1. Chapter 5 Gases

2. The nature of gases
Indefinite shape and indefinite volume
expand to fill their containers
Compressible
Fluid – they flow
Low density
1/1000 the density of the equivalent liquid or solid
Properties of a gas stem from atoms/molecules being far away from each other, great amount of space in between

3. Kinetic molecular theory
Kinetic molecular theory explains the gas laws
A gas is a collection of particles (atoms or molecules) in constant motion
A single particle moves in a straight line till it collides with the wall or another particle

4. 3 postulates of KMT 1. The size of a particle is negligibly small
Since the space between atoms is very large in comparison to the atoms themselves
2. The average kinetic energy of a particle is proportional to the temperature in kelvins
Heat/Thermal energy causes movement of the molecules
The higher the temperature, the higher the average kinetic energy
3. The collision of one particle with another (including container walls) is completely elastic
There is no loss of energy in elastic collisions
Energy can be transferred, but overall there is no net loss

5. Pressure Is equal to force/unit area P=F/A
Is caused by the collisions of molecules with the walls of a container

6. Vacuum pumps
Vacuum pumps – can remove gas from a container, in turn reducing the pressure of that container
Useful for performing air free chemistry (mainly to avoid H2O and O2 in the air)

8. GAS LAWS Boyle’s Law Charles’ Law Gay-Lussac’s Law Avogadro’sLaw
Ideal Gas Law
Daltons Law

9. Gas law intro
Each law details the relationship between the following properties of gases
Volume
Pressure
Temperature
Moles
Each law is an equation
You must memorize all of the gas law equations
Solving problems typically involves rearranging the base equation to solve for a specific unknown

10. The relationship between pressure and volume
BOYLE’S LAW
The relationship between pressure and volume

11. Boyle’s law Robert Boyle – 1627-1691
Boyle’s Law - The volume of a gas is inversely proportional to the pressure applied to the gas when the temperature and moles are kept constant.
Decrease in volume = Increase in pressure.
Increase in volume = Decrease the pressure

13. The relationship between temperature and volume

14. Charles’ law Jaques Charles – 1746-1823
At a fixed pressure and moles, the volume of a gas is directly proportional to the temperature of the gas
As the temperature increases, the volume increases
As the temperature decreases, the volume decreases
TEMPERATURES MUST BE IN KELVIN

16. The relationship between pressure and temperature
Gay-Lussac’s law
The relationship between pressure and temperature

17. Gay-Lussac’s Law Joesph Louis Gay-Lussac – 1778-1850
At a fixed volume and moles, the pressure of a gas is directly proportional to the temperature of the gas
As the temperature increases, the pressure also increases
As the temperature decreases, the pressure also decreases
TEMPERATURES MUST BE IN KELVIN

19. Avogadro’s law The relationship between volume and moles

20. Avogadro’s law Amedeo Avaogadro – 1776-1856
At a fixed pressure and temperature, the moles of a gas is proportional to the volume of the gas
As the moles increases, volume also increases
As the moles decreases, volume also decreases
n = moles

22. The Ideal Gas Law

23. Ideal gas law Combining all previous relationships into one equation
The ideal gas law is most often written as
R - universal gas constant
R = L x atm x K-1 x mol-1
R = L x torr x K-1 x mol-1
R = L x mmHg x K-1 x mol-1
R = L x kPa x K-1 x mol-1
ALL TEMPERATURES MUST BE IN KELVIN!!

24. Molar volume and STP
One mole of any gas occupies exactly 22.4 liters (dm3) at STP.
STP = Standard Temperature and Pressure
Temp = 0ºC = 273K
Pressure = 1atm = 760 mmHg = 760 torr etc.
This is often referred to as the “molar volume” of a gas.

25. Equal volumes of gases, at the same temperature and pressure, contain the same number of particles, or molecules
Thus, the number of molecules in a specific volume of gas is independent of the size or mass of the gas molecules
Therefore, the rules applies the same to all gases

26. Problems
A cylinder contains 5.00L of gas at 225K. If the temperature is increased to 345K, what will the new volume be?
Rosy has a 5.00L tank of H2 gas. If the pressure inside the tank is 800.0torr and the temperature is 300.0K, how many moles of hydrogen does her tank contain?

27. Density of a gas Density = mass/ volume What is the mass of a gas?
M = molar mass of gas (grams/mole)
m = mass of gas (grams)
n = moles of gas (moles)
V = volume of gas (Liters)
dgas = density of the gas

28. Density of a gas
Make sure to choose the R value that cancels out the correct pressure units
g/L should be the final density units

29. Dalton’s Law The Law of Partial Pressures

30. Dalton’s law John Dalton – 1766 - 1844
Dalton’s Law: The total pressure exerted by a mixture of gases is the sum of the individual pressures of each gas in the mixture
Dalton’s Equation:

31. Deep-sea diving and partial pressures
Lungs need to breathe oxygen within a certain partial pressure range atm
Hypoxia – O2 partial pressure to low, not enough O2
Oxygen toxicity – O2 partial pressure too high, too much O2

32. Problems
The air in this room contains the gases shown below at their respective partial pressures in kPa. What is the pressure your body feels from the air in this room?

33. Mole fraction (χa)
In a gas mixture, there is a certain amount of moles of each individual gas
The number of moles of one of those gases divided by the total number of moles from all the gases is the mole fraction
χa = mole fraction
na = moles of a
ntotal = total moles of gas in gas mixture

34. Problem
If you had moles of air, what is the mole fraction of O2 in that sample?

35. Stoichiometry with gases
General stoichiometry
Solution Stoichiometry
Gas Stoichiometry

36. Molar volume and stoichiometry
1 mole of gas at STP = 22.4 L
An easy way to get to moles at STP
In general
Gas reactions still apply the same stoichiometry concepts
The chemical equation relates the reactants and products
To use the chemical equation mole ratios you need to convert reactants/products to moles
This lets you go from moles of one compound to another
The only new concept is that the ideal gas law allows us another way to get to moles

37. Problem CO(g) +2H2(g)  CH3OH(g)
What volume in liters of hydrogen gas, at 355K and a pressure of 738 mmHg, is needed to synthesize 35.7g of methanol (CH3OH)?

38. Temperature and Molecular Velocities
Gas particles at a given temperature have the same average kinetic energy
Lighter particles (Hydrogen) have faster average velocities than heavier particles (Argon) to compensate for lack of mass, so the kinetic energy can be equal

39. Root mean square velocity (urms)
urms – the root of the average of the squares of the particles velocities
R = universal gas constant = (J/(mol*K))
M = molar mass of gas IN KILOGRAMS
O2 molar mass = 32g/mol = 0.032kg/mol
J = (kg*m2)/(s2), now units of kg match
T = temperature in Kelvin

40. Diffusion
Diffusion - describes the mixing of gases. The rate of diffusion is the rate of gas mixing
Lighter gas particles diffuse faster than heavier gas particles

41. Effusion
Effusion - describes the passage of gas into an evacuated chamber
Lighter particles effuse faster than heavier particles
Grahams law of effusion – rate of effusion of two gases is related

42. Real gases
Ideal gas laws are suited for conditions close to STP and are based off of the 3 kinetic theory postulates
Negligible particle size, average KE related to T, elastic collision
At lower temperatures and higher pressures that Ideal gas laws begin to become less effective

43. Real gas - Volume
Particle size has a greater impact at higher pressures (lower volumes)
This causes the actual volume to be greater than predicted with the ideal gas law

44. Correction for real behavior
n = moles
b = constant dependant on gas, use chart 

45. Real gas - Pressure
Lower temperatures allow for intermolecular forces to have a greater effect, decreasing the collisions that occur
This causes the actual pressure to be less than predicted with the ideal gas law

46. Correction and van der Waals equation
Combining the pressure and volume corrections give the van der Waals equation

47. Chapter 5….. out of gas.