1. Chapter 9
Gases

2. Gases and Gas Pressure
Gases – constituent atoms and molecules that have little attraction for one another
Free to move in available volume
Some properties of gases
Mixtures are always homogenous
Very weak attraction between gas molecules
Identity of neighbor is irrelevant
Compressible – volume contracts when pressure is applied
0.10% of volume of gas is occupied by molecules
Exert a measurable pressure on the walls of their container

3. Gases and Gas Pressure Pressure – force exerted per unit area
SI unit equals Pascal (Pa)
1 Pa = 1 N/m2 (1 N = 1 (kg•m)/s2)
Alternative units
Millimeters of mercury (mmHg)
Atmosphere (atm)
1.0 atm = 760 mmHg = 101, 325 Pa
1.0 atm = 760 torr
Unit area
Force
Pressure:

4. Atmospheric Pressure
- pressure created from the mass of the atmosphere pressing down on the earth’s surface
Standard atmospheric pressure at sea level – 760 mmHg

5. Gases and Gas Pressure Barometer:
long thin mercury filled tube sealed at once end and inverted into a dish of mercury
Downward pressure of Hg in column equals outside atmospheric pressure

6. Measuring Pressure Manometer:
U-tube filled with mercury, with one end connected to the gas – filled container and the other end open to the atmosphere.
Pgas < Patm; liquid level in the arm connected to the gas-filled cylinder will be higher
Pgas + PHg = Patm

7. Measuring Pressure
Pgas > Patm; liquid level in the arm connected to the gas – filled cylinder will be lower
Pgas = Patm + PHg
(PHg = the difference in the heights of the two mercury columns)

8. Example
What is the pressure of the gas inside the following apparatus (in mm Hg) if the outside pressure is 750 mm Hg? (1 cm Hg = 10 mm Hg)

9. The Gas Laws
Ideal Gas: A gas whose behavior follows the gas laws exactly.
The physical properties of a gas can be defined by four variables:
P pressure
T temperature
V volume
n number of moles

10. Pressure and Volume: Boyle’s Law
Showing the relationship between pressure and volume
P x V = k (constant specific temp and constant moles of gas)
k = 1.40 x 103
V = 1/P (inverse relationship)

11. Pressure and Volume: Boyle’s Law
Can predict a new volume of pressure is changed
P1V1 = k = P2V2  P1V1 = P2V2

12. The Gas Laws
Boyle’s Law a V P 1
PV = k
(constant n and T)

13. Example
A sample of helium gas has a pressure of 3.54 atm in a container with a volume of 23.1 L. This sample is transferred to a new container and the pressure is measured to be 1.87 atm. Assume constant temperature.
Will the volume of the gas increase of decrease?
What will be the new volume of the gas?

14. Volume and Temperature: Charles’s Law
Relationship between Volume and Temperature
V = bT (b is a constant)
V / T = b
Can predict the new volume or temperature
(V1/T1)= (V2/T2) =
Tfinal
Vfinal
Tinitial
Vinitial

15. The Gas Laws
Charles’ Law
= k T V
V a T
(constant n and P)

16. Example
A 2.0 L sample of air is collected at 298K and then cooled to 278 K. The pressure is held constant at 1.0 atm.
Does the volume increase of decrease?
Calculate the volume of the air at 278 K?

17. Volume and Moles: Avogadro’s Law
Relationship between volume of gas and number moles of gas
V is directly proportional to n
V = an or V / n = a (a = constant)
Can predict the new volume or new moles of gas at constant pressure and temperature
(V1/n1) = (V2/n2) =
nfinal
Vfinal
ninitial
Vinitial

18. The Gas Laws Avogadro’s Law V = k V a n n (constant T and P)
One goes up, the other one goes up.

19. Example
Consider two samples of nitrogen gas (composed N2 molecules). Sample 1 contains 1.5 mol of N2 and has a volume of 36.7 L at 25oC and 1 atm. Sample 2 has a volume of 16.0 L at 25oC and 1 atm. Calculate the number moles of N2 in sample 2

20. Summary Boyle’s Law Charles’ Law Avogadro’s Law constant T & n
constant P & n
constant P & T
V = 1/P
V = T
V = n =
Tfinal
Vfinal
Tinitial
Vinitial
ninitial
Vinitial
nfinal
Vfinal =
PinitialVinitial = PfinalVfinal

21. 9.3 The Ideal Gas law
Different gasses show similar physical behavior (unlike solid or liquid)
Relationship of variable – gas laws
Ideal gas – behavior follows the gas laws exactly

22. 9.3 The Ideal Gas law
Describes how the volume of a gas is affected by changes in pressure, temperature and moles.
PV = nRT;
R =
K mol
L atm

23. 9.3 The Ideal Gas Law Ideal Gas Law: PV = nRT
R is the gas constant and is the same for all gases.
R =
K mol
L atm
T = 0 °C ( K)
Standard Temperature and Pressure (STP) for Gases
Standard pressure is actually 1 bar.
Gas law problems must use Kelvin!!!!!!
P = 1 atm

24. The Ideal Gas Law What is the volume of 1 mol of gas at STP? (1 atm)
The closer the molar volume of a gas is to L at STP, the more ideal the behavior.
(1 atm)
(1 mol)
K mol
L atm
( K) P
nRT
V = =
= L

25. Example
A helium gas cylinder of the sort used to fill balloons have a volume of 43.8 L and pressure of 1.51 x 104 kPa at 25.0oC. How many moles of helium are in the tank?
What volume is occupied by mol of carbon dioxide gas at 25.0oC and 371 torr?
A mol sample of argon gas has a volume of 9.00L at a pressure of 875 mmHg. What is the temperature (in oC) of the gas?

26. Stoichiometric Relationships with Gases
The reaction used in the deployment of automobile airbags is the high temperature decomposition of sodium azide, NaN3, to produce N2 gas. How many liters of N2 at 1.15 atm and 30.0oC are produced by the decompostion of 45.0g NaN3?
2Na(s) + 3N2(g)
2NaN3(s)

27. Examples Consider the reaction represented by the equation
P4(s) H2(g)  4H3(g)
What is the amount of P4 is required to react with 5.39 L of hydrogen gas at 27.0oC and 1.25 atm?

28. Example
Ammonia is commonly used as a fertilizer to provide a source of nitrogen for plants. A sample of NH3(g) occupies a volume of 5.00 L at STP. What moles will this sample occupy?

29. Combine Gas Law
is an expression obtained by mathematically combining Boyle’s and Charles’ law
P1V1 = P2V2 @ constant n
T T2
can predict P, V or T when condition is changed

30. Examples
A sample of diborane gas B2H6, a substance that bursts into flames when exposed to air, has a pressure of atm at a temperature of -15oC and a volume of 3.48L. If condition are changed so that the temperature is 36oC and the pressure is atm, what is the new volume of the sample?

31. Examples
Consider a sample of hydrogen gas of 63oC with a volume of 3.65L at a pressure of 4.55 atm. The pressure is changed to 2.75 atm and the gas is cooled to -35oC. Calculate the new volume of the gas

32. 13.6 Dalton’s Law of Partial Pressure
A. Gas laws apply to mixtures of gases
B. Dalton's law of partial pressure –
Ptotal = P1 + P2 + P3 + ….. at constant V, T
where P1, P2, ….refer to the pressure of the individual gases in the mixture
Mole Fraction (X) =
Total moles in mixture
Moles of component
Xi =
ntotal ni
Xi =
Ptotal Pi or

33. Partial Presssure
C. Partial pressures refer to the pressure each individual gas would exert if it were alone in the container (P1, P2, …)
1. Total pressure depends on the total molar amount of gas present
Ptotal = ntotal (RT/V)

34. Examples
A 2.0 L flask contains a mixture of nitrogen gas and oxgyen gas at 25.0oC. The total pressure of the gas mixture is 0.91 atm, and the mixture is known to contain mol of N2. Calculate the partial pressure of oxygen and the moles of oxygen present

35. Examples
Mixture of helium and oxygen are use in the “air” tanks of underwater divers for deep dives. For a particular dive, 12.0L of O2 at 25.0oC and 1.0 atm and 46.0 L of He at 25oC and 1.0 atm were both pumped into a 5.0 L tank. Calculate the partial pressure, moles fraction of each gas and the total pressure in the tank at 25.0oC

36. The Kinetic Molecular Theory of Gas
A. Model that can explain the behavior of gases
.Assumptions
1. A gas consists of particles in constant random motion
2. Most of the volume of a gas is empty spaces
3. The attractive and repulsive forces between molecules of gases are negligible
4. The total kinetic energy of the gas particles is constant at constant T
5. Average Ek α T

38. The Kinetic-Molecular Theory of Gases
molar
mass
average
speed

39. The Kinetic-Molecular Theory of Gases

40. Graham’s Law: Diffusion and Effusion of Gases
Diffusion: The mixing of different gases by molecular motion with frequent molecular collisions

41. Graham’s Law: Diffusion and Effusion of Gases
Effusion: The escape of a gas through a pinhole into a vacuum without molecular collisions. a
Rate 1 m
Graham’s Law:
m is mass.

42. The Behavior of Real Gases
The volume of a real gas is larger than predicted by the ideal gas law.

43. The Behavior of Real Gases
Attractive forces between particles become more important at higher pressures.
Particles are closer together at higher pressures due to the increased attractive forces.

44. The Behavior of Real Gases
van der Waals equation
Correction for intermolecular attractions. a n2 P +
V - n b
= nRT V2
Correction for molecular volume.

45. examples
Assume that you have mol of N2 in a volume of 0.600L at 300K. Calculate the pressure in the atmosphere using both the ideal gas law and the van der Waals equation. For N2, a = 1.35 (L2·atm)mol2, and b = L/mol