Question

Consider the following statements:
$P{V}_m=RT(1+\frac{B}{V_m}+\frac{B}{V_m^2}+...)$
Then molar volume, $V_m$:

• A. is independent of temperature
• B. is equal to $\frac{RT}{P}$ at Boyle's temperature
• C. has the dimension of molar volume
• D. all of the above

Answer 1

Answer: (B), (C)

The correct options are
B is equal to $\frac{RT}{P}$ at Boyle's temperature
C has the dimension of molar volume

The temperature at which a real gas behaves like an ideal gas over an appreciable range of pressure is known as Boyle's temperature ($T_B$ ). It means that at this temperature, the value of PV remains constant for an appreciable range of pressure, i.e. Boyle's Law is obeyed. Mathematically we may express the Boyle temperature
$\delta \left(PV\right)/\delta P=0$ when $P\to 0$.
so at this temperature, molar volume $V_m=\frac{RT}{P}$