Recall that the van der Waals equation of state—an extension of the ideal gas equation—attempts to better capture the behavior of real gases. It can be written to parallel the PV = nRT form of the ideal gas equation:
(P + an2/V2) (V − nb) = nRT
a) For one mole of a van der Waals gas, derive an expression for the work done by a reversible and isothermal change in volume. In other words, evaluate the following integral for the van der Waals gas
w = − {integral with limits from v1 to v2} PdV.
b) What are physical interpretations of the van der Waals constants a and b?
c) If for helium, the van der Waals constant b is equal to 2.43 × 10–5m3 mol-1, using this value for b, calculate the diameter of the helium atom.
Trending nowThis is a popular solution!
Step by stepSolved in 4 steps with 5 images
- For both circumstances (reversible and irreversible) what is the change in enthalpy dS for the gas, the surroundings (assuming ideal isothermal bath), and the universe?arrow_forwardSuppose that attractions are the dominant interaction between gas molecules, and the equation of state is p = nRT/V – n2a/V2. Determine the work (W(non-ideal gas)) of reversible, isothermal expansion of such a gas from initial volume V (initial) = 20.0 L to final volume V(final) = 40.0 L if n = 2.00 mol, T = 300 K, and a = 3.621 atm-L2/mol2. Watch your units. Determine the work (W(ideal gas) of reversible, isothermal expansion of an ideal gas from initial volume V (initial) = 20.0 L to final volume V(final) = 40.0 L if n = 2.00 mol and T = 300 K. Show the difference W(non-ideal) – W(ideal). If all your calculations are done correctly, this result shows you the effect of attractive interaction between gas particles on the work done by the system.arrow_forwardConsider a gas obeying van der waals equation. Let one mole of the gas expands reversibly from volume ΔΗ, under isothermal condition. The expression of ORT 1 1 V ·b V -b m2 m1 bRT a V m2 1 Vm2-b V V ORT In- m1 V -b m2 V-b m1 1 m1 V b -b m for this process is: a m2 + 2a V m2 a V + m1 2a V. m1 V V m1 to m2arrow_forward
- gas undergoes an adiabatic expansion from 10 − 3 m 3 to 8 × 10 − 3 m 3 . The adiabatic line for the gas is given by P 3 V 5 = C (C is a constant). (a) Calculate the reversible work performed along the adiabatic line if the initial pressure is 10 5 P a and the initial volume = 10 − 3 m 3 . (b) What is the value of the constant C ? What is the unit of C ? (c) The gas reaches the final state in a two step process. An expansion at a constant initial pressure to the final volume followed by a decrease in pressure to the final volume 8 × 10 − 3 m 3 . What is the reversible work and heat in this process?arrow_forward4. Calculate the work done under isothermal conditions for 5.5 mols of an ideal gas expanding from 10.0 bar to 2.00 bar at –20.0°C both for a reversible (a) and irreversible (b) process. For the latter, Pext = 2.00 bar. The general expression for work is, w=-[P_dVarrow_forward(a) Suppose that attractions are the dominant interaction between gas molecules, and the equation of state is p = nRT/V – n2a/V2. Determine the work (W(non-ideal gas)) of reversible, isothermal expansion of such a gas from initial volume V (initial) = 20.0 L to final volume V(final) = 40.0 L if n = 2.00 mol, T = 300 K, and a = 3.621 atm-L2/mol2. Watch your units. (b)Determine the work (W(ideal gas) of reversible, isothermal expansion of an ideal gas from initial volume V (initial) = 20.0 L to final volume V(final) = 40.0 L if n = 2.00 mol and T = 300 K. (c) Show the difference W(non-ideal) – W(ideal). If all your calculations are done correctly, this result shows you the effect of attractive interaction between gas particles on the work done by the system.arrow_forward
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistryChemistryISBN:9781259911156Author:Raymond Chang Dr., Jason Overby ProfessorPublisher:McGraw-Hill EducationPrinciples of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning
- Organic ChemistryChemistryISBN:9780078021558Author:Janice Gorzynski Smith Dr.Publisher:McGraw-Hill EducationChemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningElementary Principles of Chemical Processes, Bind...ChemistryISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY