Question

For ethane, P_c = 48.2 atm and Tc = 305.4 K. Calculate the pressure exerted by 50.0 g of C₂H₆ in a 200-cm³ vessel at 37.5°C.

(c) the Redlich–Kwong equation; (d) the virial equation, given that for ethane B = -179 cm³/mol and C = 10400 cm⁶/mol² at 30°C, and B = -157 cm³/mol and C = 9650 cm⁶/mol² at 50°C.

(c) P = ? atm

(d) P = ? atm

Answer 1

Given Data:

Pc= 48.2 atm

Tc= 305.4 K

V= 200 cc

Molar Mass of ethane: 30.07 gm/mol

Weight of ethane: 50 gm

P at 37.5 ^oC= ?

First calculate, molar volume of ethane at 37.5 ⁰C,

Number moles of ethane (n): weight/molar mass= 50/ 30.07= 1.66 mol

Molar volume V_m= V/n = 200/1.66 = 120.48 cc/mol

C) Using Redlich-Kwong equation:

P= (RT/Vm-b)- (a/ (Vm (Vm+b) T^1/2))…………………i

Where a,b are constant and given by following equations

a= 0.04275 (R² Tc^2.5) / Pc …………………………..(II) &

b= 0.0866 RTc/Pc   …………………………………..(III)

Now calculate these values

a= (0.04275 * 82.057² * 305.4^2.5) / 48.2 = 97340356.6

b= (0.0866*82.057*305.4)= 45.025

Now put the values of a, b, Vm, R, T in the equation 1

P= (82.057*310.65)/(120.48-45.025) – (97340356 / 120.48 (120.48+45.025) 310.65^1/2)= 60.88 atm

d) Using Virial equation:

PVm/RT = 1+ B/Vm + C/Vm² + D/Vm³ +…………..                            (IV)

Given data for ethane B = -179 cm³/mol and C = 10400 cm⁶/mol² at 30°C, and B = -157 cm³/mol and C = 9650 cm⁶/mol² at 50°C.

Assume the terms D/Vm³ are negligible and can be ignored

Now calculate

P at 30 oC = ((82.057*303.15)/12.048) (1 + -179/120.48 + 10400/120.48²)

                   = 47.63 atm

Now P at 50 oC = ((82.057*323.15)/120.48) (1+ -157/120.18 + 9650/120.48²)

                            = 79.23 atm