The van der Waals coefficients of CO2 are: a=3.6 atm dm^6 mole^-2 b =4.3 x10^-2
ID: 869033 • Letter: T
Question
The van der Waals coefficients of CO2 are: a=3.6 atm dm^6 mole^-2 b =4.3 x10^-2 dm3 mole^-1 For He, they are: a=0.03 atm dm^6 mole^-2 b=2.4 x10^-2 dm^3 mole^-1 a) What are the critical temperature, the critical pressure, and the critical volume of CO2 and He? (5 pts) b) At, approximately, what pressure and temperature will one mole of He be in the same state as, and behave in a similar way to, one mole of CO2 at 145 K and 73 atmosphere. Describe what that state is (i.e. liquid, gas )? (10 pts) c) Suppose you exert a very large pressure on one mole of He. How small can you possibly make the volume, according to the van der Waals equation? Same question for CO2. Why do you think the minimal volume for CO2 is larger than that of He? (10 pts)Explanation / Answer
a) Tc=critical temperature=8a/27bR
Pc=critical pressure=a/27b2
Vc=critical volume=3nb
R=universal gas constant=0.082 dm3 atm k-1 mol-1
n =number of moles
For CO2,
using above equations,
Tc=8*3.6/27*4.3*10-2 * 0.082=302.51 k
Pc=3.6/27*4.2*10-2=3.174 atm
Vc=3*4.2*10-2=0.126dm3
For He,
using above equations,
Tc=8*0.03/27*2.4*10-2 * 0.082=4.519 k
Pc=0.03/27*2.4*10-2=0.462 atm
Vc=3*2.4*10-2=0.072dm3
b
c)He is more compressible than Co2 .So the minimal volume of Co2 is larger than He
compressibility factor for co2= Z=1+bP/RT
=1+4.3*10-2/0.082 * 273
=1.001(ideal) less compressible
compressibility factor for He=1+bP/RT
=1+2.4*10-2/0.082 * 273=0.0001 (less) more compressible
Volume cant be decreased much for CO2 at STP
.
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