Question

 Estimate the following: (a) The volume occupied by 18 kg of ethylene at 328.15 K (55°C) and 35 bar. (b) The mass of ethylene contained in a 0.25-m3 cylinder at 323.15 K (50°C) and 115 bar. 

Answer 1

Part a

$T_r=\frac{T}{T_c}=\frac{328.15}{282.3}=1.162 ; P_r=\frac{P}{P_c}=\frac{35}{50.4}=0.694$

From the table , $Z_o=0.838, Z_1=0.033$

The correlation of the comprehensibility factor is $Z= Z_0+ωZ_1 = 0.838+0.087*0.033=0.841$

Hence, PV=ZnRT$\implies n = \frac{m}{M}= \frac{18}{28}=0.6428 Kmol$

$V= \frac{ZnRT}{P}= \frac{0.841*0.6428*10^3*8.314*32815}{35*10^5}=0.421 m^3$

Part b

$T_r=\frac{T}{T_c}=\frac{323.15}{282.3}=1.145 ; P_r=\frac{P}{P_c}=\frac{115}{50.4}=2.282$

From the table , $Z_o=0.482, Z_1=0.126$

The correlation of the comprehensibility factor is $Z= Z_0+ωZ_1 = 0.482+0.087*0.126=0.493$

Hence, PV=ZnRT$\implies n = \frac{PV}{ZRT}= \frac{115*10^5*0.25}{0.493*8.314*323.15}=2.171 Kmol$