1. Chapter 5 Gases

2. 5.1 Measurements of Gases Key variables in the measurement of gases:
Volume
Amount
Temperature
Pressure
Unlike liquids and solids, gases
expand to fill their containers;
are highly compressible;
have extremely low densities.

3. Volume, Amount and Temperature
A gas expands uniformly to fill the container in which it is placed
The gases volume will be the container volume
Common units are L, mL, or cm3 (1mL = 1cm3)
The temperature of a gas must be indicated on the Kelvin scale
Recall that K = °C
Amount of a gas is measured in moles (n)

4. Pressure Pressure is force per unit area
In the English system, pounds per square inch or psi
Standard atmospheric pressure is 14.7 psi
Units of pressure =
- Pascals (1 Pa = 1 N/m2)
- 1 bar = 105 Pa = 100 kPa
- mm Hg or torr
(1 atm = 760 mm)

5. Measuring Pressure - The Barometer
The barometer measures atmospheric pressure in terms of the height of a column of liquid mercury
The atmosphere exerts a force on a pool of mercury, causing it to rise
Standard atmospheric pressure is a column of mercury 760 mm high

6. Gas Pressure Measurement – The Manometer
The manometer is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.
The height of the column of liquid is proportional to the pressure of the gas in the container
Gas pressure can be more or less than atmospheric pressure

7. It is equal to: 760 torr (760 mm Hg) 101.325 kPa
Standard Pressure
Normal atmospheric pressure at sea level is referred to as standard pressure.
It is equal to:
1.00 atm
760 torr (760 mm Hg)
kPa

8. 5.2 The Ideal Gas Law Basic Gas Laws: Charles’ Law Boyle’s Law
Gay-Lussac’s Law
Relationship between moles and pressure
Combined Gas Law

9. A plot of V versus T will be a straight line.
Charles’s Law
The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.
Temperature MUST be in KELVIN!
V1 = V2
T1 T2
A plot of V versus T will be a straight line.

10. Boyle’s Law
-The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure. -Volume and pressure units must match P1V1 =P2V2

11. As P and V are inversely proportional
A plot of V versus P results in a curve.
Since
V = k (1/P)
This means a plot of V versus 1/P will be a straight line.
PV = k

12. Gay-Lussac’s Law -Pressure and Temperature are directly proportional
-Pressure units must match and temperature units must be in Kelvin
P1 = P2
T1 T2

13. Mathematically, this means
Avogadro’s Law
The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.
Mathematically, this means
V = kn

14. Combined Gas Law
-Looking at the basic gas laws they can easily be summed together to form one law
P1V1 = P2V2
n1T1 n2T2

15. Relationships between the variables:
V vs. T = direct
V vs. n = direct
V vs. P = inverse
P vs. T = direct
Pattern:
Variables are a product = inverse
Variables are a quotient = direct

16. V  nT P Ideal-Gas Equation So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
Combining these, we get
V  nT P

17. Ideal-Gas Equation
The constant of proportionality is known as R, the gas constant.

18. PV = nRT nT P V  nT P V = R or Ideal-Gas Equation then becomes
The relationship nT P
V  nT P
V = R
then becomes or
PV = nRT

19. Standard Temperature and Pressure
STP
1 atm P
273 K
At STP, the molar volume of a gas can be calculated as follows:

20. Density of Gases Density is an intensive property
Does not depend on the amount of substance
Density of a gas does depend on:
Pressure
Temperature
Molar mass

21. Balloons

22. Molar Mass and Density Density = mass/volume
Recall that the molar mass has units of grams per mole (MM = m/n)
Now, look at the ideal gas law:
Substitute m/MM for n
PV = mRT MM
Substitute Density for m/V
P=mRT P=DRT D=P MM
V MM MM RT

23. 5.3 Gas Law Calculations
Final and initial problems (Basic laws; 1’s and 2’s)
Single-state problems (PV = nRT)
Density problem (D=MMxP/RT)

24. Example 5.3

25. Example 5.3

26. 5.4 Stoichiometry in Gaseous Reactions
Gases can participate as reactants or products in any chemical reaction
All substances in a balanced chemical equation are related by mole ratios

27. 5.5 Gas Mixtures: Partial Pressures
The ideal gas law applies to all gases, so it applies to mixtures of gases as well
A new term is needed for a mixture of gases
Partial pressure, the part of the total pressure due to each gas in the mixture
Sum of the partial pressures is the total pressure

28. Dalton’s Law of Partial Pressures
The total pressure of a gas mixture is the sum of the partial pressures of the gases in the mixture
PT = P1 + P2 + P3 …
When one collects a gas over water, there is water vapor mixed in with the gas.
The vapor pressure of a substance is the pressure of the gaseous form of that substance
Vapor pressure is an intensive property
Vapor pressure depends on temperature

29. Collecting a Gas Over Water
When a gas is collected over water, the total pressure is the pressure of the gas plus the vapor pressure of water

30. Wet Gases P H2O is the vapor pressure of water
P H2O is dependent on temperature
Consider H2 gas collected over water:

31. Effusion of Gases Diffusion
Gases move through space from a region of high concentration to a region of low concentration
You can smell an apple pie baking as the particles responsible for the odor diffuse through the room
Effusion
Gas particles will escape through a small hole in a container
Air will slowly leak out of a tire or balloon through pores in the rubber

32. Diffusion
Diffusion is the spread of one substance throughout a space or throughout a second substance.

33. Effusion
The difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster.

34. Graham’s Law of Effusion
The rate at which gas B escapes divided by the rate at which gas A escapes is equal to the square root of the ratio of the molar mass of gas A to gas B

35. Kinetic-Molecular Theory
This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

36. 5.6 Kinetic Theory of Gases
The kinetic-molecular model
1. Gases are mostly empty space. The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.
Gas molecules are in constant, random motion.
Attractive and replusive forces between gas molecules are negligible. There are no IMFOA.
Collisions of gas particles are elastic.
Gas pressure is caused by collisions of molecules with the walls of the container.

37. Main Tenets of Kinetic-Molecular Theory
Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

38. Results from Kinetic Energy of Translational Motion
At a given temperature, all molecules of all gases have the same average kinetic energy
The average kinetic energy of a gas particle is directly proportional to the Kelvin temperature

39. Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

40. Liquefaction of Gases All gases can be liquefied
Lowering the temperature
Increasing the pressure
When a gas is liquefied, the attractive forces between gas particles becomes significant
The closer a gas is to the liquid state, the more it will deviate from the ideal gas law

41. Real Gases
Even the same gas will show wildly different behavior under high pressure at different temperatures.

42. Real Gases
Recall that the molar volume of a gas at STP is 22.4 L (Avogadro’s Hypothesis)
There are deviations from this volume that depend on the gas being studied
The molar volume of a real gas is less than that calculated by the ideal gas law

43. Real Gases
In the real world, a real gas is MOST ideal under the following conditions:
Molecules have low molar masses
Molecules are nonpolar
High temperatures
Low pressures

44. Corrections for Nonideal Behavior
The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.
The corrected ideal-gas equation is known as the van der Waals equation.

45. The van der Waals Equation
) (V − nb) = nRT
n2a V2
(P +

46. Two Factors for Real Gases
Two factors are important to real gases
1. The attractive forces between the gas particles
2. The volume of the gas particles
Both of these are ignored by the ideal gas law

47. Attractive Forces
Note that the observed molar volume for gases is lower than that calculated by the ideal gas law
The forces between particles pull the particles together
The volume occupied by the gas is then decreased
This is a negative deviation from the ideal gas law

48. Particle Volume
The volume of the gas particles becomes a more significant factor in determining the volume of the gas as the pressure increases