Page 36 - Physical chemistry eng

NUMERICAL PROBLEMS 13

gas thermometer macroscopic variables temperature scale
ideal gas mole fraction thermal equilibrium
ideal gas constant open system thermodynamic equilibrium
ideal gas law partial pressure thermodynamic temperature scale
intensive variable surroundings thermometer
isolated system system van der Waals equation of state
kelvin system variables wall
macroscopic scale temperature zeroth law of thermodynamics

Conceptual Problems

Q1.1 Real walls are never totally adiabatic. Use your attractive part of the potential has no influence in this expres-
experience to order the following walls in increasing order sion. Justify this behavior using the potential energy diagram
with respect to their being diathermal: 1-cm-thick concrete, of Figure 1.10.
1-cm-thick vacuum, 1-cm-thick copper, 1-cm-thick cork. Q1.9 Give an example of two systems separated by a wall
Q1.2 The parameter a in the van der Waals equation is greater that are in thermal but not chemical equilibrium.
for H O than for He. What does this say about the difference in Q1.10 Which of the following systems are open? (a) a dog,
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the form of the potential function in Figure 1.10 for the two gases? (b) an incandescent light bulb, (c) a tomato plant, (d) a can of
Q1.3 Give an example based on molecule–molecule interac- tomatoes. Explain your answers.
tions excluding chemical reactions, illustrating how the total Q1.11 Which of the following systems are isolated? (a) a
pressure upon mixing two real gases could be different from bottle of wine, (b) a tightly sealed, perfectly insulated ther-
the sum of the partial pressures. mos bottle, (c) a tube of toothpaste, (d) our solar system.
Q1.4 Can temperature be measured directly? Explain your Explain your answers.
answer. Q1.12 Why do the z and y components of the velocity not
Q1.5 Explain how the ideal gas law can be deduced for the change in the collision depicted in Figure 1.2?
measurements shown in Figures 1.5 and 1.8. Q1.13 If the wall depicted in Figure 1.2 were a movable
Q1.6 The location of the boundary between the system and piston, under what conditions would it move as a result of the
the surroundings is a choice that must be made by the thermo- molecular collisions?
dynamicist. Consider a beaker of boiling water in an airtight Q1.14 The mass of a He atom is less than that of an Ar
room. Is the system open or closed if you place the boundary atom. Does that mean that because of its larger mass, Argon
just outside the liquid water? Is the system open or closed if exerts a higher pressure on the container walls than He at
you place the boundary just inside the walls of the room? the same molar density, volume, and temperature? Explain
Q1.7 Give an example of two systems that are in equilib- your answer.
rium with respect to only one of two state variables. Q1.15 Explain why attractive interactions between mole-
Q1.8 At sufficiently high temperatures, the van der Waals cules in gas make the pressure less than that predicted by the
equation has the form P L RT>(V m - b) . Note that the ideal gas equation of state.

Numerical Problems

Problem numbers in red indicate that the solution to the prob- atmosphere if the final pressure in the cylinder is
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lem is given in the Student’s Solutions Manual. 1.80 * 10 Pa ? Assume ideal behavior and that the gas
P1.1 Approximately how many oxygen molecules arrive temperature is unchanged.
each second at the mitochondrion of an active person with a P1.3 Calculate the pressure exerted by Ar for a molar vol-
mass of 84 kg? The following data are available: Oxygen con- ume of 1.31 L mol –1 at 426 K using the van der Waals equa-
sumption is about 40. mL of O 2 per minute per kilogram of tion of state. The van der Waals parameters a and b for Ar are
–1
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body weight, measured at T = 300. K and P = 1.00 atm . In 1.355 bar dm mol –2 and 0.0320 dm mol , respectively. Is
an adult there are about 1.6 * 10 10 cells per kg body mass. the attractive or repulsive portion of the potential dominant
Each cell contains about 800. mitochondria. under these conditions?
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P1.2 A compressed cylinder of gas contains 2.74 * 10 g P1.4 A sample of propane (C H ) is placed in a closed ves-
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of N 2 gas at a pressure of 3.75 * 10 Pa and a temperature sel together with an amount of O 2 that is 2.15 times the
of 18.7°C. What volume of gas has been released into the amount needed to completely oxidize the propane to CO 2 and