Question

Calculate the density as a real gas of 1 mol of nitrogen gas at -106 ° C and 100 atm. The critical parameters are Pc = 33.5 atm and Tc = 126.20 K.

Answer 1

Given,

Moles of gas =1

The pressure of the gas = 100 atm

P_c = 33.5 atm and T_c = 126.20 K , T = -106^o C = (273 - 106 ) K = 167 K

Real gas law .....

( P + a / V²) ( V - b) = RT ------------------- i

Now , a = 27R²T_c² / 64 P_c = 1.35 , where R = 0.0821 atm.L. mol^-1K^-1

b = RT_c / 8P_c = 0.039

Putting the values in equation i , we get

(100 + 1.35 / V²) ( V - 0.039) = 0.0821*167

=> (100V³ + 1.35 V - 3.9 V² - 0.05265) - 13.7107V² = 0

Only real value of V is

V = 0.091 L

Now , 1 mole of nitrogen means 28 grams of molecular weight.

Hence density = Mass / Volume = 28 / 0.091 = 341.047 g / l