GASES

1
GASES

• Chapter 5

2
A Gas

• Uniformly fills any container.
• Mixes completely with any other gas
• Exerts pressure on its surroundings.

3
Simple barometer invented by Evangelista
Torricelli
4
Barometer
Vacuum

• The pressure of the atmosphere at sea level will
  hold a column of mercury 760 mm Hg.
• 1 atm 760 mm Hg

760 mm Hg
1 atm Pressure
5
Manometer

• Column of mercury to measure pressure.
• h is how much lower the pressure is than outside.

h
Gas
6
Manometer

• h is how much higher the gas pressure is than the
  atmosphere.

h
Gas
7
Simple Manometer
8
Units of pressure

• 1 atmosphere 760 mm Hg
• 1 mm Hg 1 torr
• 1 atm 101,235 Pascals 101.325 kPa
• 14.69 psi1Atm
• Can make conversion factors from these.
• What is 724 mm Hg in atm
• in torr?
• in? kPa?

9
Pressure

• is equal to force/unit area
• SI units Newton/meter2 1 Pascal (Pa)
• 1 standard atmosphere 101,325 Pa
• 1 standard atmosphere 1 atm
• 760 mm Hg 760 torr

10
Pressure Unit Conversions

• The pressure of a tire is measured to be 28 psi.
  What would the pressure in atmospheres, torr, and
  pascals.
• (28 psi)(1.000 atm/14.69 psi) 1.9 atm
• (28 psi)(1.000 atm/14.69 psi)(760.0
  torr/1.000atm) 1.4 x 103 torr
• (28 psi)(1.000 atm/14.69 psi)(101,325 Pa/1.000
  atm) 1.9 x 105 Pa

11
Volume of a gas decreases as pressure increases
at constant temperature
12
Boyles Law

• P1V1 P2V2 (T constant)
• (Holds precisely only at very low pressures.)

Boyles Law Pressure and volume are inversely
related at constant temperature.
13
V
P (at constant T)
14
Boyles Law Calculations

• A 1.5-L sample of gaseous CCl2F2 has a pressure
  of 56 torr. If the pressure is changed to 150
  torr, will the volume of the gas increase or
  decrease? What will the new volume be?
• Decrease
• P1 56 torr
• P2 150 torr
• V1 1.5 L
• V2 ?

V1P1 V2P2 V2 V1P1/P2 V2 (1.5 L)(56
torr)/(150 torr) V2 0.56 L
15
Boyles Law Calculations

• In an automobile engine the initial cylinder
  volume is 0.725 L. After the piston moves up,
  the volume is 0.075 L. The mixture is 1.00 atm,
  what is the final pressure?
• P1 1.00 atm
• P2 ?
• V1 0.725 L
• V2 0.075 L

V1P1 V2P2 P2 V1P1/V2 P2 (0.725 L)(1.00
atm)/(0.075 L) P2 9.7 atm
Is this answer reasonable?
16
Volume of a gas increases as heat is added when
pressure is held constant.
17
Charless Law

• The volume of a gas is directly proportional to
  temperature, and extrapolates to zero at zero
  Kelvin.

18
Charless Law
19
Examples

• What would the final volume be if 247 mL of gas
  at 22ºC is heated to 98ºC , if the pressure is
  held constant?

20
Combined Gas Law

• If the moles of gas remains constant, use this
  formula and cancel out the other things that
  dont change.
• P1 V1 P2 V2
  . T1 T2

21
Examples

• A deodorant can has a volume of 175 mL and a
  pressure of 3.8 atm at 22ºC. What would the
  pressure be if the can was heated to 100.ºC?

22
Avogadros Law

• For a gas at constant temperature and pressure,
  the volume is directly proportional to the number
  of moles of gas (at low pressures).

23
At constant temperature and pressure, increasing
the moles of a gas increases its volume.
24
AVOGADROS LAW

• V1/n1 V2/n2

25
Avogadro simple

• A 5.20L sample at 18.0 C and 2.00 atm pressure
  contains 0.436 moles of gas . If we add an
  additional 1.27 moles of the gas at the same
  temperature and pressure, what will the total
  volume occupied by the gas be ?

26
AVOGADROS LAW dif

• A 12.2 L sample containing 0.50 mol of oxygen
  gas, O2, at a pressure of 1.00 atm and a
  temperature of 25 oC is converted to ozone, O3,
  at the same temperature and pressure, what will
  be the volume of the ozone? 3 O2(g) ---gt 2 O3(g)
• (0.50 mol O2)(2 mol O3/3 mol O2) 0.33 mol O3
• V1 12.2 L
• V2 ?
• n1 0.50 mol
• n2 0.33 mol

V2 (12.2 L)(0.33 mol)/(0.50 mol) V2 8.1 L
27
Ideal Gas Law

• An equation of state for a gas.
• state is the condition of the gas at a given
  time.
• PV nRT

28
IDEAL GAS

• 1. Molecules are infinitely far apart.
• 2. Zero attractive forces exist between the
  molecules.
• 3. Molecules are infinitely small--zero molecular
  volume.

29
REAL GAS

• 1. Molecules are relatively far apart compared to
  their size.
• 2. Very small attractive forces exist between
  molecules.
• 3. The volume of the molecule is small compared
  to the distance between molecules.

30
Ideal Gas Law

• PV nRT
• R proportionality constant
• 0.0821 L atm ??? mol??
• P pressure in atm
• V volume in liters
• n moles
• T temperature in Kelvins
• Holds closely at P lt 1 atm

31
Ideal Gas Law Calculations

• A 1.5 mol sample of radon gas has a volume of
  21.0 L at 33 oC. What is the pressure of the
  gas?
• p ?
• V 21.0 L
• n 1.5 mol
• T 33 oC 273
• T 306 K
• R 0.0821 Latm/molK

pV nRT p nRT/V p (1.5mol)(0.0821Latm/molK)(3
06K) (21.0L) p 1.8 atm
32
Ideal Gas Law Calculations

• A sample of hydrogen gas, H2, has a volume of
  8.56 L at a temperature of O oC and a pressure of
  1.5 atm. Calculate the number of moles of
  hydrogen present.
• p 1.5 atm
• V 8.56 L
• R 0.0821 Latm/molK
• n ?
• T O oC 273
• T 273K

pV nRT n pV/RT n (1.5 atm)(8.56L)
(0.08206 Latm/molK)(273K) n 0.57 mol
33
Standard Temperature and Pressure

• STP
• P 1 atmosphere
• T ??C or 273K
• The molar volume of an ideal gas is 22.42 liters
  at STP

34
Molar Volume

• pV nRT
• V nRT/p
• V (1.00 mol)(0.08206 Latm/molK)(273K)
• (1.00 atm)
• V 22.4 L

35
Gases at STP

• A sample of nitrogen gas has a volume of 1.75 L
  at STP. How many moles of N2 are present?
• (1.75L N2)(1.000 mol/22.4 L) 7.81 x 10-2 mol N2

36
MOLAR MASS OF A GAS

• n m/M
• n number of moles
• m mass
• M molar mass

37
MOLAR MASS OF A GAS

• P mRT/VM
• or
• P DRT/M
• therefore
• M DRT/P

38

• A gas at 34.0C and 1.75 atm has a density of
  3.40 g/L. Calculate the molar mass.

39

• What is the density of 2L of O2 gas at STP?

40
GAS STOICHIOMETRY

• 1. Mass-Volume
• 2. Volume-Volume

41
Gas Stoichiometryat STP

• Quicklime, CaO, is produced by heating calcium
  carbonate, CaCO3. Calculate the volume of CO2
  produced at STP from the decomposition of 152 g
  of CaCO3. CaCO3(s) ---gt CaO(s) CO2(g)
• (152g CaCO3)(1 mol/100.1g)(1mol CO2/1mol CaCO3)
  (22.4L/1mol) 34.1L CO2
• Note This method only works when the gas is at
  STP!!!!!

42
Volume-Volume

• If 25.0 L of hydrogen reacts with an excess of
  nitrogen gas, how much ammonia gas will be
  produced? All gases are measured at the standard
  temperature and pressure.
• 2N2(g) 3H2(g) ----gt 2NH3(g)

43

• 16.7 L NH3

44
Gas StoichiometryNot at STP (Continued)

• p 1.00 atm
• V ?
• n 1.28 x 10-1 mol
• R 0.08206 Latm/molK
• T 25 oC 273 298 K

pV nRT V nRT/p V (1.28 x 10-1mol)(0.08206Lat
m/molK)(298K) (1.00 atm) V 3.13 L O2
45
Daltons Law of Partial Pressures

• For a mixture of gases in a container,
• PTotal P1 P2 P3 . . .

46
Daltons Law of Partial Pressures Calculations

• A mixture of nitrogen gas at a pressure of 1.25
  atm, oxygen at 2.55 atm, and carbon dioxide at
  .33 atm would have what total pressure?
• PTotal P1 P2 P3
• PTotal 1.25 atm 2.55 atm .33 atm
• Ptotal 4.13 atm

47
Water Vapor Pressure

• 2KClO3(s) ----gt 2KCl(s) 3O2(g)
• When a sample of potassium chlorate is decomposed
  and the oxygen produced is collected by water
  displacement, the oxygen has a volume of 0.650 L
  at a temperature of 22 oC. The combined pressure
  of the oxygen and water vapor is 754 torr (water
  vapor pressure at 22 oC is 21 torr). How many
  moles of oxygen are produced?
• Pox Ptotal - PHOH
• Pox 754 torr - 21 torr
• pox 733 torr

48

• Daltons Law 
• Mixtures of helium and oxygen can be used in
  scuba diving tanks to help prevent the bends.
  For a particular dive, 46L 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.

49

• A Volume of 2.0 L of He at 46 C and 1.2 ATM
  pressure was added to a vessel that contained
  4.5L of N2 at STP. What is the total pressure of
  each gas at STP after the He is added .
• RB P 128

50
MOLE FRACTION

• -- the ratio of the number of moles of a given
  component in a mixture to the total number of
  moles of the mixture.
• ?1 n1/ ntotal
• ?1 V1/ Vtotal
• ?1 P1 / Ptotal (volume temperature constant)

51

• The partial pressure of Oxygen gas was observed
  to be 156 torr in the air with a total atmosphere
  pressure of 743 torr . Calculate the mole
  fraction of O2 present.

52
Mole Fraction

• The mole Fraction of nitrogen in the air is
  .7808. Calculate the partial pressure of N2 in
  the air when the atmospheric pressure is 760.

53
Root mean square velociyy

• Kelvin temperature is an index of the random
  motions of gas particles (higher T means greater
  motion.)

54
Calculate the root mean square velocity for the
atoms in a sample of helium gas at 25C.
and100C.
55
Example

• Calculate the root mean square velocity of
  carbon dioxide at 25ºC.
• Calculate the root mean square velocity of
  chlorine at 25ºC.

56
Diffusion describes the mixing of gases. The
rate of diffusion is the rate of gas mixing.

• Effusion describes the passage of gas into an
  evacuated chamber.

57
Effusion of a gas into an evacuated chamber
58
Effusion
Diffusion
59
Grams Law

• Calculate the ratio of effusion rates of hydrogen
  gas and uranium hexafluoride.

60

• A compound effuses through a porous cylinder 3.20
  time faster than helium. What is its molar mass?

61
Kinetic Molecular Theory

• 1. Volume of individual particles is ? zero.
• 2. Collisions of particles with container walls
  cause pressure exerted by gas.
• 3. Particles exert no forces on each other.
• 4. Average kinetic energy ? Kelvin temperature of
  a gas.

62
Real Gases

• Real molecules do take up space and they do
  interact with each other (especially polar
  molecules).
• Need to add correction factors to the ideal gas
  law to account for these.

63
Volume Correction

• The actual volume free to move in is less because
  of particle size.
• More molecules will have more effect.
• Corrected volume V V - nb
• b is a constant that differs for each gas.
• P nRT (V-nb)

64
Pressure correction

• Because the molecules are attracted to each
  other, the pressure on the container will be less
  than ideal
• depends on the number of molecules per liter.
• since two molecules interact, the effect must be
  squared.

65
Pressure correction

• Because the molecules are attracted to each
  other, the pressure on the container will be less
  than ideal
• depends on the number of molecules per liter.
• since two molecules interact, the effect must be
  squared.

(
)
2
Pobserved
P - a
66
Altogether
(
)

• Pobs nRT - a n 2 V-nb
  V
• Called the Van der Walls equation if
  rearranged
• Corrected Corrected Pressure Volume

67
Where does it come from

• a and b are determined by experiment.
• Different for each gas.
• Bigger molecules have larger b.
• a depends on both size and polarity.
• once given, plug and chug.

68
Example

• Calculate the pressure exerted by 0.5000 mol Cl2
  in a 1.000 L container at 25.0ºC
• Using the ideal gas law.
• Van der Waals equation
• a 6.49 atm L2 /mol2
• b 0.0562 L/mol

69
Real Gases

• Must correct ideal gas behavior when at high
  pressure (smaller volume) and low temperature
  (attractive forces become important).

70
Plots of PV/nRT vs. P for several gases at 200
K. Note the significant deviation from ideal
behavior.
71
Real Gases
?
?
corrected pressure
corrected volume
Pideal
Videal
72
Concentration for some smog components vs. time
of day
73
NO2(g)? NO(g) O(g)
O(g) O2(g) ? O3(g)
NO(g) 1/2 O2(g) ? NO2(g)
__________________________
3/2 O2(g) ? O3(g)
What substances represent intermediates?
Which substance represents the catalyst?
74
Chemistry is a gas!!