1. Chapter 10:
Gases

2. Overview Pressure Standard Conditions Gas Laws
Barometer & Atmospheric Pressure
Standard Conditions
Gas Laws
Boyle’s Law
Charles’ Law
Avogadro’s Law
Ideal Gas Law

3. Gas Laws under Two Conditions Gas Densities
Darlton’s Law of Partial Pressure
Kinetic Molecular Theory
Molecular Effusion/Diffusion
Graham’s Law
Deviation from Ideality

4. Characteristics Solids Liquids Gases have own shape and volume
particles close together with strong interaction
Liquids
have own volume but assume shape of container
particles farther apart but have moderate interaction
Gases
assume shape and volume of container
particles far apart with little/no interaction
highly compressible

5. Pressure P = F/A Barometer Standard Pressure Force in Newtons
Area in m2
Barometer
P in N/m2 = Pascal unit
1 x 105 N/m2 = 1 x 105 Pa or 100 kPa
Standard Pressure
1 atm = 760 mm Hg = x 105 Pa = kPa (or torr)

6. force of the atmosphere force of the column
when atmospheric force equals the force of the column the atmospheric pressure is measured as “h”

7. Gas Laws Boyle’s Law Charles’ Law Avogadro’s Law P µ 1/V constant T, n
volume increases as pressure decreases
Charles’ Law
V µ T constant P, n
volume increases as temperature increases
Avogadro’s Law
V µ n constant P, T
volume increases as moles of gas (n) increases

8. Ideal Gas Law combines all gas laws PV = nRT
R = L-atm mol-K
any volumes must be in liters
any temperatures must be in kelvin
any pressures must be in atmospheres
STP or SC -- standard temperature/pressure
P = 1 atm (same as 760 mm Hg)
T = 273 K (same as 0° C)

9. Problem 10. 3: A flashbulb contains 2. 4 x 10 -4 mol of O2 gas at 1
Problem 10.3: A flashbulb contains 2.4 x mol of O2 gas at 1.9 atm and 19°C . What is the volulme?
PV = nRT or V = nRT P
V = 2.4x10 -4 mol x L-atm x K mol-K atm
V = 3.0 x L or mL or cm3

10. Gas Laws Under Two Conditions
P1V1 = P2V T T2
Problem 10.4: Pressure in a tank is kept at 2.20 atm. When the temp. is -15°C the volume is 28,500 ft3. What is the volume is the temp. is 31°C
P1 = P2 = 2.20 atm T1 = 258 K T2 = 304 K V1 = 28,500 ft3
V2 = P1 V1 T P2 T1
V2 = 28,500 ft3 x 304 K = K
33,600 ft3

11. Gas Densities n = P from PV = nRT V RT d = PMM RT
n = moles x g/mol = g = d = PMM V L L RT
d = PMM RT
(atm)g mol L atm ( K) mol K

12. Dalton’s Law of Partial Pressures
total pressure of a mixture = sum of each partial pressure
PT = P1 + P2 + P
each partial pressure = the pressure each gas would have if it were alone
P1 = n1RT P2 = n2RT P3 = n3RT V V V3
PT = n1RT + n2RT + n3RT = (n1 + n2 + n3) RT V V V V
volumes are the same

13. P1 = n1 therefore P1 = n1 PT PT nT nT n1 = X1 mole fraction nT P1 = X1 PT

14. Kinetic Molecular Theory
Gases consist of particles in constant, random motion
Volume of gas particles is negligible
Attractive and repulsive forces are negligible
Average kinetic energy is proportional to temperature
Collisions are elastic

15. molecular speed
u = root mean square speed or speed of molecule with average kinetic energy
R is the gas constant (8.314 J/mol-K), T is temp. in K & MM is molar mass
What is the rms speed of an He atom at 25°C?
u = (3 x kg-m2/s2-mol-K x K)1/ ( x kg/mol )
u =
1.36 x 103 m/s

16. Effusion/Diffusion
small molecules will effuse/diffuse faster than large molecules
effusion diffusion

17. Graham’s Law
where r is rate of speed & MM is the molar mass
Problem 10.14: Calculate the ratio of the effusion rates of N2 and O2.
rN2 = rO2

18. Deviation from Ideality
Occurs at very high pressure or very low temperature
Correction due to volume
ideal law assumes molecules have no volume
for molecules which are far apart, this is a good assumption
must correct for the volume of the molecules themselves

19. Correction due to attraction of molecules
ideal law assumes the molecules have no attraction to each other
for molecules which are far apart, this is a good assumption
must correct for actual attraction of molecules
correction for molecular volume
correction for molecular attraction