1. Ch. 11: Molecular Composition of Gases
Volume-Mass Relationships of Gases

2. Pressure P : force per unit area on a surface
Newton – SI unit for force (1 kg*m/s2)
why would shoes with smaller diameter heel not be allowed on gym floor?
As surface area decreases, pressure increases
Pressure exerted by a gas depends on
volume
temperature
number of molecules

3. Measuring Pressure barometer
instrument used to measure atmospheric pressure
first one created by Torricelli in early 1600s
glass tube filled with mercury is inverted in a dish
mercury flows out of the tube until pressure of the Hg inside the tube is equal to the atmospheric pressure on the Hg in the dish

4. Measuring Pressure manometer: measures pressure of gas in a container
gas has less pressure than atmosphere if the Hg is closer to chamber
gas has more pressure than atmosphere if the Hg is further from chamber

5. Units of Pressure millimeters of mercury (mmHg) torr (torr)
from mercury barometer
torr (torr)
from Toricelli inventing barometer
atmosphere of pressure (atm)
Pascal (Pa) = 1N/m2 (SI unit)
named after French scientist
1 atm = 760 mmHg = 760 torr = kPa

6. Practice Conversions
Convert atm to
mmHg
torr
kPa

7. Practice Conversions
Convert kPa to
atm
mmHg
torr

8. The pressure of a gas is measured as 49 torr
The pressure of a gas is measured as 49 torr. Convert this pressure to atmospheres, kiloPascals, and mmHg.

9. Boyle’s Law: P and V as one increases, the other decreases
inversely proportional
pressure is caused by moving molecules hitting container walls
If V is decreased and the # of molecules stays constant, there will be more molecules hitting the walls per unit

10. Boyle’s Law: P and V
Boyle’s Law: the V of fixed mass of gas varies inversely with P at a constant T.
PV = k
k is a constant for a certain sample of gas that depends on the mass of gas and T
What kind of graph is V vs. P?
If we have a set of new conditions for the same sample of gas, they will have same k so:

11. Boyle’s Law

12. Boyle’s Law: P and V Discovered by Irish chemist, Robert Boyle
Used a J-shaped tube to experiment with varying pressures in multistory home and effects on volume of enclosed gas

13. Example: Boyle’s Law
Consider a 1.53-L sample of gaseous SO2 at a pressure of 5.6 x 103 Pa. If the pressure is changed to 1.5 x 104 Pa at constant temperature, what will be the new volume of the gas?

14. Charles’ Law: V and T if P is constant, gases expand when heated
when T increases, gas molecules move faster and collide with the walls more often and with greater force
to keep the P constant, the V must increase

15. Charles’ Law: V and T
Problem: if we use Celsius, we could end up with negative values from calculations in gas laws for volumes
we need a T system with no negative values: Kelvin Temperature Scale
starts at ° C = absolute zero = 0 K
lowest possible temperature
balloon going into liquid nitrogen

16. Charles’ Law: V and T
Charles’ Law: the V of fixed mass of gas at constant P varies directly with Kelvin T.
V = kT
k is a constant for a certain sample of gas that depends on the mass of gas and P
What kind of graph is V vs. T?
If we have a set of new conditions for the same sample of gas, they will have same k so:

17. Charles’ Law discovered by French physicist, Jacques Charles in 1787
first person to fill balloon with hydrogen gas and make solo balloon flight

18. Example: Charles’ Law & Temp.
A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38°C and 1 atm?

19. A weather balloon is released at a pressure of 744 mmHg with a volume of 12 L. What will the volume be at a pressure of 704 torr?

20. Gay-Lussac’s Law of Combining Volumes of Gases
at constant T and P, coefficients in balanced equation represent ratio of volumes of gaseous reactants too
2H2(g) + O2(g)  2H2O(g)
2 L 1 L 2 L

21. Gay-Lussac’s Law: P and T
Gay-Lussac’s Law: the P of fixed mass of gas at constant V varies directly with Kelvin T.
P = kT
k is a constant for a certain sample of gas that depends on the mass of gas and V
What kind of graph is P vs. T?
If we have a set of new conditions for the same sample of gas, they will have same k so:

22. Example: Gay-Lussac’s Law
The gas in an aerosol can is at a pressure of 3.00 atm at 25°C. Directions on the can warn the user not to keep the can in a place where temperature exceeds 52°C. What would the gas pressure be in the can at 52°C?

23. Example
3O2(g)  2O3(g)
How many liters of O3 can be made from 12 L of O2?
How many moles of O2 are needed to make 24 moles of O3?
How many molecules of O3 can be made from 18 molecules of O2?

24. Avogadro’s Law
equal volumes of gases at the same T and P contain equal numbers of molecules
at same T and P, volumes varies directly with number of moles (n)
V = kn

25. Molar Volume of Gases like molar mass but with volume
mass of one mole of substance
but with volume
volume of one mole of substance
because of Avogadro’s law, one mole of any gas has the same volume as any other gas at the same T and P

26. Molar Volume of Gases Standard Molar Volume of Gas
volume of one mole of gas at 1 atm and 0°C is 22.4
22.4 L of any gas has one mole of particles but has different masses
Standard Temperature and Pressure
STP
1 atm and 0°C

27. Molar Volume of Gases

28. Example
A chemical reaction produces mol of oxygen gas. What volume in liters is occupied by this gas sample at STP?
1 mol : 22.4 L

29. Example 2
A chemical reaction produced 98.0 mL of sulfur dioxide gas at STP. What was the mass of gas made?
convert mL to L
convert L to moles using molar volume
convert moles to grams using molar mass

30. Example 3
A chemical reaction produced 3.1 g of CO2 gas. What volume will it have in mL at STP?
convert grams to moles
convert moles to liters
convert liters to milliliters

31. Example 4
How many moles of gas are in a container with a volume of 2.46 L at STP?

32. Combined Gas Law a gas often changes in T, P, and V all at once
the other gas laws can be combined into one law
Combined Gas Law- relationship between P, V, and T of a fixed amount of gas

33. Example: Combined Gas Law
A Helium-filled balloon has volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at atm and 10.°C?

34. Example
A balloon containing 5.5 L of air at 25C and 755 torr is put at the bottom of the ocean. The new temperature is 4 C and the new volume is 230 mL. What is the new pressure?

35. Dalton’s Law of Partial Pressure
John Dalton
responsible for atomic theory
also studied gas mixtures
the P of gas mixture is the sum of the individual pressures of each gas alone
the P that each gas exerts in the mixture is independent of the P that are exerted by other gases

36. Dalton’s Law of Partial Pressure
the total P of a mixture of gases is equal to the sum of partial P of component gases, no matter how many different gases
PT = P1 + P2 + P3 + …
Partial Pressure- P of each gas in mixture

37. Why?
the particles of each gas in a mixture have an equal chance to hit the walls
so each gas exerts P independent of that exerted by other gases
total P is result of the total # of collisions per unit of wall area

38. Water Displacement
gas produced is less dense than water so it replaces the water in the bottle
gas collected is not pure because it contains vapor from the water
PT = Pgas + Pwater
set for a certain T
equal to atmospheric pressure

39. Example
Oxygen gas from decomposition of KClO3 was collected by water displacement. The barometric pressure and the temperature during the experiment were torr and 20.0°C respectively. If the partial pressure of water vapor is 17.5 torr at 20.0°C. What was the partial pressure of oxygen collected?
PT = PO2 + PH2O
731.0 torr = PO
PO2 = torr

40. Example
Find the partial pressure by 2 gases (A and B) mixed if the overall pressure is 790 mmHg. The percent by volume is A: 20% and B: 80%.
PT = PA + PB = 790 mmHg
A: 0.20 x 790 = 158 mmHg
B: 0.80 x 790 = 632 mmHg

41. Ch. 11: Molecular Composition of Gases
Ideal Gas Law

42. Ideal Gas Law
relationship among P, V, T, and number of moles of gas (n)
combination of all the laws we learned
helps us approximate “real” gas behavior
where
R: ideal gas constant
L atm/mol K (use most often)
8.314 J/mol K (only for when P is in Pascals)
check units before using equation

43. Example
What is the P in atm exerted by a mol sample of nitrogen gas in a 10.0 L container at 298 K?

44. Example
What is the volume in liters of mol of oxygen gas at 20.0°C and atm?

45. Example
What mass of chlorine gas is in a 10.0 L tank at 27°C and 3.50 atm?

46. Finding Molar Mass mass of one mole of substance units : g/mol
represented by M

47. Finding Molar Mass
At 28°C and atm, 1.00 L of gas has a mass of 5.16g. What is the molar mass?

48. Finding Density

49. Finding Molar Mass
The density of dry air at sea level (with pressure of exactly 1 atm) is g/L at 15°C. What is the molar mass of air?

50. Finding Density
What is the density of carbon monoxide gas at STP?

51. Finding Density
A sample of gas has a mass of 50.0 g and volume of 26.0 L at 25C and 1.2 atm. What is the molar mass of the gas?

52. Ch. 11: Molecular Composition of Gases
Stoichiometry of Gases

53. Stoichiometry of Gases
Remember that coefficients give you
ratio of moles
ratio of molecules
ratio of volumes
even if the gases have different conditions
only when gases are all at same T and P

54. Calculations Review getting moles from grams?
molar mass (periodic table)
getting volume from moles for gas?
at STP only
Molar Volume (22.4 L = 1 mol)
any conditions
Ideal Gas Law (PV = nRT, solve for V)
getting from one type gas to new gas
mole ratio (coefficients in equation)

55. CaCO3(s)  CaO(s) + CO2(g)
Example 1
Calcium carbonate can be heated to make calcium oxide according to the following equation:
CaCO3(s)  CaO(s) + CO2(g)
How many grams of CaCO3 must be decomposed to make 5.00 L of CO2 at STP?
volume of CO2  moles CO2 (molar volume)
moles CO2  moles CaCO3 (mole ratio)
moles CaCO3  grams CaCO3 (molar mass)

56. Example 1 find moles of CO2 convert mol CO2 to mol CaCO3
convert mol CaCO3 to grams

57. WO3(s) + 3H2(g)  W(s) + 3H2O(l)
Example 2
Tungsten is made industrially by:
WO3(s) + 3H2(g)  W(s) + 3H2O(l)
How many liters of hydrogen gas at 35°C and atm are needed to react completely with 875 g WO3?
grams of WO3  moles WO3 (molar mass)
moles WO3  moles H2 (mole ratio)
moles H2  volume H2 (PV = nRT)

58. Example 2
find moles of WO3
find moles of H2
find volume of H2

59. CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
Example 3
Combustion of methane gas produces carbon dioxide gas and water vapor.
CH4(g) + 2O2(g)  CO2(g) + 2H2O(g)
If the reaction produces 213 L of CO2 at STP, what volume of O2 must have been used at 23C and 0.89 atm?
volume of CO2  moles CO2 (molar volume)
moles CO2  moles O2 (mole ratio)
moles O2  volume O2 (PV = nRT)

60. Example 3 find moles of CO2 convert mol CO2 to mol O2
Find volume of O2