Question

The following equations of state are occasionally used for the approximate calculation on gases:
Gas(X): $ RT\left( {1 + \dfrac{b}{{{V_m}}}} \right) $
Gas(Y): $ p\left( {{V_m} - b} \right) = RT $
Assuming that the gas(X) and (Y) actually obeyed above equation of state respectively then choose the correct statement:
(A) Gas (X) is more liquefiable than gas (Y)
(B) Gas (X) and Gas (Y) both are liquefiable
(C) Neither gas (X) nor gas (Y) is liquefiable
(D) Gas (Y) is more liquefiable than gas (X)

Answer 1

Hint: The equation of state is an equation which relates the variables of state like T,P,V. further as we know that the given equation resembles the vander waals equation that is studied under thermodynamics.

Complete step by step solution:
Firstly as it is given here that the equations of state so we will firstly discuss about it in detail. So, the equation of state is an equation which relates the variables of state like T,P,V. It's basically useful when you get to know the effect of a change in one of the variables of state. further as we know that the given equation resembles to the vander waals equation that is studied under thermodynamics.further as we know that the ideal gas equation is given as :
 $ PV = nRT $
Further when we talk about the volume we come to know that the volume that the real gas takes up gets replaced as $ \left( {{V_m} - b} \right) $ according to the vander waals equation also here the $ {V_m} $ stands for molar volume.further when put this in the above equation it becomes:
 $ p\left( {{V_m} - b} \right) = RT $
Further talking about the compressibility of the ideal gas we come to know that it is given by the equation according to the vander waal :
 $ RT\left( {1 + \dfrac{b}{{{V_m}}}} \right) $
Hence from this discussion we come to know that the correct option is B (Gas (X) and Gas (Y) both are liquefiable).

Note:
We should know that the vander waals equation is mathematically simple but it nevertheless predicts experimentally observed transition between vapour and liquid and further predicts critical behaviour.