Question #208547

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.

Expert's answer

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+\u03c9Z_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+\u03c9Z_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"

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