behaves ideally, what would be the value of the compressibility factor (Z)?

Given the van der Waals constants for two gases: Gas A ($a = 0.21,\text{atm L}^2 \text{mol}^{-2}$, $b = 0.017,\text{L mol}^{-1}$) and Gas B ($a = 3.59,\text{atm L}^2 \text{mol}^{-2}$, $b = 0.043,\text{L mol}^{-1}$). Which gas is expected to be more easily liquefied and why?

At very high pressures, the van der Waals equation for 1 mole of a real gas can be approximated as $P(V-b) = RT$. What does this approximation suggest about the behavior of the gas at very high pressures?

The critical temperature ($T_c$) for a gas is given by $T_c = \frac{8a}{27Rb}$. Which of the following statements is true regarding the critical temperature and liquefaction?