Kinetic energy of gasses (theory questions) Flashcards
Two H2 molecules can react with one O2 molecule to produce two H2O molecules. How many
moles of hydrogen molecules are needed to react with one mole of oxygen molecules?
2 moles, as that will contain twice as many molecules as the 1 mole of oxygen
A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas
is measured to indicate its temperature?
pressure
In the last chapter, free convection was explained as the result of buoyant forces on hot fluids.
Explain the upward motion of air in flames based on the ideal gas law.
The flame contains hot gas (heated by combustion). The pressure is still atmospheric pressure, in
mechanical equilibrium with the air around it (or roughly so). The density of the hot gas is
proportional to its number density N/V (neglecting the difference in composition between the gas
in the flame and the surrounding air). At higher temperature than the surrounding air, the ideal
gas law says that / = / N V p kTB is less than that of the surrounding air. Therefore the hot air has
lower density than the surrounding air and is lifted by the buoyant force.
If one kind of molecule has double the radius of another and eight times the mass, how do
their mean free paths under the same conditions compare? How do their mean free times
compare?
The mean free path is inversely proportional to the square of the radius, so it decreases by a
factor of 4. The mean free time is proportional to the mean free path and inversely proportional
to the rms speed, which in turn is inversely proportional to the square root of the mass. That
gives a factor of sqrt(8) in the numerator, so the mean free time decreases by a factor of sqrt(2).
Why do the atmospheres of Jupiter, Saturn, Uranus, and Neptune, which are much more
massive and farther from the Sun than Earth is, contain large amounts of hydrogen and helium?
Since they’re more massive, their gravity is stronger, so the escape velocity from them is higher.
Since they’re farther from the Sun, they’re colder, so the speeds of atmospheric molecules
including hydrogen and helium are lower. The combination of those facts means that relatively
few hydrogen and helium molecules have escaped from the outer planets.
One cylinder contains helium gas and another contains krypton gas at the same temperature.
Mark each of these statements true, false, or impossible to determine from the given information.
(a) The rms speeds of atoms in the two gases are the same. (b) The average kinetic energies of
atoms in the two gases are the same. (c) The internal energies of 1 mole of gas in each cylinder
are the same. (d) The pressures in the two cylinders are the same.
a. false; b. true; c. true; d. true
An ideal gas is at a temperature of 300 K. To double the average speed of its molecules, what
does the temperature need to be changed to?
1200 K
Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is
at atmospheric pressure when the bulb has a temperature of 20.0 C° . (a) Find the gauge pressure
inside such a bulb when it is hot, assuming its average temperature is 60.0 C° (an
approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b)
The actual final pressure for the light bulb will be less than calculated in part (a) because the
glass bulb will expand. Is this effect significant?
a. 0.137 atm. b. 0.99973
Calculate the number of moles in the 2.00-L volume of air in the lungs of the average person.
Note that the air is at 37.0 C° (body temperature) and that the total volume in the lungs is
several times the amount inhaled in a typical breath as given in the example Calculating the
Number of Molecules in a Cubic Meter of Gas.
7.84 x 10^-2
A company advertises that it delivers helium at a gauge pressure of in a
cylinder of volume 43.8 L. How many balloons can be inflated to a volume of 4.00 L with that
amount of helium? Assume the pressure inside the balloons is and the temperature
in the cylinder and the balloons is 25.0 °C .
1.87 x 10^3
An expensive vacuum system can achieve a pressure as low as 27– × 10 00.1 N/m at 20 degrees celcius
How many molecules are there in a cubic centimeter at this pressure and temperature?
2.47 x 10^7
- A bicycle tire contains 2.00 L of gas at an absolute pressure of 25 × 10 00.7 N/m and a
temperature of 18.0 C° . What will its pressure be if you let out an amount of air that has a
volume of 100 cm^3 at atmospheric pressure? Assume tire temperature and volume remain
constant.
6.95 x 10^5 Pa; 6.86 atm
Calculate the depth to which Avogadro’s number of table tennis balls would cover Earth.
Each ball has a diameter of 3.75 cm. Assume the space between balls adds an extra 25.0% to
their volume and assume they are not crushed by their own weight.
40.7 km
Five bicyclists are riding at the following speeds: 5.4 m/s, 5.7 m/s, 5.8 m/s, 6.0 m/s, and 6.5
m/s. (a) What is their average speed? (b) What is their rms speed?
Solution
a. 5.88 m/s; b. 5.89 m/s
Typical molecular speeds )( rms v are large, even at low temperatures. What is rms v for helium
atoms at 5.00 K, less than one degree above helium’s liquefaction temperature?
177 m/s
The escape velocity from the Moon is much smaller than that from the Earth, only 2.38 km/s.
At what temperature would hydrogen molecules (molar mass is equal to 2.016 g/mol) have a
root-mean-square velocity rms v equal to the Moon’s escape velocity?
458 K
There are two important isotopes of uranium, U 235 and U 238 ; these isotopes are nearly
identical chemically but have different atomic masses. Only U 235 is very useful in nuclear
reactors. Separating the isotopes is called uranium enrichment (and is often in the news as of this
writing, because of concerns that some countries are enriching uranium with the goal of making
nuclear weapons.) One of the techniques for enrichment, gas diffusion, is based on the different
molecular speeds of uranium hexafluoride gas, UF6 . (a) The molar masses of U 235 and
are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their typical speeds rms v ? (b)
At what temperature would their typical speeds differ by 1.00 m/s? (c) Do your answers in this
problem imply that this technique may be difficult?
a. 1.004; b. 764 K; c. This temperature is equivalent to 915 ºF , which is high but not impossible
to achieve. Thus, this process is feasible. At this temperature, however, there may be other
considerations that make the process difficult. (In general, uranium enrichment by gaseous
diffusion is indeed difficult and requires many passes.)
Dry air consists of approximately 78% nitrogen, 21% oxygen, and 1% argon by mole, with
trace amounts of other gases. A tank of compressed dry air has a volume of 1.76 cubic feet at a gauge
pressure of 2200 pounds per square inch and a temperature of 293 K. How much oxygen does it
contain in moles?
65 mol
(a) Given that air is 21% oxygen, find the minimum atmospheric pressure that gives a relatively
safe partial pressure of oxygen of 0.16 atm. (b) What is the minimum pressure that gives a partial
pressure of oxygen above the quickly fatal level of 0.06 atm? (c) The air pressure at the summit of
Mount Everest (8848 m) is 0.334 atm. Why have a few people climbed it without oxygen, while some
who have tried, even though they had trained at high elevation, had to turn back?
a. 0.76 atm; b. 0.29 atm; c. The pressure there is barely above the quickly fatal level.
A sealed, rigid container of 0.560 mol of an unknown ideal gas at a temperature of 30.0 °C is
cooled to −40.0 °C. In the process, 980 J of heat are removed from the gas. Is the gas
monatomic, diatomic, or polyatomic?
polyatomic
Heliox, a mixture of helium and oxygen, is sometimes given to hospital patients who have
trouble breathing, because the low mass of helium makes it easier to breathe than air. Suppose
helium at 25 °C is mixed with oxygen at 35 °C to make a mixture that is 70% helium by mole.
What is the final temperature? Ignore any heat flow to or from the surroundings, and assume the
final volume is the sum of the initial volumes.
29.2 °C
Find the rms speed for nitrogen
molecules at 295 K.
513 m/s
At what temperature do oxygen molecules have the same rms speeds as helium atoms (M = 4 g/mol)
have at 300 K?
2400 K
