Page 72 - Modern physical chemistry

References 61

3.7 (a) What is the rotational energy of 1.000 g oxygen molecules at 25 0 C? (b) What is the rota-
tional energy of 1,000 mol benzene molecules at 100 0 C?
3.8 What is the molecular diameter of a sulfur molecule, if its critical temperature is 1313 K and
its critical pressure 116 atm?
3.9 Calculate the volume occupied by 1.000 mol water at 500 0 C and 200 atm pressure using (a)
the ideal gas equation (b) the compressibility factor from figure 3.4.
3.10 For molecular nitrogen at 25 0 C, calculate (a) the cross section, (b) the mean relative speed,
and (c) the collision rate density at 1.000 bar. Consider the effective radius of N2 to be 1.90
A under the given conditions.
3.11 Calculate the hypothetical. maximum specific reaction rate kAA for the process in problem 3.10.

3.12 A strip of ideal rubber has the equation of state

where F is the force needed to stretch the strip to length L at absolute temperature T while
¢(L) represents a function of L. If 100 g force stretches a rubber band 1.00 cm at 0 0 C, how
much force is needed to cause the same elongation at 35 0 C?
3.13 At what temperature is the root-mean-square speed of an O2 molecule the same as that of
an H2 molecule at _90 0 C? What is this speed?
3.14 Assume that the rate of flow of a gas through a small hole is nearly proportional to the mean
speed of its molecules and that the mean speed is proportional to the root- mean-square speed.
Calculate how long it will take for a millimole of He to flow through a pinhole under the same
driving pressure and temperature used to force a millimole of H2 through in 10.0 min.
3.15 What is the translational energy of 1.000 g oxygen molecules at 25 0 C?
3.16 Calculate the energy associated with thermal agitation in 1.000 mol hydrogen molecules
at 100 0 c .
3.17 Calculate the volume occupied by 1.000 mol HzO at 500 0 C and 200 atm pressure using van
der Waals' equation. In this calculation, an approximate V may be employed in the a/V'2 term;
the resulting linear equation is solved. An improved V may be estimated and used in a/V'2 .
The new linear equation is then solved. Repeat until successive approximations check.
3.18 In a thermonuclear plasma, there are 1.00 x 10 21 ions per cubic meter and the same con-
centration of electrons. The average energy of an ion and of an electron is 30 keY. Calcu-
late the pressure P, remembering that 1 eV is 1.602 x 10- 19 J.
3.19 Using the Berthelot equation, calculate the temperature at which 0.400 mol CO2 fills 10.01
at o. 900 atm pressure.
3.20 Suppose that the atmosphere is at equilibrium at 25 0 C and that the partial pressure of N2
at ground level is 0.800 atm. Then what is its partial pressure at an altitude of 10.0 km?
3.21 Calculate the collision rate density for the reaction

H+Br2 ~ HBr+ Br
at 25 0 C and 1.000 bar, when the mole fraction of Br2 is 0.500 and that of H 0.000100. Take
the effective radii of H and Br2 to be 1.00 A and 2.35 A, respectively.
3.22 For the reaction in problem 3.21, calculate the hypothetical specific reaction rate kAB at 25 0 C.

References
Books

Curtiss, C. F.: 1967, "Real Gases," in Eyring, H. (editor), Physical Chemistry An Advanced Trea-
tise, vol. II, Academic Press, New York, pp. 285-338.
Curtiss considers how the virial coefficients for a given substance are related to various
intermolecular potentials for the material. Statistical mechanical formulas are employed.