Page 71 - Modern physical chemistry

60 Gases and Collective Properties

From formulas (3.104) and (3.105), we see that

Questions
3.1 What do we mean by collective behavior?
3.2 Define macroscopic (thermodynamic) state, extensive property, intensive property.
3.3 Cite examples of extensive and intensive properties.
3.4 What is a phase?
3.5 Distinguish between steady and equilibrium states.
3.6 Define ideal gas.
3.7 What role do collisions play in a gas?
3.8 How can we neglect collisions in deriving the law PV = (2/3) E tr?
3.9 Define heat, thermal agitation.
3.10 When is E t! N a measure of temperature T?
3 11 How did we introduce the Boltzmann constant?
3 12 What determines the unit of temperature?
3.13 How may (a) R, (b) To be measured?
3.14 What is the ideal gas law? How does it apply to a gaseous solution?
3.15 What is the energy associated with (a) a translational mode, (b) a rotational mode, (c) a
vibrational mode, classically excited?
3.16 How do quantum restrictions alter these results?
3.17 Give an approximate justification for the van der Waals equation.
3.18 How are parameters a and b for the van der Waals equation determined?
3.19 How is the law of corresponding states a generalization of the van der Waals equation?
3.20 Define the virial coefficients.
3.21 Show how equivalent particles are distributed in a potential field at equilibrium.
3.22 On what symmetries is the Maxwell distribution law based?
3.23 Derive the Maxwell distribution law.
3.24 What physical processes lead to the distributions described by the Boltzmann and
Maxwell laws?
3.25 Show how the collision rate density is determined.

Problems
3.1 What is the translational energy of the molecules in an ideal gas that fills 3.251 at 0.932 atm?
3.2 Calculate the root-mean-square speed of a benzene gas molecule at 100° C.
3.3 What is the density of molecules in a vacuum of 1.00 x 10-3 torr at 25° C?
3.4 At 730 torr pressure and 27° C a given amount of oxygen filled 5.00 1. Calculate (a) the
number of moles, (b) the number of molecules, and (c) the weight in the system.
3.5 A 1.000 1 vessel at 20° C contains 2.50 g N 2 , 1.05 g ° , and 0.56 g CO 2 , Calculate the partial
2
pressure of each gas and the total pressure, assuming ideal conditions.
3.6 The following densities were obtained for methyl chloride:
Pressure, atm 1.0000 0.5000 0.2500
Density at 0° C, g 1-1 2.3074 1.1401 0.5666
Calculate the ratio of density to pressure at each pressure. Consider this ratio to be a linear
function of pressure and extrapolate to zero pressure. From the result, calculate the mole-
cular mass of methyl chloride.