1. Volume-Mass Relationships of Gases
Chapter 11-1
Volume-Mass Relationships of Gases

2. Measuring and Comparing Volumes of Gases
Gay-Lussac’s Law of combining volumes of gases-
At constant pressure and temperature, the volumes of reacting gaseous reactants and products can be expressed as ratios of small whole numbers.

3. Avagadro’s Law
Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

4. Avagadro’s Law- continued
In other words, Avogadro's number (6.022 X 1023 ) is the number of molecules of any gas present in a volume of L, at standard temperature and pressure .
It is the same for the lightest gas (hydrogen) as it is for a heavy gas such as carbon dioxide or bromine.
One mole of an ideal gas occupies 22.4 liters at STP.

5. Standard Molar Volume 22.4L is the standard molar volume of a gas.
1mol/22.4L can be used as a conversion factor to find the number of moles in a given sample, (and the mass), and vice versa.

6. Try these:
A chemical reaction produces mol of ethane, C2H6. What volume in liters is occupied by this gas sample at STP?
7.62 L
At STP, what is the volume of 4.05 mol of H2O(g)?
90.7 L
A chemical reaction produced mL of nitrogen monoxide gas at STP. What was the mass in grams of the gas produced?
0.180 g

7. Home Fun
Pg q 1-5
Pg 357 q

8. Chapter 11-2
The Ideal Gas Law

9. The Ideal Gas Law PV = nRT
The mathematical relationship among pressure, volume, temperature and the number of moles of a gas.
PV = nRT
R is the ideal gas constant and it’s value varies according to the units of pressure and volume. (See table 11-1, page 342).
You, however, will not have access to the table and will be expected to convert units of pressure, volume, temperature and masses. )

10. How the Ideal Gas Law is Derived
Boyle’s Law- V  1/P
Charles’s Law- V  T
Avagadro’s Law- V  n
These proportions are then combined
V  ( 1/P) (T)(n)
Adding a constant gives an equality: R is the ideal gas constant.
V = nRT/P
Generally, R = L •atm/(mol• K)

11. Try these:
How many moles of methane gas, CH4, are present in a 4.0 g sample?
0.25 mol
Find the pressure, in torr, exerted by the CH4 gas sample when its temperature is 27°C and its volume is mL.
PV=nRT plug and go.
V=volume, n=number of moles, T= temp in K
R= L •atm/(mol• K), or L•kPa/(mol•K), or 62.4mm Hg.
1600 torr

12. A sample that contains 6. 25 mol of gas at 22
A sample that contains 6.25 mol of gas at 22.0°C has a pressure of 680 mm Hg. What is the volume of the gas?
170 L
Chlorine in the upper atmosphere can destroy ozone molecules, O3. The reaction can be represented by the following equation: Cl2(g) + 2O3(g) → 2ClO(g) + 2O2(g) How many liters of ozone can be destroyed at K and 5.0 kPa if g of chlorine gas react with it?
2.0 x 103 L

13. An engineer pumps 5.00 mol of carbon monoxide gas into a cylinder that has a capacity of 20.0 L. What is the pressure in kPa of CO inside the cylinder at 25°C?
619 kPa
A student collects 425 mL of oxygen at a temperature of 24°C and a pressure of atm. How many moles of oxygen did the student collect?
1.57 x mol O2

14. APPLICATIONS OF THE IDEAL GAS LAW
The Ideal gas law can also be used to find molar masses and densities.
How you ask?
When you know the amount and identity of the substance, you can use its molar mass to calculate its mass. The number of moles (n) is equal to the mass(m) /molar mass(M).
n = m/M

15. If you substitute the expression m/M for n in the ideal-gas-law equation, you get the following equation:
This version of the ideal gas law can be solved for any of the five variables P, V, m, M, or T.

16. Practice:
Determine the molar mass of an unknown gas that has a volume of 72.5 mL at a temperature of 68°C, a pressure of atm, and a mass of g.
81.6 g/mol
A sample of an unknown gas has a mass of g. It occupies a volume of 25.0 mL at a temperature of 127°C and has a pressure of kPa. Calculate the molar mass of the gas.
99.6 g/mol

17. One more:
When arsenic(III) sulfide is roasted in air, it reacts with oxygen to produce arsenic(III) oxide and sulfur dioxide . When 89.5 g of As2S3 is roasted with excess oxygen, what volume of SO2 is produced? The gaseous product is measured at 20°C and 98.0 kPa.
Balance the equation As2S3(s) + 9O2(g) 2As2O3(s) 6SO2(g)
Use the molar mass of As2S3 to determine the number of moles that react.
Use the mole ratio from the balanced chemical equation to determine the amount in moles of SO2 formed.
Use the ideal-gas-law equation to determine the volume of SO2 formed from the amount in moles.

18. The two V terms cancel and the equation is rearranged to give:
This equation can also be related to the density of a gas. Density is mass per unit volume
D=m/V  m=DV Substitute DV for m in the gas law equation:
The two V terms cancel and the equation is rearranged to give:

19. Determine the density of hydrogen bromide gas at 3.10 atm and -5°C.
What is the density of silicon tetrafluoride gas
at 72°C and a pressure of kPa?

20. Home Fun
Pg 346 q 1-5
Pg q 16-22

21. 11-3
Gas Stoichiometry

22. The Chemical Equation Indicates molar amounts, and mole ratios.
ALSO INDICATES VOLUME RATIOS
EX : 2CO + O2  2CO2
What does this mean in terms of molecules?
In terms of mol?
In terms of volume the possible ratios are :
2 volumes CO or volumes CO2
2 volumes CO volumes CO
2 volumes CO or 1 volume O2
1 volume O2 2 volumes CO
There is 1 more that you should be able to find on your own.

23. Practice Ammonia can react with oxygen to produce nitrogen and water
4NH3(g) + 3O2(g)  2N2(g) + 6H2O(l)
If 1.78 L of O2 reacts, what volume of nitrogen will be produced? Assume that temperature and pressure remain constant.

24. What volume of oxygen will be used in a reaction of 2800 L of NH3 ?
In one method of manufacturing nitric acid, ammonia is oxidized to nitrogen monoxide and water.
4NH3(g) +5O2(g)  4NO(g) +6H2O(l)
What volume of oxygen will be used in a reaction of L of NH3 ?
What volume of NO will be produced? All volumes are measured under the same conditions.
3500 L O2
2800 L NO

25. Gas volumes can be related by mole ratios only when the volumes are measured under the same conditions of temperature and pressure.
If they are not, then the volume of one of the gases must be converted to the conditions of the other gas.
You will need to use the combined gas law for this conversion.

26. Ethylene gas burns in air according to the following equation:
C2H4(g) + 3O2(g)  2CO2(g) 2H2O(l)
If 13.8 L of C2H4 measured at 21°C and atm burns completely with oxygen, calculate the volume of CO2 produced, assuming the CO2 is measured at 44°C and atm.
Use the volume ratio of C2H4 to CO2 to calculate the volume of CO2 at the same conditions as C2H4 .
Convert to the volume of CO2 for the given conditions using the combined gas law.

27. Practice
A sample of ethanol burns in O2 to form CO2 and H2O according to the following equation:
C2H5 OH + 3O2  2CO2 3H2O
If the combustion uses mL of oxygen measured at atm and 40.°C, what volume of CO2 is produced when measured at STP?
Dinitrogen pentoxide decomposes into nitrogen dioxide and oxygen. If L of N2O5 reacts at STP, what volume of NO2 is produced when measured at 64.5°C and 1.76 atm?
7.02 L
73.3 mL CO2

28. Home fun
Pg 350 q 1-4
Pg q 23-29
30-38 for tomorrow night

29. Effusion and Diffusion
11-4
Effusion and Diffusion

30. Velocity depends only on the size and temperature of the gas.
Reminder
Diffusion – The mixing of gases due to random motion.
Effusion- The movement of a gas through a small opening.
Velocity depends only on the size and temperature of the gas.

31. Temperature is defined as the average kinetic energy of the particles of a substance. K.E. = 1/2mv2
  Therefore, if two gases are at the same temperature, their particles must have the same average kinetic energy:
at equal temperatures - K.E. gas 1 = K.E. gas 2

32. Graham’s Law of Effusion
"The relative rates at which two gases under identical conditions of temperature and pressure will diffuse vary inversely as the square roots of the molecular masses of the gases.“ 
Rate1 is the rate of effusion of the first gas (volume or number of moles per unit time). Rate2 is the rate of effusion for the second gas.
M1 is the molar mass of gas 1.
M2 is the molar mass of gas 2.

33. The density of gas varies directly with its molar mass therefore density can be used in place of molar mass .
Try This:
Nitrogen effuses through a pinhole 1.7 times faster than another gaseous element at the same conditions. Estimate the other element’s molar mass and determine its probable identity.
81 g/mol
Determine the molecular mass ratio of two gases whose rate of diffusion have a ratio of 16:1
256:1

34. Home fun
pg q
Mixed review pg 359 q 43-51