2) a) Virial equation of state of real gases is expressed as Z = (PV / nRT) = 1 + (nB / V) + (n2C / V2). Derive the second virial coefficient B and the relation expressing the 3. virial coefficient C depending on the constants a and b in the van der Waals equation. b) The volume of a gas conforming to the van der Waals equation at a certain temperature and pressure of 4.00 x 106 Pa is 4.00 x 10-4 m3 / mol. For this gas, calculate the first and second Virial coefficients since it is known as a = 0.76 m6 Pa mol-2 and b = 0.13 lt / mol.

Q: P1C.12 The critical constants of a van der Waals gas can be found by setting the following…

A: GIVEN: To Calculate: Vc=? Pc=? Tc=?

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Q: The molar volume of oxygen, O2, is 3.90 dm3 mol-1 at 10.0 bar and 200 °c. Assuming that the…

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Q: The van der Waals equation of state for a real gas is P+ V-nb =nRT y2 In this equation, the van der…

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Q: For a van der Waals gas with given values of a and b, identify the conditions for which Z < 1 and…

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Q: 2. Deduce the first four virial coefficients of (ii) a Van der Waals gas.

A:

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Q: 20. A mixture consisting of 6 kg of O, and 9 kg of N, has a pressure of 3 bar and temperature of…

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Q: What are the following partial derivatives for the van der Waals equation of state? The number of…

A: Given:  Vander wall equation of state   (P+a/V2) (V-b) = RT To Determine: a) (∂P/∂a)V,T,b     b)…

Q: Calculate the density of propane (C3H8) gas given p = 10° Pa and T = 273.15 K.

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Q: Explain how the function pv/RT can be used to show gases behave non-ideally at high pressure.

A:

Q: 1. i. Carbon dioxide (CO2) is a major greenhouse gas when it diffuses into the earth atmosphere.…

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Q: given these virial equations:  Z = 1 + 2B’ p + 3 C’ p2 + D’ p3 + E’ p4 + ….. Z = 1 + 4B (1/Vm) +…

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Kinetic-Theory of Gases

Kinetic theory of gases is the model or method which was developed in the 19th century by Maxwell and Boltzmann. This is possible as the interatomic force which is of short-range forces that are important for solids and liquids can be neglected for gases. This theory or gas law gives a molecular interpretation of the pressure and temperature of a gas and is consistent with gas laws and Avogadro’s hypothesis. This theory is very helpful to correctly explain the specific heat capacities of many gases, kinetic energy and it also explains the transport qualities such as viscosity, thermal conductivity, and diffusion with molecular parameters. As stated in the kinetic-molecular theory, the temperature of a substance or gas particle is related to the average kinetic energy of the particles of that substance. When a substance is heated, some of the absorbed energy is stored within the particles, while some of the energy increases the motion of the particles, called average kinetic energy.