4. Determine expressions for the critical point using the van der Waals equation of state. a. the critical point will occur at the point of inflection in the P-V isotherm, which can be found as a zero in both the first and second derivative of P with respect to V (holding T constant). (Hint, you'll have two equations and two unknowns - T and V at the critical point; assume one mole). b. Use the Vc and Tc you just found and substitute back into the equation of state to solve for the critical pressure (Pc). c. The van der Waals parameters for CO₂ are a=3.59 L2 atm/mol² and b=0.0427L/mol. Calculate the critical pressure and temperature for CO₂.

4. Determine expressions for the critical point using the van der Waals equation of state. a. the critical point will occur at the point of inflection in the P-V isotherm, which can be found as a zero in both the first and second derivative of P with respect to V (holding T constant). (Hint, you'll have two equations and two unknowns - T and V at the critical point; assume one mole). b. Use the Vc and Tc you just found and substitute back into the equation of state to solve for the critical pressure (Pc). c. The van der Waals parameters for CO₂ are a=3.59 L2 atm/mol² and b=0.0427L/mol. Calculate the critical pressure and temperature for CO₂.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter1: Gases And The Zeroth Law Of Thermodynamics

Section: Chapter Questions

Problem 1.32E

See similar textbooks

Similar questions

P1A.5 Deduce the relation between the pressure and mass density, ρ, of a perfect gas of molar mass M. Confirm graphically, using the following data on methoxymethane (dimethyl ether) at 25 °C, that perfect behaviour is reached at low pressures and the molar mass of the gas. p/kPa 12.223 25.20 36.97 60.37 85.23 101.3 ρ/(kgm–3) 0.225 0.456 0.664 1.062. 1.468 1.734
Consider Argon (Ar) gas at a pressure of 1 bar and temperature of 300 K. The equivalent hardsphere radius (known as the Van Der Waal radius) of an Argon molecule is 188 picometers (pm)and its atomic mass is 39.948u. Note that 1u = 1.6605 x 10-27kg. a)How many molecules are contained in a cube 1 cm by 1 cm by 1 cm? b)Estimate the mean free path. At scales much larger than this, a continuum description holds. c)What is the density of the gas? d)Estimate the "root mean squared" molecular speed, i.e. SQRT( (V^2) ) e)Estimate the dynamic and kinematic viscosities. Compare these with literature values, forexample from webbook.nist.edu. f) Plot the variation of dynamic viscosity with temperature in the range between 300K and3000K at a fixed pressure of 1 bar. Use Matlab, Python, Mathematica, or any other softwareyou may choose.
The Dieterici equation of state is similar to the van der Waals equation in that they both employ gas-specific constants a and b to attempt to account for the interaction between molecules and the nonzero volume of the individual molecules of gas. However, the Dieterici equation of state has a significantly different functional form: ?(? − ?) = ??? -a ⁄ (RVT) Note that a and b are constants (n is implicitly constant as volume is expressed as molar volume). What are the following partial derivatives for the Diererici equation of state? a) (∂P/∂T)V b) (∂V/∂P)T
Calculate the molar volume of methane at 300 K and 100 atm given that the second virial coefficient (B’) of methane is -0.0017 atm-1. Assume that all other coefficients are zero. Compare you results with that obtained using the ideal gas equation and the van de Waals Equation of Sate if P =45.4atm;V =0.0990Lmol-1 andT =190.2K
Show complete solutions and enclose all final answers in a box. Round off final answers to 4 decimal places and use floating values for intermediate answers. A gas column is separated into two segments by a non-permeable partition. On the first segment is 1.63 moles of Helium with volume V1 and on the second segment is 3.84 moles of Oxygen gas with volume V2. Consider both gases to be ideal and at the same pressure P and temperature T. If the partition is removed, calculate the change in entropy of the gaseous system.
The molecular weight of two components A and B of a gas mixture are 24 and28 respectively. The molecular weight of gas mixture is found to be 30. If themass concentration of the mixture is 1.2 kg/m3, compute the following:a) Density fo component A and Bb) Molar Fractionsc) Mass fractionsd) Total pressure if the temperature of the mixture is 290K
A certain gas obeys the van der Waals equation with a = 0.54 m6.Pa.mol−2. Its volume is found to be 2.5 × 10−4 m3.mol−1 at 293 K and 2.0 MPa. Calculate the van der Waals constant (b) and the compression factor (z) for this gas at the prevailing temperature and pressure? R = 8.3145 JK-1mol-1, 1 Pa.m3 = 1 J
The virial equation of state may also be written as an expansion in terms of pressure: Z = 1 + B'p + ... The critical constants for water, H2O, are 218.3 atm. 55.3 cm3 mol-1 and 647.4 K. Assuming that the expansion may be truncated after the second term, calculate the value of the second virial coefficientB' at the critical temperature.
Use the virial equation of state to calculate the pressure exerted by 1.00 mol CH4, at 273 K confined to a volume of 1.00 cm3 , given the value of the second virial coefficient, B = -53.6 cm3 mol-1, at this temperature. You may assume that the expansion may be truncated after the second term.
Given the van der Waals constants for ethane gas as a = 5.562L2bar/mol2, b = 0.06380L/mol, for 10.0 mol of ethane at 300 K and under 30 bar i.Calculate the second virial coefficient B at this temperature. ii.What does this imply about the nature of the interactions between the molecules at this temperature? iii.Calculate the compression factor (Z) from the first two terms of the virial equation of state. iv. Estimate the molar volume from Z.
P1A.3 The following data have been obtained for oxygen gas at 273.15K. From the data, calculate the best value of the gas constant R. p/atm 0.750 000. 0.500 000 0.250 000 Vm/(dm3 mol−1) 29.8649 44.8090 89.6384
Given the van der Waals constants for ethane gas as a = 5.562 L2bar/mol2, b = 0.06380L/mol, for 10.0 mol of ethane at 300 K and under 30 bar, [9]i. Calculate the second virial coefficient B at this temperature.ii. What does this imply about the nature of the interactions between themolecules at this temperature?iii. Calculate the compression factor (Z) from the first two terms of the virialequation of state.iv. Estimate the molar volume from Z