1 Molecular Composition of Gases Chapter 11. 2 Gay-Lussac’s law of combining volumes of gases At...
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Transcript of 1 Molecular Composition of Gases Chapter 11. 2 Gay-Lussac’s law of combining volumes of gases At...
1
Molecular Composition of Gases
Chapter 11
2
Gay-Lussac’s law of combining volumes of gases
• At constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers
3
Example
• When 2 L of hydrogen react with 1 L of oxygen 2 L of water vapor are produced.
• Write the balanced chemical equation:
4
You try
• When 1 L of hydrogen gas reacts with 1 L of chlorine gas, 2 L of hydrogen chloride gas are produced.
• Write the balanced chemical equation:
5
Avogadro's Law
• Equal volumes of gases at the same pressure and temperature contain the same number of molecules• Atoms can’t split diatomic
molecules• Gas volume is proportional to the
number of moleculesknV
6
Molar Volume
• 1 mole of any gas contains 6.022 x 1023 molecules.
• According to Avogadro’s law, 1 mole of any gas must have the same volume.
• Standard molar volume: molar volume of 1 mole of any gas at STP• 22.4 L
7
Example
• You are planning an experiment that requires 0.0580 mol of nitrogen monoxide gas. What volume in liters is occupied by this gas at STP?
• 1.30 L NO
8
You try
• A chemical reaction produces 2.56 L of oxygen gas at STP. How many moles of oxygen are in this sample?
• 0.114 mol O2
9
Example
• Suppose you need 4.22 g of chlorine gas. What volume at STP would you need to use?
• 1.33 L Cl2
10
You try
• What is the mass of 1.33 x 104 mL of oxygen gas at STP?
• 19.0 g O2
11
Discuss
• Explain Gay-Lussac’s law of combining volumes
• State Avogadro’s law and explain its significance.
12
Review
• Boyles Law:
• Charles Law:
• Avogadro’s Law:
PV
1
TV
nV
13
Math
• A quantity that is proportional to each of several quantities is also proportional to their product. Therefore:
nTP
V 1
14
More math
• Convert a proportionality
xy
kxy
• to an equality by multiplying by a constant
15
Therefore
• We can covert
nTP
V 1
• to
nTP
RV 1
16
More neatly
P
nRTV
or
nRTPV
17
This means….
• The volume of a gas varies directly with the number of moles and the temperature in Kelvin.
• The volume varies indirectly with pressure.
18
What if…
• n and T are constant?• nRT is a constant, k
• Boyle’s Law
• n and P are constant?• nR/P is a constant, k
• Charles’s Law
kPV
kTV
19
What if…
• P and T are constant?• RT/P is a constant, k
• Avogadro’s law
knV
20
The ideal gas constant
• R• Value depends on units• SI units:
Kmol
J 314.8
R
21
Other units
22
Solving ideal gas problems
• Make sure the R you use matches the units you have.
• Make sure all your units cancel out correctly.
23
Example
• A 2.07 L cylinder contains 2.88 mol of helium gas at 22 °C. What is the pressure in atmospheres of the gas in the cylinder?
• 33.7 atm
24
You try
• A tank of hydrogen gas has a volume of 22.9 L and holds 14.0 mol of the gas at 12 °C. What is the reading on the pressure gauge in atmospheres?
• 14.3 atm
25
Example
• A reaction yields 0.00856 mol of oxygen gas. What volume in mL will the gas occupy if it is collected at 43 °C and 0.926 atm pressure?
• 240. mL
26
You try
• A researcher collects 9.09 x 10-3 mol of an unknown gas by water displacement at a temperature of 16 °C and 0.873 atm pressure (after the partial pressure of the water vapor has been subtracted). What volume of gas in mL does the researcher have?
• 247 mL
27
Finding mass
• Number of moles (n) equals mass (m) divided by molar mass (M).
nRTPV
M
mRTPV
PV
mRTM
28
Example
• What mass of ethene gas, C2H4, is contained in a 15.0 L tank that has a pressure of 4.40 atm at a temperature of 305 K?
• 74.0 g
29
You try
• NH3 gas is pumped into the reservoir of a refrigeration unit at a pressure of 4.45 atm. The capacity of the reservoir is 19.4 L. The temperature is 24 °C. What is the mass of the gas in kg?
• 6.03 x 10-2 kg
30
Example
• A chemist determines the mass of a sample of gas to be 3.17 g. Its volume is 942 mL at a temperature of 14 °C and a pressure of 1.09 atm. What is the molar mass of the gas?
• 72.7 g/mol
31
Density
PV
mRTM
V
mD
P
DRTM
32
You try
• The density of dry air at sea level (1 atm) is 1.225 g/L at 15 °C. What is the average molar mass of the air?
• 29.0 g/mol
33
Stoichiometry
• Involves mass relationships between reactants and products in a chemical reaction
• For gases, the coefficients in the balanced chemical equation show volume ratios as well as mole ratios• All volumes must be measured at the
same temperature and pressure
34
Volume-Volume calculations
• From volume of one gas to volume of another gas
• Use volume ratios just like mole ratios in chapter 9
35
Example
• Xenon gas reacts with fluorine gas to produce the compound xenon hexafluoride, XeF6. Write the balanced equation for this reaction.• Xe(g) + 3F2(g) XeF6(g)
• If a researcher needs 3.14 L of XeF6 for an experiment, what volumes of xenon and fluorine should be reacted?• 3.14 L of Xe and 9.42 L of F2
36
Example
• Nitric acid can be produced by the reaction of gaseous nitrogen dioxide with water.3NO2(g) + H2O(l) 2HNO3(l) + NO(g)
• If 708 L of NO2 gas react with water, what volume of NO gas will be produced?
• 236 L
37
You try
• What volume of hydrogen gas is needed to react completely with 4.55 L of oxygen gas to produce water vapor?
• 9.10 L
38
You try
• At STP, what volume of oxygen gas is needed to react completely with 2.79 x 10-2 mol of carbon monoxide gas, CO, to form gaseous carbon dioxide?
• 0.313 L
39
You try
• Fluorine gas reacts violently with water to produce hydrogen fluoride and ozone according to the following equation:3F2(g) + 2H2O(l) 6HF(g) + O3(g)
• What volumes of O3 and HF gas would be produced by the complete reaction of 3.60 x 104 mL of fluorine gas?
• 1.20 x 104 mL O3 and 7.20 x 104 mL HF
40
You try
• Ammonia is oxidized to make nitrogen monoxide and water4NH3(g) + 5O2(g) 4NO(g) + 6H2O(l)
• At STP, what volume of oxygen will be used in a reaction of 125 mol of NH3? What volume of NO will be produced?
• 3.50 x 103 L O2 and 2.80 x 103 L NO
41
Volume-mass and mass-volume
• Converting from volume to mass or from mass to volume
• Must convert to moles in the middle
• Ideal gas law may be useful for finding standard conditions
42
Example
• Aluminum granules are a component of some drain cleaners because they react with sodium hydroxide to release both heat and gas bubbles, which help clear the drain clog. The reaction is:2NaOH(aq) + 2Al(s) + 6H2O (l) 2NaAl(OH)4(aq) + 3 H2(g)
• What mass of aluminum would be needed to produce 4.00 L of hydrogen gas at STP?
• 3.21 g
43
Example
• Air bags in cars are inflated by the sudden decomposition of sodium azide, NaN3 by the following reaction:2NaN3(s) 3N2(g) + 2Na(s)
• What volume of N2 gas, measured at 1.30 atm and 87 °C, would be produced by the reaction of 70.0 g of NaN3?
• 36.6 L
44
You try
• What volume of chlorine gas at 38°C and 1.63 atm is needed to react completely with 10.4 g of sodium to form NaCl?
• 3.54 L Cl2
45
Example
• A sample of ethanol burns in O2 to form CO2 and H2O according to the following reaction.C2H5OH + 3O2 2CO2 + 3H2O
• If the combustion uses 55.8 mL of oxygen measured at 2.26 atm and 40.°C, what volume of CO2 is produced when measured at STP?
• 73.3 mL CO2
46
You try
• Dinitrogen pentoxide decomposes into nitrogen dioxide and oxygen. If 5.00 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 NO2
47
Review
• Diffusion: the gradual mixing of gases due to their random motion
• Effusion: gases in a container randomly pass through a tiny opening in the container
48
Rate of effusion
• Depends on relative velocities of gas molecules.
• Velocity varies inversely with mass• Lighter particles move faster
49
Kinetic energy
• Depends only on temperature• Equals
• For two gases, A and B, at the same temperature
• Each M stands for molar mass
2
2
1mv
22
2
1
2
1BBAA vMvM
50
Algebra time
22
2
1
2
1BBAA vMvM
22BBAA vMvM
A
B
B
A
M
M
v
v2
2
A
B
B
A
M
M
v
v
51
Rate of effusion
• Depends on relative velocities of gas molecules.
A
B
M
M
B ofeffusion of rate
A ofeffusion of rate
52
Graham’s law of effusion
• The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.
53
Graham’s law
• Graham experimented with densities of gases, not molar masses.
• Density and molar mass are directly proportional
• So we can replace molar mass with density in the equation
A
B
density
density
B ofeffusion of rate
A ofeffusion of rate
54
Use of Graham’s law
• Finding the molar mass• Compare rates of effusion of a gas
with known molar mass and a gas with unknown molar mass
• Use Graham’s law equation to solve for the unknown M
• Used to separate isotopes of uranium
55
Example
• Compare the rates of effusion of hydrogen and helium at the same temperature and pressure.
• Hydrogen diffuses about 1.41 times faster
56
Example
• Nitrogen effuses through a pinhole 1.7 times as fast as another gaseous element at the same conditions. Estimate the other element’s molar mass and determine its probable identity.
• 81 g/mol, krypton
57
You try
• Estimate the molar mass of a gas that effuses at 1.6 times the effusion rate of carbon dioxide.
• 17 g/mol