Physical Chemistry Real gases Estimate a molar volume e Estimate the molar volume of CO 2 at 500 K and 100 atm by treating it as a van der Waals gas.(the van der waals e coefficients of cO are: a=3.592 atmL2 mo1- 2. 6=4267x10-2L mo Answer Vn3-0453V2+(3.59×102)n-(1.53×10-3)=0 Solve for the molar volume =0.366Lmol1 For a perfect gas =0.410LmOl RT(8:206×102 Latmk- mol)×(500K) 0.410Lmol1 100atm
Estimate a molar volume Estimate the molar volume of CO2 at 500 K and 100 atm by treating it as a van der Waals gas. (the van der Waals coefficients of CO2 are: a=3.592 atmL2mol-2 , b=4.26710-2 L mol-1 ) Answer. Solve for the molar volume 1 0.366 − V = Lmol m For a perfect gas 1 0.410 − V = Lmol m 1 2 1 1 0.410 100 (8.206 10 ) (500 ) − − − − = = Lmol atm LatmK mol K P RT 0.453 (3.59 10 ) (1.53 10 ) 0 3 2 2 3 − + − = − − Vm Vm Vm Physical Chemistry Real Gases
Physical Chemistry Real gases Equation of State(eos) The van der Waals and R-K equations are cubic equations of state a cubic algebraic equations al ways has three roots e above the critical temperature T two of the roots are complex numbers, one will be a real number At the critical temperature t three equal real roots Below the critical temperature To three unequal real roots a cubic equation of states isotherm in the two-phase region below Te will resemble the dotted line in Fig. 8.3
Equation of State (eos) The van der Waals and R-K equations are cubic equations of state. Physical Chemistry Real Gases A cubic algebraic equations always has three roots. Above the critical temperature Tc , two of the roots are complex numbers, one will be a real number. At the critical temperature Tc , three equal real roots. Below the critical temperature Tc , three unequal real roots. A cubic equation of states isotherm in the two-phase region below Tc will resemble the dotted line in Fig. 8.3
Physical Chemistry Real gases Condensation P H HO G 4000C 374°C 3000C L+Ⅴ 200°C K Isotherms of ho
Condensation Physical Chemistry Real Gases Isotherms of H2O Vm 400 oC U R J N Y 374 oC 300 oC 200 oC H2O L + V L V L G H T S K M W P l Vm v Vm
Physical Chemistry Real gases virial equation of state PVm=RT[+B(T)P+C(T)P2+D'(T)P+1(8.5 A more convenient expansion is(in many applications B C PIm=rt1+2+g+ PV=RT first second third coefficients The virial equation is an example of a common procedure in physical chemistry, in which a simple law is treated as the first term in a series in powers of a variable(por ym)
virial equation of state [1 '( ) '( ) '( ) ] PVm = RT + B T P +C T P 2 + D T P 3 + (8.5) = 1+ + 2 + m m m V C V B PV RT A more convenient expansion is (in many applications) PVm = RT first second third coefficients The virial equation is an example of a common procedure in physical chemistry, in which a simple law is treated as the first term in a series in powers of a variable (P or Vm). Physical Chemistry Real Gases