1. Chemistry 100
Gases and Gas Laws

2. The Definition of a Gas
Gas - a substance that is characterised by widely separated molecules in rapid motion.
Mixtures of gases are uniform. Gases will expand to fill containers.

3. Examples of Gaseous Substances
Common gases O2 and N2, the major components of "air"
Other gases F2, Cl2, H2  gaseous diatomic molecules
H2 and He are the ‘lighter than air’ gases
N2O (laughing gas)

4. Three States of Matter
Solids
Liquids
Gases

5. Gases (cont’d)
Most molecular compounds are solids or liquids at room temperature, but they can be converted to a gas relatively easily
Important exception  ionic solids (e.g., NaCl) can't be easily coverted to gases

6. Gases and Vapours What is the difference between a gas and a vapour?
Gases  normally in the gaseous state at 25°C and 1 atm pressure
A vapour is the gaseous form of any substance that is normally in the liquid or solid state at normal temperatures and pressures

7. The Definition of Pressure
The pressure of a gas is best defined as the forces exerted by gas on the walls of the container
Define P = force/area
The SI unit of pressure is the Pascal
1 Pa = N/m2 = (kg m/s2)/m2

8. The Measurement of Pressure
How do we measure gas pressure?
Barometer - invented by Torricelli
Gas pressure conversion factors
1 atm = 760 mm Hg = 760 Torr
1 atm = kpa = bar

9. The Barometer

10. The Gas Laws
Four variables were sufficient to fully describe the state of a gas
Pressure (P)
Volume (V)
Temperature (T)
The amount of the gas in moles (n)

11. Boyle's Law The gas volume/pressure relationship
The volume occupied by the gas is inversely proportional to the pressure
V  1/P
Temperature and the amount of the gas are fixed
V = k1/ P or PV = k1
k1 is a proportionality constant

12. Boyle's Law

13. Charles and Gay-Lussac's Law
Defines the gas volume/temperature relationship
V  T (constant pressure and amount of gas)
Note T represents the temperature on Lord Kelvin's temperature Scale
V = k2 T
k2  proportionality constant

14. Charles and Gay-Lussac's Law

15. An Aside The Kelvin temperature scale -
Lord Kelvin recognised the significance of the intercept in the volume/temperature relationship
All temperature (°C) vs. volume plots extrapolated to 0 volume at °C
Kelvin - absolute 0
all thermal motion ceases

16. The Kelvin Temperature Scale
Relating Kelvin scale and the Celcius scale
T (K) = [ tc (°C) °C] K/°C
Freezing point of water: tc = 0 °C; T = K
Boiling point of water: tc = 100 °C; T = K
Room temperature: tc = 25 °C; T = 298 K
NOTE tc = C; T (K) = K NO DEGREE SIGN

17. Amonton’s Law The pressure/temperature relationship
For a given quantity of gas at a fixed volume, P  T
P = k3 T
P1 = k3T1
P2 = k3T2  P1 / T1 = P2 / T2 Amonton's law

18. Amonton’s Law
P / atm
t / C
t = C V1 V2 V3 V4

19. V = k4 n => n = number of moles of gas
Avogadro’s Law
The volume of a gas at constant T and P is directly proportional to the number of moles of gas
V = k4 n => n = number of moles of gas

20. Avogadro’s Law

21. The Ideal Gas Equation of State
We have four relationships
V  1/P; Boyle’s law
V  T; Charles’ and Gay-Lussac's law
V  n; Avogadro’s law
P  T; Amonton’s law

22. Ideal Gas Equation of State
We combine these relationships into a single fundamental equation of state  the ideal gas equation
PV = nRT
R is the universal gas constant
R = L atm / (K mol)
= J / (K mol)

23. The Definition of an Ideal Gas
An ideal gas is a gas that obeys totally the ideal gas law over its entire P-V-T range
Ideal gases - molecules have negligible intermolecular attractive forces
Occupy a negligible volume compared to the container volume

24. Standard Temperature and Pressure
Define: STP (Standard Temperature and Pressure)
Temperature  0.00 °C = K
Pressure  atm
The volume occupied by mole of an ideal gas at STP is L!

25. Gas Density Calculations
A simple expression for calculating the molar mass of an unknown gas.
Molar mass and gas density
M = (dRT) / P
d = the gas density

26. Partial Pressures
Let's consider two ideal gases (gas 1 and gas 2) in a container of volume V. 1 2

27. Dalton's Law of Partial Pressure
In a gaseous mixture,
each gas exerts the same pressure as if it was alone and occupied the same volume.
the partial pressure of each gas, Pi, is related to the total pressure by Pi = Xi PT
Xi is the mole fraction of gas i.

28. Partial Pressures (cont’d)
The pressure exerted by the gases is the sum of the partial pressures of the individual gases
Let P1 and P2 be the partial pressures of gas 1 and 2, respectively.
PT = P1 + P2 = nT (RT/V),
PT = n1 (RT/V) + n2 (RT / V)

29. The Mole Fraction The mole fraction is defined as follows
For a two component mixture
n1 = moles of substance 1
n2 = moles of substance 2
nT = n1 + n2
X1 = n1 / nT; X2 = n2 / nT

30. Gas Collection Over Water

31. Gas Collection Over Water
Many gas measurements are carried out over water.
Water vapour is collected with the gas.
PT = Pgas + PH2O

32. Kinetic Molecular Theory of Gases
Macroscopic (i.e., large quantity) behaviour of gases.
The kinetic molecular theory of gases attempts to explain the behaviour of gases on a molecular level.

33. Kinetic Theory of Gases
Gases consist of molecules widely separated in space. Volume of molecules is negligible compared to total gas volume.
Gas molecules are in constant, rapid, straight-line motion. Collisions are elastic.
Average kinetic energy (K.E.) of molecules depends on absolute temperature (T) only.
Attractive forces between molecules are negligible.

34. Kinetic Theory of Gases

35. Gas Laws Explanations
Gas pressure results from collisions of gas molecules with the container walls.
Pressure depends on
the number of collisions per unit time
how hard gas molecules strike the container wall!

36. More collisions of gas with container wall.
Avogadro’s Law
Let's increase the amount of gas in the container (T, P constant)
More collisions of gas with container wall.
V  n at constant P, T.

37. Boyle's Law
Let's decrease the volume of the container (constant n and T).
More collisions of the gas molecules with
the container wall and P increases. (V  1/P)

38. Charles’ and Gay-Lussac’s Law
Let container volume increase (P, n are held constant).
High Temp.
Low Temp.
The molecules must move faster
T must increase.

39. Molecular Speeds K.E. = 1/2 M U2
M = the molar mass of the gas
U2 =the mean square speed of the gas
This speed is an average speed (some will always be fast, some slow).

40. The Mean Square Speed
Kinetic Molecular Theory of Gases allows us to relate macroscopic measurements to molecular quantities
P, V are related to the molar mass and mean square seed, U2
P V = 1/3 n M U2 = n R T

41. The Root Mean Square Speed
1/3 MU2 = RT
U2 = 3RT / M
(U2)1/2 = urms = (3RT/M)1/2
urms = the root mean square speed

42. The Root Mean Square Speed

43. The Mean Free Path
Gas molecules encounter collisions with other gas molecules and with the walls of the container
Define the mean free path as the average distance between successive molecular collisions

44. The Mean Free Path

45. The Mean Free Path
As the pressure of the gas increases, the mean free path decreases, i.e., the higher the pressure, the greater the number of collisions encountered by a gas molecule.

46. Diffusion
Diffusion - gradual mixing of gas molecules caused by kinetic properties.
Graham's Law  Under constant T, P, the diffusion rates for gaseous substances are inversely proportional to the square roots of their molar masses.

47. Graham’s Law r1/r2 = (M2 / M1)1/2
r1 and r2 are the diffusion rates of gases 1 and 2.
M1 and M2 are the molar masses of gas 1 and gas 2, respectively.

48. Effusion
Effusion - the process by which a gas under pressure goes (escapes) from one compartment of a container to another by passing through a small opening.

49. Effusion

50. The Effusion Equation
Graham’s Law - estimate the ratio of the effusion times for two different gases.
t1/t2 = (M1 / M2)1/2
t1 and t2 are the effusion times of gases 1 and 2.
M1 and M2 are the molar masses of gas 1 and gas 2, respectively.

51. Deviations from Ideal Gas Behaviour
The ideal gas equation is not an adequate description of the P,V, and T behaviour of most real gases.
Most real gases depart from ideal behaviour at deviation from
low temperature
high pressure

52. Deviations from Ideal Gas Behaviour at Low Temperatures

53. Deviations from Ideal Gas Behaviour at High Pressures

54. Deviations from Ideal Behaviour
Look at assumptions for ideal gas
Real gas molecules do attract one another.
(i.e., Pid = Pobs + constant).
Real gas molecules do not occupy an infinitely small volume (they are not point masses).
(Vid = Vobs - const.)

55. The Van der Waal’s Equation
Vid = Vobs - nb where b is a constant for specific different gases.
Pid = Pobs + a (n / V)2 where a is also different for different gases.
Ideal gas Law Pid Vid = nRT

56. The Van der Waal's Equation (cont’d)
(Pobs + a (n / V)2) x (Vobs - nb) = nRT
Van der Waals’s equation of state for real gases.
Two constants (a, b) that are experimentally determined for each separate gas
Table 10.3 in text.