Question

Calculate the volume for n-butane at 313.28℃ and 75.92 bar according to:

1. The ideal gas equation

2. The theorem of corresponding states

3. Generalised correlation for the Compressibility factor

4. Generalised correlation for the Second virial coefficient.

Answer 1

1. For ideal gas, PV=RT;

V=RT/P where R=0.0821 litre atm k^-1,T= 313.28C or 586.4K and P= 75.92bar or convert into atm P=74.92atm

therefore, V= 0.0821X586.4/ 74.92

= 0.642 litres

2. For law of corresponding states, it is said that if two substances have same reduced pressure and same reduced temperatures, they must have same reduced volume. Thus,

( =

3. compressibility factor z= PV/nRT . For ideal gases, z=1 but for real gases z is less than or greater than 1 depending on P and T

4. PV=RT (1+ B/V + C/V² +.......) where cefficients B,C are known as second viral coefficient, third viral coefficient and so on. (note: viral means force in latin)

thus z = 1+ B/V = 1+ BP/RT ( putting V= RT/P)

z = 1+ B X 74.92/0.0821 X 586.4 = 1+ 1.55 B

and then calculating V as V = zRT/P