Unit 3 ICP: Gas Laws
Atmospheric pressure is produced by the force (weight) of the atmosphere above the area of measurement. At sea
level the atmospheric pressure will support a column of mercury 760 mm high.
Common units of pressure: 1 atm=760 mmHg=1.01 a 105 Pa=101 kPa
Boyle’s Law: relationship between pressure and volume
1. A sample of SF6 occupies a container of variable volume. If the sample originally occupies a volume of 50.0 ml
at 755 mmHg, calculate the pressure which must be exerted to lower the volume to 25.0 ml.
Avogadro’s Law: volume of gas is directly related to the number of moles of gas
2. 3O2 (g) → 2O3 (g)
Suppose we have a 12.2 L sample containing 0.50 moles of oxygen gas at a pressure of 1 atm and 25°C. If all of
the oxygen were converted to ozone at the same temperature and pressure what would be the volume?
Charles’ Law: relationship between temperature and volume
Gay Lussac’s Law: relationship between temperature and pressure
Temperature in problems can create a problem because 0°C can yield answers that make no sense mathematically.
Therefore, we use a temperature scale that has no zero…Kelvin scale.
K=°C+273
ANY problem involving gas laws must have temperature in Kelvin!
Combined Gas Law
3. A 545 ml sample of nitrogen gas initially at -220°C is heated to 100°C. Calculate the new volume, assuming the
pressure does not change.
4. Calculate the volume of a sample of helium at -330°C and 1.23 atm if it occupies a volume of 2.34L at 54.5°C
and 1026 mmHg.
Dalton’s Law of Partial Pressures: For ideal gases, the total pressure of a mixture is simply the sum of the pressures of
the component gases if they were alone in the container. If we collect a gas over water, the equation can be written as:
PT=Patm=PH2O + Pgas
5. Experimentally oxygen gas is frequently collected over water. When a sample of oxygen, produced from a
chemical reaction, is collected over water at 24°C, the total pressure was 765 mmHg. Calculate the pressure
due only to oxygen.
STP: 1atm and 273K
6. A 235 mL sample of gas collected over water at a temperature of 28°C and a low pressure day of 738 torr.
Report what volume it would have at dry STP conditions.
Mole Fractions: What fraction of the gas is a certain element. Can also use to determine partial pressure of the gas.
XA =
nA
nA + nB + nC +…
PA = (XA)(Ptot)
7. The mole fraction of nitrogen in air is 0.7808. Calculate the partial pressure of nitrogen in air when the
atmospheric pressure is 760 torr.
8. The partial pressure of oxygen was observed to be 156 torr with an atmospheric pressure of 743 torr. Calculate
the mole fraction of oxygen present.
Ideal Gas Law: The central equation from which all gas laws come from. Use this equation when conditions remain the
same.
PV=nRT
R=0.0821 L•atm/mol•K
1mol=22.4L at STP
9. What pressure is required to confine 0.460 mol of an ideal gas at 33.0°C in a volume of 9.50 L?
10. Determine what volume 1.00 mol of a gas at STP would occupy.
11. Calculate the density of oxygen gas at STP.
12. A compound has the empirical formula CHCl. A 256 mL flask, at 373 K and 750 torr, contains 0.80 g of the
gaseous compound. Give the molecular formula.
Gas Stoichiometry
13. Hydrogen can be prepared by passing steam through a hollow air tube which has been heated to high
temperature. Calculate the volume of hydrogen formed at 0.98 atm and a temperature of 450°C when 98.3 g of
water are passed through an iron tube.
4H2O(g) + 3Fe(s) → Fe3O4(s) + 4H2(g)
Kinetic Molecular Theory: All ideal gases behave in a certain way based on assumptions known as this theory.
1. Gases consist of submicroscopic molecules which are in continuous, random motion.
2. The disease between molecules is large compared with the size of the molecules themselves. The volume
occupied by a gas consists mostly of empty space.
3. Gas molecules have no attraction for one another.
4. Gas molecules move in straight lines in all directions, colliding frequently with one another and with the
walls of the container.
5. No energy is lost by the collision of a gas molecule or with the walls of the container. All collisions are
perfectly elastic.
6. The average kinetic energy for molecules is the same for all gases at the same temperature, and its value is
directly proportional to the absolute temperature.
GASES ARE MOST IDEAL AT HIGH TEMP AND LOW PRESSURE…why????
14. Using the postulates of the KMT, explain why pressure increases as temperature increases.
Kinetic Energy:
√
1/2 mv2 = (3/2)RT
KEavg= (3/2)RT
v=urms= (3RT/MM)
Any gas will have the same KE if it is at the same temperature; the molecules will just be moving at different speeds.
Since using energy, the R value has different units, so a different value: R=3.814 J/mol•K MM in kg/mol
A gas will diffuse at a rate that is proportional to its speed. Thus, if we were to see how one gas will diffuse compared
to another one, we should set up a ratio of their speeds.
Graham’s Law
√(3RT/MM )
= √(3RT/MM )
r1 = u1 =
1
r2 = u2
2
√MM
√MM
2
1
15. Calculate the average velocity of a sample of He atoms at 25°C?
16. Oxygen diffuses at a rate which is 2.23 times faster than a sample of a reddish-brown gas. Determine the molar
mass of the unknown gas.
17. Consider three identical flasks filled with different gases.
Flask A: CO at 760 torr at 0°C
Flask B: N2 at 250 torr and 0°C
Flask C: H2 at 100 torr and 0°C
a. In which flask will the molecules have the greatest kinetic energy? Why?
b. In which flask will the molecules have the greatest root mean square velocity? Why?
Non Ideal Gases: Postulates are for ideal gases, which do not exist! Real gases deviate from postulates 2 and 3.
 2nd Postulate – The volume occupied by a real gas is not negligible; it does occupy space. The higher the
pressure, the more gas molecules are present and the more significant their volume becomes
 3rd Postulate – Gas particles of real gases do experience attractive forces. The slower the gas molecule is
moving, the more chance it has of experiencing an attraction for another molecule.
A real gas deviates from ideal gas behavior at high pressure and low temperature!
Real Gas equation aka van der Waals equation:
a = constant unique to each gas which correct for the forces of attraction between gas particles
nb = correction factor for the finite volume of the gas particles; value of b is unique to each gas
18. Explain in terms of the van der Waal equation why hydrogen chloride is much less ideal than hydrogen gas.