1. Properties of Gases Important properties of a Gas Quantity n = moles
Volume V = container size (usually L or mL)
Temperature T ≈ average kinetic energy of molecules (must be in K for all “gas laws”)
Pressure P = force/area
Units of pressure: SI unit is the pascal (Pa)
1 atm = 101,325 Pa (not commonly used) = 14.7 psi
More important:
1 mm Hg = 1 torr
1 atm = 760 torr = 760 mm Hg
Exact!

2. Measuring Pressure
Barometer
Manometer

3. Pressure - Volume - Temperature Relationships
Boyle’s Law (at constant T and n)
V ∝ 1/P or PV = constant
Charles’ Law (at constant P and n)
V ∝ T or V/T = constant
Gay-Lussac’s Law (at constant V and n)
P ∝ T or P/T = constant
Combined Gas Law (for constant n)
PV/T = constant or
(remember that T must be in units of K -- practice problems in book!)
P1V1
P2V2 = T1 T2

4. Ideal Gas Law Avogadro’s Principle The Ideal Gas Equation PV = nRT
At constant P and T, V ∝ n
i.e. at constant T and P, equal volumes of gases contain equal numbers of moles
The Ideal Gas Equation
PV = nRT
where R = “universal gas constant”
= L•atm/mole•K memorize!
{useful in many different kinds of calculations involving gases!}
Standard Molar Volume
At Standard Temperature and Pressure (0 °C and 1 atm), 1 mole of any gas occupies 22.4 L (i.e L/mol)

5. Example Problems Now use ideal gas law to find volume of C2H2:
At STP, the density of a certain gas is 4.29 g/L. What is the molecular mass of the gas?
(4.29 g/L) x (22.4 L/mol) = 96.1 g/mol
Acetylene (welding gas), C2H2, is produced by hydrolysis of calcium carbide.
CaC2(s) + 2 H2O --> Ca(OH)2(s) + C2H2(g)
Starting with 50.0 g of CaC2, what is the theoretical yield of acetylene in liters, collected at 24 °C and a pressure of 745 torr?
1st find yield in moles:
Now use ideal gas law to find volume of C2H2:

6. Dalton’s Law of Partial Pressures
For a mixture of gases: Ptotal = Pa + Pb + Pc + …
Mole fraction: Xa = moles a/total moles = Pa/Ptotal
Gases are often prepared and collected over water:
Ptotal = Pgas + Pwater
where Pwater = vapor pressure of water (depends on temperature)
e.g. at 25 °C, Pwater = torr
at 50 °C, Pwater = torr

7. Example Problem
A sample of N2 gas was prepared and collected over water at 15 °C. The total pressure of the gas was 745 torr in a volume of 310 mL. Calculate the mass of N2 in grams. (vapor pressure of water at 15 °C = 12.8 torr)
Answer:
Ptotal = Pgas + Pwater
745 torr = Pgas torr
Pgas = 732 torr
(732 torr) x (1 atm/760 torr) x (0.310 L)
n =
= mol N2
( L atm/mol K) x (288 K)
mass N2 = ( mol N2) x ( g N2/mol N2) = g N2

8. Kinetic Theory of Gases -- READ BOOK
Basic Postulate -- A gas consists of a very large number of very small particles, in constant random motion, that undergo perfectly elastic collisions with each other and the container walls.
There is a distribution of kinetic energies of the particles.
Temp ∝ average KE
The kinetic theory “explains” the gas laws, pressure, etc. based on motion and kinetic energy of gas molecules.
e.g. Boyle’s Law (P = 1/V) ~ at constant Temp (same average KE)
If volume of container is reduced, there are more gas particles per unit volume, thus, more collisions with the container walls per unit area.
 higher pressure

9. Temperature & Molecular Velocities
Kinetic molecular theory states that all particles have the same average kinetic energy at a given temperature.
KE = ½mv2
If m is smaller, v is bigger! i.e. small particles move faster.
Quantitatively,
where urms = root mean square velocity (a kind of average),
M = formula mass (in kg/mol!),
and R = universal gas constant, but in J/mol∙K rather than L∙atm/mol∙K!
R = J/mol∙K = L∙atm/mol∙K
urms =
3RT M

10. Graham’s Law of Effusion
diffusion “mixing” of gases throughout a given volume
effusion “leaking” of a gas through a small opening
mean free path average distance between collisions
Graham’s Law: effusion rate ∝ 1/√ M where M = formula mass
So, effusion rates of two gases can be compared as a proportion:
e.g. He (FM = 4.0 g/mol) effuses 2 times faster than CH4 (FM = 16.0)
rateA
rateB = MB MA

11. Real Gases -- Deviations from Ideal Gas Law
For real gases, small corrections can be made to account for:
Actual volume of the gas particles themselves, and
intermolecular attractive forces
One common approach is to use the Van der Waals’ Equation:
Don’t memorize!
where a and b are empirical parameters that are dependent on the specific gas (e.g. Table 5.5)
a ≈ intermolecular attractive forces
b ≈ molecular size 2
P + a (V – nb) = nRT n V

12. Sample Problems
Hydrogen gas is produced when metals such as aluminum are treated with acids. Calculate the volume (in mL) of M HCl solution that is required to produce a total gas pressure of 725 torr in a 2.50-L vessel if the hydrogen gas (H2) is collected over water at 25 °C. (The vapor pressure of water at 25 °C is 24 torr.)
2 Al(s) + 6 HCl(aq) --> 2 AlCl3(s) + 3 H2(g)
A gas mixture contains 25.0 g of CH4, 15.0 g of CO and 10.0 g of H2. If the total pressure of the mixture is 1.00 atm, what is the partial pressure of CH4 in torr?

13. Chemistry in the Atmosphere
Air Pollutants
SOx
e.g 2 SO2(g) + O2(g) + 2 H2O(g)  2 H2SO4(aq) acid rain
NOx
e.g. 4 NO2(g) + O2(g) + 2 H2O(g)  4 HNO3(aq) acid rain
O3 (ozone) CO
solid particles
Ozone Layer
Stratospheric ozone
≠ ground-level ozone
CFC’s produce Cl, and
O3(g) + UV light  O2(g) + O(g)
Cl(g) + O3(g)  ClO(g) + O2(g)
ClO(g) + O(g)  Cl(g) + O2(g)
Freons are being replaced
by other less harmful refrigerants.