Question

Given cyclopentane at 1000kPa, calculate the following:

a) The saturation temperature associated with the pressure that you were given, assuming that the system is in vapour-liquid equilibrium. Use an equation of state method to solve this problem.

b) The molar volume of the vapour and liquid phase.

d) The fugacity at saturation.

Answer 1

Cyclopentane is a hydrocarbon with formula C₅H₁₀

Pressure Given = 1000 kPa or 1000 kilo Pascal

a)----> The Saturation Temperature needs to be calculated:

One simple and easy approach is the square-root square-root formula:

T _Sat = √ √P x 100 (where T _Sat is the Saturation temperature and P is the Pressure)

= √ √1000 x 100 = √10 √10 x 100 = (√10 x 3.16 ) x 100 = 3.16 x 3.16 x 100 = 9.9856 x 100 = 998.56^o C or equivalent to 100^o C

But, here we need to employ the State Method

State Method is also known as Direct Method or phi-phi method according to which:

p = pRTz

where p is the molar density, z is the compressibility coefficient, T is temperature and R is gas constant

Molar Density of C₅H_{10 =} 70.13 g/mol, z = 1

Gas Constant, R = 8.314 * 10³ J/ mol.K

Now, T = 1000/70.13 x 8.314 * 10³= 1000/583.06 * 10³= 171.5 K

b) The molar volume of the vapour and liquid phase is to be determined now:

V_m (Molar Volume) = M (Molar Mass)/ (Mass Density)

Here, C₅H₁₀ (Cyclepentane) Molar Mass, M = 70.1 g/mol

  C₅H₁₀ (Cyclepentane) Mass Density, = 751 kg/m³

  Thus, V_m = 70.1/751 g/mol kg/m³= .0701/751 kg/mol kg/m³ = 9.334 m³/mol