1. Gases

2. Ideal Gases Ideal gases are imaginary gases that perfectly
fit all of the assumptions of the kinetic molecular
theory.
Gases consist of tiny particles that are far apart
relative to their size.
Collisions between gas particles and between
particles and the walls of the container are
elastic collisions
No kinetic energy is lost in elastic collisions

3. Ideal Gases (continued)
Gas particles are in constant, rapid motion. They
therefore possess kinetic energy, the energy of
motion
There are no forces of attraction between gas
particles
The average kinetic energy of gas particles
depends on temperature, not on the identity
of the particle.

4. The Nature of Gases Gases expand to fill their containers
Gases are fluid – they flow
Gases have low density
1/1000 the density of the equivalent liquid or solid
Gases are compressible
Gases effuse and diffuse

5. Pressure
Is caused by the collisions of molecules with the walls of a container
is equal to force/unit area
SI units = Newton/meter2 = Pascal (Pa)
1 atmosphere = 101,325 Pa
1 atmosphere = 1 atm = 760 mm Hg = 760 torr

6. Measuring Pressure The first device for measuring atmospheric
pressure was developed by Evangelista Torricelli
during the 17th century.
The device was called a “barometer”
Baro = weight
Meter = measure

7. An Early Barometer
The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.

8. Standard Temperature and Pressure “STP”
P = 1 atmosphere, 760 torr
T = 0°C, 273 Kelvin
The molar volume of an ideal gas is liters at STP

9. Converting Celsius to Kelvin
Gas law problems involving temperature require
that the temperature be in KELVIN!
Kelvin = C + 273
°C = Kelvin - 273

10. Are You Ready For Some Practice Time?
Please complete handout 2-2 Practice Problems
#1-10 & 13-2 Practice Problems (on back) #1-8 only!!!
Units of Pressure
1 atm = 760mm Hg
760 torr
101,325 Pa
29.2 in Hg
14.7 lb/in2

11. The Combined Gas Law
The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.
Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.

12. Boyle’s Law Pressure is inversely proportional to volume
when temperature is held constant.
Diving
Spaceman

13. Volume vs Pressure

14. Volume vs 1/Pressure
PV = K
Slope = K

15. Charles’s Law
The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.
(P = constant)

16. Volume vs Temperature
Absolute Zero

17. Gay Lussac’s Law The pressure and temperature of a gas are
directly related, provided that the volume
remains constant.

18. Pressure vs Temperature

19. Avogadro’s Law
For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).
V = an
a = proportionality constant
V = volume of the gas
n = number of moles of gas

20. Volume vs Moles

21. What is the balanced equation?
Suppose we have a 12.2 L sample containing 0.50 mol oxygen gas (O2) at a pressure of 1 atm and a temperature of 25oC. If all the O2 were converted to ozone (O3) at the same temperature and pressure, what would be the volume of the ozone?
What is the balanced equation?
3O2 (g) O3 (g)
How many moles of O3 were produced?
0.33 mol O3

22. Avogadro’s law: V = an Rearrange to give: V = a V V n = n n
Suppose we have a 12.2 L sample containing 0.50 mol oxygen gas (O2) at a pressure of 1 atm and a temperature of 25oC. If all the O2 were convertedto ozone (O3) at the same temperature and pressure, what would be the volume of the ozone?
Avogadro’s law: V = an
Rearrange to give: V = a V V n = n n
So…..what is our volume
of ozone?

23. 8.1 L
HAPPY? OR SAD?

24. Good Luck Ready for a challenge? Each gas is at STP.
Make a table on your whiteboard with 4 columns (one for each gas) and fill in the following rows: Volume, Pressure, Temperature, Mass of gas and # of atoms/molecules
Good Luck

25. PV = nRT Ideal Gas Law P = pressure in atm V = volume in liters
n = moles
R = proportionality constant
= L atm/ mol·K
T = temperature in Kelvin
Holds closely at P < 1 atm

26. Standard Molar Volume
Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
- Amedeo Avogadro

27. Gas Density
… so at STP…

28. Density and the Ideal Gas Law
Combining the formula for density with the Ideal
Gas law, substituting and rearranging algebraically:
M = Molar Mass
P = Pressure
R = Gas Constant
T = Temperature in Kelvin

29. Gas Stoichiometry #1
If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.
3 H2(g) N2(g)  NH3(g)
3 moles H mole N  moles NH3
3 liters H liter N  liters NH3

30. Gas Stoichiometry #2
How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?
3 H2(g) N2(g)  NH3(g)
12 L H2 2
L NH3
= L NH3
8.0 3
L H2

31. Gas Stoichiometry #3
How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
22.4 L O2
g KClO3
2 mol KClO3
1 mol O2
= L O2
13.7

32. Gas Stoichiometry #4
How many liters of oxygen gas, at 37.0C and atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
= “n” mol O2
0.612
mol O2
g KClO3
2 mol KClO3
= 16.7 L

33. Kinetic Energy of Gas Particles
At the same conditions of temperature, all gases
have the same average kinetic energy.
K.E. = 1/2 mv2

34. Gas Stoichiometry #3
How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
22.4 L O2
g KClO3
2 mol KClO3
1 mol O2
= L O2
13.7

35. Gas Stoichiometry #4
How many liters of oxygen gas, at 37.0C and atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
= “n” mol O2
0.612
mol O2
g KClO3
2 mol KClO3
= 16.7 L

36. Magnesium metal reacts with hydrochloric acid to produce
hydrogen gas. Calculate the volume of hydrogen produced
at 28oC and 665 mm Hg from mol Mg and excess HCl.

37. Ammonium sulfate is produced by reacting ammonia with
sulfuric acid. What volume of ammonia at 15oC and 1.15 atm is required to produce 75.0 g of ammonium sulfate?

38. Dalton’s Law of Partial Pressures
For a mixture of gases in a container,
PTotal = P1 + P2 + P
This is particularly useful in calculating the pressure of gases collected over water.

39. Try This!
Mixtures of helium and oxygen can be used in scuba diving
tanks to help prevent “the bends.” For a particular dive, 46 L He
at 25oC and 1.0 atm and 12 L O2 at 25oC and 1.0 atm were
pumped into a tank with a volume of 5.0 L. Calculate the
partial pressure of each gas and the total pressure in the tank
at 25oC.
Calculate the number of moles of
each gas
Good Luck!
Wanna hint?

40. And the answer is……….. PHe = 9.3 atm PO2 = 2.4 atm PT = 11.7 atm χ1
nHe = 1.9 mol
nO2 = 0.49 mol
PHe = 9.3 atm
PO2 = 2.4 atm
PT = atm
Mole Fraction:
The ratio of the number of moles of a given
component in a mixture to the total number
of moles in the mixture. n1 n1
Χ = =
nTOTAL
n1 + n2 + n3 +……
And…..the mole fraction of each component in a mixture of ideal gases
is directly related to its partial pressure! n1 P1
Χ1 = = χ1
So…..
P1 =
X PTOTAL
nTOTAL
PTOTAL

41. Try This! An aqueous solution of hydrochloric acid contains
36% HCl by mass. Calculate the mole fraction of
HCl in the solution.
Moles of HCl = 0.99 mol HCl
Moles of H2O = 3.6 mol H2O
0.99
ΧHCl =
= 0.22
4.6

42. And……Another! A mixture of helium (8.00 g) and argon (40.0 g) in a
Container at 300 K has a total gas pressure of
0.906 atmosphere. What is the partial pressure of
Helium in the mixture?
Mol He = mol He
Mol Ar = mol Ar
2.00 mol
ΧHe =
= 0.667
3.00 mol
PHe = χHePtotal = (0.667) (0.906 atm) = atm

43. Collecting Gas Over Water
Vapor pressure of water = the pressure exerted by the water
vapor on the liquid phase with which it is in equilibrium.

44. A sample of solid potassium chlorate (KClO3) was heated
in a test tube and decomposed by the following reaction:
2KClO3 (s) KCl (s) + 3O2 (g)
The oxygen produced was collected by displacement of water
At 22oC at a total pressure of 754 torr. The volume of the gas
collected was L, and the vapor pressure of the water at 22oC is 21 torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed.
Wanna hint?
FIRST………..find the
partial pressure of O2

45. PTOTAL = PO2 + PH2O 754 torr = PO2 + 21 torr
PO2 = 754 torr – 21 torr = 733 torr.
Now…………use the ideal gas law to find the number of
moles of O2
2.59 x 10-2 mol of O2
Now………calculate the mass of KClO3 in the sample.
2.12 g KClO3

46. Kinetic Molecular Theory
Particles of matter are ALWAYS in motion
Volume of individual particles is  zero.
Collisions of particles with container walls cause pressure exerted by gas.
Particles exert no forces on each other.
Average kinetic energy µ Kelvin temperature of a gas.

47. Diffusion
Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

48. Effusion
Effusion: describes the passage of gas through a tiny orifice into an evacuated chamber.

49. Graham’s Law Rates of Effusion and Diffusion

50. Calculate the ratio of the effusion rates of hydrogen gas (H2) and uranium hexafluoride (UF6), a gas used in the enrichment process to produce fuel for nuclear reactors.
13.2 =

51. Warmup Time Before Next Week’s Test
Ideal gases vary from real gases at conditions of:
High temperature and low pressure
High temperature and high pressure
Low temperature and low pressure
Low temperature and high pressure
Both high density and low pressure
ANSWER: D At low temperature and high pressure, the molecules are
closer together and therefore the forces between the molecules become
more important as they are stronger. The actual (finite) volume of individual
molecules also becomes more important as more of the total space is actually
occupied by finite molecular volume.

52. What is the volume of 3.00 mol of gas @ STP?
3 x 22.4 L
3 x 22.4 L x 760
3 x 22.4 x 273/760
It cannot be determined without knowing which gas is involved.
ANSWER: B The molar volume of all gases at STP is about 22.4 L, so
three moles would occupy 22.4 L / mol x 3 moles.

53. An ideal gas of volume 189. mL is collected over water at 30oC and
777 torr. The vapor pressure of water is 32 30oC. What pressure
is exerted by the dry gas under these conditions?
320 torr
745 torr
777 torr
32/77 torr
32 x 777 torr
ANSWER : B The total pressure = 777 torr. Of this, 32 torr is due to the
water vapor, hence = 745 torr of pressure are allocated to the
dry gas.

54. A 14. 0-L cylinder contains 5. 60 g N2, 39. 95 g Ar and 6. 40 g O2
A 14.0-L cylinder contains 5.60 g N2, g Ar and 6.40 g O2. What is
the total pressure in atm at 27oC? (R = the ideal gas constant.)
20 R
26 R
30 R
60 R
120 R
ANSWER : C Use Ptotal = NtotalRT/V to determine the pressure. From the mass
of each of the gases you can find mol of N2, 1.00 mol of Ar, and mol
of O2 to give a total number of moles (n) of 1.4 mol. Therefore:
Ptotal = R x 1.40 mol x 300 K / 14.0 L = 30 R.

55. In a closed inflexible system, 7.0 mol CO2, 7.0 mol Ar, 7.0 mol N2 and
4.0 mol Ne are trapped, with a total pressure of 10.0 atm. What is the
partial pressure exerted by the neon gas?
1.6 atm
4.0 atm
10.0 atm
21.0 atm
29.0 atm
ANSWER : A The total number of moles is 25 ( = 25),
hence the Ne is 4/25 of the total amount of gas and exerts 4/25 of the total
pressure, or 4/25 x 10 atm = 1.6 atm.

56. Consider the reaction C2H6(g) + 7/2 O2(g) 2CO2(g) + 3H2O(g). If 6
Consider the reaction C2H6(g) + 7/2 O2(g) CO2(g) + 3H2O(g). If 6.0 g ethane, C2H6(g) burn (as shown above), what volume of CO2(g) will be formed at STP?
0.20 L
0.40 L
2.2 L
9.0 L
22.4 L
ANSWER: D 6.0 g of ethane / 30. g/mol yields 0.20 mol of ethane,
which forms twice that number of moles of carbon dioxide. Since one
mole of gas occupies 22.4 L at STP, 22.4 L/mol x 0.20 mol x 2 CO2 / C2H6
= 8.96 L of carbon dioxide (rounded to two sigfigs = 9.0 L)

57. Cl2 and F2 combine to form a gaseous product; one volume of Cl2 reacts
with three volumes of F2 yielding two volumes of product. Assuming
constant conditions of temperature and pressure, what is the formula
of the product?
ClF
Cl2F2
ClF2
Cl2F
ClF3
ANSWER: E This problem assumes you understand Avogadro’s Law,
“At constant temperature and pressure, the volume of a gas is directly
proportional to the number of moles of the gas”. To apply that to this
problem, 1 volume Cl2 + 3 volumes F volumes ClxFx. The
simplest formula for the product becomes ClF3

58. Decreasing the temperature of an ideal gas from 80oC to 40oC causes
the average kinetic energy to
Decrease by a factor of two
Decrease by a factor of four
Increase by a factor of two
Increase by a factor of four
Decrease by less than a factor of two.
ANSWER: E Be careful here to note the difference between the kinds
of temperature scales and what they mean. Even though the Celsius
temperature is half as much, the average kinetic energy is proportional
to the Kelvin temperature. In this case that ratio is only 353/313 = 1.13
so the average kinetic energy decreases only by a factor of 1.13

59. The effusion rate of helium gas, He, compared with that of
Methane gas, CH4 is
Four times greater for helium
Four times less for helium
Twice as great for helium
Twice as great for methane
Sixteen times as great for helium
ANSWER: C Effusion rates are inversely proportional to the square root
of the molecular masses of the gases.

60. “van der Waals equation”
Real Gases
Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).
corrected pressure
corrected volume
Videal
Pideal
“van der Waals equation”

61. The average speed of the molecules of a gas is proportional to the
Volume of the container
Reciprocal of absolute temperature
Absolute temperature
Square root of the absolute temperature
Square of the absolute temperature
ANSWER: D in this case the question is about the average speed (not
the energy) of the molecules.