Volume using Compressibility Factor

[MechE2015]

Homework Statement

Find the volume of 2 kg of ethylene at 270 K, 2500 kPa using Z

Homework Equations

Method to Solve for Z, Using Tr and Pr

PV = ZnRT

The Attempt at a Solution

Tr = 0.9561
Pr = 0.496
Z found to be approx. 0.75
R given on a table at 0.2964 kJ/kg K

From here, I should have all information needed, I was just confused on units at this point.
V = ZnRT/P
V = (0.75)*(n)*(0.2964 kJ/kg K)*(270 K) / (2500 kPa)

At this point, my main questions are (probably very simple):

What is n, and why? My best guess: (2000 g)/(28 g/mol) = 71.43 mol

What are units for P? My best guess: atm, -> 2500 kPa*24.67 atm/kPa = 61675 atm

Using these numbers, I get Volume to be way too low, corrections needed somewhere. Help appreciated.

 

[thepatient]

Homework Statement

Find the volume of 2 kg of ethylene at 270 K, 2500 kPa using Z

Homework Equations

Method to Solve for Z, Using Tr and Pr

PV = ZnRT

The Attempt at a Solution

Tr = 0.9561
Pr = 0.496
Z found to be approx. 0.75
R given on a table at 0.2964 kJ/kg K

From here, I should have all information needed, I was just confused on units at this point.
V = ZnRT/P
V = (0.75)*(n)*(0.2964 kJ/kg K)*(270 K) / (2500 kPa)

At this point, my main questions are (probably very simple):

What is n, and why? My best guess: (2000 g)/(28 g/mol) = 71.43 mol

What are units for P? My best guess: atm, -> 2500 kPa*24.67 atm/kPa = 61675 atm

Using these numbers, I get Volume to be way too low, corrections needed somewhere. Help appreciated.

Take a look at your units. If you're using kj/kg K for R, you should use equation:
PV = mRT, where R is the gas constant for that gas and m is the mass in kilograms. If you use PV = nRuT (Where Ru is the universal gas constant), then you'll need to use the number of moles.

Also, use the fact that 1 Pa*m^3 = 1 J.