Answer to Question #179197 in Inorganic Chemistry for Vinay

Question

Write the equation of the corresponding states and explain the meaning of the terms involved in it.

Answer 1

Ideal gas equation of state is PV =RT for one mole of gas

Van der Waals equation of state proposed the following equation to explain the P-V-T behaviour of real gases

The pressure term in ideal gas equation replaced by P + (a/V²)

and Volume term is replaced by (V - b )

Where b is the volume per mole of the gas

(P + a/V²)(V-b) = RT

V is the molar volume of the gas

V_C = 3b,. T_C = 8a/27Rb.

P_C = (RT_C/2b)-(a/9b²)

on solving equations of T_C and V_C we get Van der Waals constants as

a= 27R²T_C²/64P_C

b= RT_C/8P_C

T_C and P_C are critical temperature and critical pressure

a and b are the van der Waals constant

P is the actual pressure of the gas

The principal states that all gases when compared at the same reduced temperature and the reduced pressure, have approximately the same compressibility factor and all deviate from the ideal behaviour to the same extent

Reduced pressure P_r = P/P_C

Reduced temperature T_r = T/T_C and

Reduced Volume V_r = V/V_C

Where V, T and P are the actual Volume, temperature and pressure

(P_r + 3/V_r²)(3V_r - 1) = 8T_r ________(a)

above equation is known as Van der Waals equation of state in reduced formed