Question

Estimate the vapor pressure of carbon dioxide at 284 K using the Redlich-Kwong equation of state. You want your can of Coca Cola at 284 K to only have liquid in it with no vapor. Assume Coca Cola is a mixture of 4 mol % CO_2 in water. Use Raoult's law to calculate high the pressure in the can must be.

Answer 1

a) the equation of redich kwong is so we have than

RT

2 2.5 9(V2P .42748 Pe

RTC = 0.08664 3 P

now than we have the equations need the value so

R = 0.082atm l /mol K for the CO₂ the pressure critc is 72.8atm and your Tc is 30.98C = 303.98K

Vm = RT to 284K the Vm = 0.082l/mol K x 284IK = 23.288l

$a = \frac{1}{9(\sqrt[3]{2}-1)}\frac{0.082^{2}303.98^{2.5}}{72.81} = 042748\frac{0.082^{2}303.98^{2.5}}{72.81}$

a = 63.60

$b = 0.08664\frac{0.082x303.98}{72.81}$

b = 0.030

remember than T is T ambien in this case 284K

RT

only replacing value and get

P = 7.33x10^-3atm

the rault laws say than the P partial of a gas = Pure for your molar fraction so

Pco = P Xco as the cocacola is a 4% M of CO₂ yout X = 4/100 = 0.04 so your Partial pressure is

Pco = 0.04x7.33x10^-3atm = 3x10^-4atm