For a van der Waals gas, which of the following statements are correct?

AAt very low pressure the equation reduces to $P V_{m} = RT - \frac{a}{V _{m}}$ when $b$ is neglected
BAt very high pressure the equation reduces to $P V_{m} = RT + P b$ when $a$ is neglected
CThe constant $b$ equals the actual volume of one mole of molecules
DThe quantity $a / V_{m}^{2}$ is often called the internal pressure of the gas

Answer: A, B, D

At low pressure

V_{m}

is large, so

V_{m} - b \approx V_{m}

and

(P + a / V_{m}^{2}) V_{m} = RT

gives

P V_{m} = RT - a / V_{m}

(A true). At high pressure

a / V_{m}^{2}

is small compared with

P

, so

P (V_{m} - b) = RT

gives

P V_{m} = RT + P b

(B true).

b

is four times the actual molecular volume per mole, not equal to it (C false).

a / V_{m}^{2}

is the correction to pressure due to attraction and is called the internal or cohesive pressure (D true).