I’m trying to understand this thermodynamics problem that I am stuck on can you

Question

I’m trying to understand this thermodynamics problem that I am stuck on can you please explain this problem

It is a 340K isotherm for a van der Waals substance with a critical point at 121°C and 121 bar 0.1 0.12 0.14 (0.16 0.18 0.06 0.08 10 (.2 (.22 0.24 0.26 0.28 0.3 10 6 A 4 0.06 0.08 (.1 (0.12 (0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 (0.3 Molar Volume (L/mol) IF If 12.5 moles of this substance are confined to a 1 .00 L volume at 340K, would the actual RT a pressure be higher or lower than that found from evaluating P = V-, ET

Explanation / Answer

for the given problem
given n = 12.5 moles in V = 1 L
so molar volume = V/n = 0.08 L/molfrom the graoh this corresponds to a pressure of about 2.5 MPa

also form wanderwall's equaiton
constants are a and b
now Pc = 121 bar = 1.21*10^7 Pa
Tc = 121 C = 394.15 K

now, Pc = a/27b^2
Tc = 8a/27Rb

Tc/Pc = 8a*27b^2/27Rb*a = 8b/R
394.15/1.21*10^7 = 8b/8.31
b = 3.3836*10^-5
and a = 0.374

so P = (RT/(V - b)) - a/V^2 = (8.31*340/(0.08*10^-3 - 3.3836*10^-5)) - 0.374/(0.08*0.001)^2 [ T = 340 K given]
P = 2766035.222251 Pa

this pressure is smaller than the pressure obtained from the graph
so actual pressure is greater than the pressure obtained form the wanderwalls equationj

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