1. Gases
Chapter 10

2. Characteristics of Gases
Common gases are nonmetallic elements (11) and several common compounds
Most abundant in the atmosphere:N2, O2, CO2, Ar
Greenhouse gases: CO2, CH4, SO2
When other substances are in gaseous phase, they are referred to as vapors (water vapor)
Properties: expand to fill container, compressible, show thermal expansion, diffuse rapidly to create homogeneous mixtures, show little or no interaction between particles, volume of particles is negligible (<0.1% of total volume)

3. Pressure Defined as the force applied over an area
Atmospheric pressure can be measured with a barometer – compares pressure of the atmosphere with a vacuum
F = ma agravity = 9.8 m/s2
Therefore a 1mx1m column of air has a mass of 10,000 kg.
Unit of pressure is pascal (N/m2)
1 N = 1 kgm/s2

4. Pressure conversions 101,300 Pa = 101.3 kPa 101.3 kPa = 1 atm
1 atm = 760 mm Hg
1 atm = 760 torr
Each of these values represents standard atmospheric pressure – the pressure of the atmosphere at sea level

5. Enclosed Gases
Samples of gas inside closed containers may be measured with a manometer
Closed end manometer compares the pressure of the sample to a vacuum
Open end manometers compare the sample to the atmosphere (MS MST project)
Sphygmomanometer is an everyday example of one of these devices

6. Boyle’s law
The pressure and volume of any sample of a gas are indirectly related as long as the temperature and amount of gas are constant
Mathematically, PV = k or P1V1 = P2V2
Be able to graph V vs P or V vs 1/P

7. Charles’s law
In any sample of gas, the volume and temperature will be directly related as long as the pressure and amount of gas are constant
Mathematically, V/T = k or V1/T1 = V2/T2
Be able to graph V vs T
Extrapolation of this curve allowed the calculation of absolute zero

8. Law of Combining Volumes
Described by Louis Gay-Lussac
At constant pressure and temperature, the volumes of gases that react with one another are in the ratios of small whole numbers
2H2 + O2  2H2O

9. Combined Gas Law
Incorporates Boyle’s law, Charles’s law, and the Law of Combining Volumes
As long as the amount of gas is held constant, the pressure, volume, and temperature of a sample of gas will change proportionally
Mathematically, =
A very useful application of these laws

10. Avogadro’s law
The volume of a gas maintained at constant temperature and pressure will be directly related to the number of moles of the gas
Mathematically, V/n = k or V1/n1 = V2/n2
Molar volume of any gas at STP = 22.4 L

11. Ideal gas law Mathematically, V nT/P
Proportionality implies a constant, therefore the value R was calculated
R = the ideal gas law constant
PV = nRT
The ideal gas law is completely described by the kinetic-molecular theory and the ideal gas equation

12. Ideal gas law constant Values for R: 0.08206 atmL/molK
1.987 cal/molK
8.314 J/molK
8.314 m3Pa/molK
62.36 Ltorr/molK
You should be able to interconvert any of these units
Temperature must always be Kelvin

13. Gas Density
The ideal gas law may be used to determine the density of any gas
PV = nRT may be rearranged as n/V = P/RT
The units for n/V are mol/L so multiplying both sides of the equation by the molar mass of the gas (M), density will be equal to PM/RT
Determine the density of CCl4 vapor at 714 torr and 125oC.
Answer = 4.42 g/L

14. Molar Mass
To determine the molar mass of an unknown gas, rearrange the previous formula to obtain:
M = dRT/P

15. Mixtures of Gases & Partial Pressure
Dalton’s law of partial pressure states that the sum of the partial pressures of each gas in a homogeneous mixture of gases will be equal to the total pressure of the mixture.
Mathematically, PT = P1 + P2 + … + Pn
Or, nT = n1 + n2 + … + nn
This law works with mole fractions as well…
P1 = n1 n1/n2 = X (mole fraction)
P2 n2

16. Gas Collection
Most gas samples are collected over water to ensure pure gaseous samples, however this creates a mixture of the gas and water vapor.
The pressure of the sample can be determined, but the partial pressure of water must be subtracted from the total pressure
PT = Psample + Pwater
Vapor pressure of water is dependent solely on temperature (see Appendix B)

17. Kinetic-Molecular Theory (KMT)
Model explaining the behavior of gases as conditions change
Gases consist of large numbers of molecules in continuous random motion
Volume of molecules is negligible compared to the total occupied volume
Attractive & repulsive forces between molecules are negligible
Energy may be transferred between particles in collisions, but the avg KE of molecules will not change with time (elastic collisions)
Avg KE is proportional to absolute temperature (for any given temperature, all molecules have same KE)

18. Molecular Energy
At any given temperature, all molecules have the same average kinetic energy
Some molecules have more Ek, some have less
At higher temps, a greater % of molecules are moving fast
Root-mean-square (rms) speed (u) is the speed of a molecules possessing a given amount of energy – not identical to average speed, but close in value
Avg Ek () = ½ mu2

19. Effusion/Diffusion of Gases
Effusion: ability of a gas to pass through a barrier into evacuated space
Diffusion: ability of a gas to pass through another substance or into empty space
According to KMT any gas at the same temp has the same  ( ½ mu2) therefore lighter gases must be traveling faster than heavier gases

20. Graham’s Law
The rate of effusion (diffusion) of any gas is indirectly related to the square root of its average atomic mass (M)
Hydrogen balloons deflate more rapidly than helium balloons or
for 2
gases

21. Diffusion
Diffusion is generally slower than the average molecular speed because the molecular collisions affect the rate of diffusion
Collisions constantly change the direction of the gas molecules
At STP, any particular molecule of gas experiences 1010 collisions/second
Average distance traveled by a molecule between collisions is called the mean free path; varies indirectly with pressure

22. Real Gases
Deviate from KMT and ideal gas behavior primarily for 2 reasons:
Real gases have finite volumes
Real gases exhibit attractions for other particles
This difference in behavior can be accounted for and quantized

23. The van der Waals Equation
2 corrections to the ideal gas equation:
b = actual volume occupied by a mole of gas molecules (L/mol)
a = attractive forces between molecules (L2atm/mol2)
a and b values are different for each gas, though they tend to increase as molar mass increases