Honors Chemistry
Chapter 5
Gases
5.1 Gases
• Temperature vs. Intermolecular attraction
• Atomic Gases
• Noble Gases, H2, N2, O2, F2, Cl2
• Molecular Gases
• Usually light molecules with weak attraction forces
• Eg: HCl, CO2, NH3, H2S, NO2
• Ionic Compounds
• Strong forces; not normally gases
5.2 Pressure
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Force per unit area
P = F/A
N/m2 unit defined as Pascal (Pa)
Standard air pressure = 101.325 kPa
Also called 1 atmosphere (atm)
Measured by unequal mercury levels
Manometers and barometers
Common unit called mmHg (or Torr)
Standard air pressure = 760 mmHg
5.2 Dimensional Analysis
• Convert 75.0 kPa to mmHg
• 75.0 kPa 760 mmHg
----------- x --------------- = 563 mmHg
1
101.325 kPa
• Try this one
• Convert 1.25 atm to kPa
5.3 Boyle’s Law
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Pressure is inversely proportional to volume
Hold temperature and amount of gas constant
V a 1/P
V = k x (1/P)
PV = k
Best used with changing conditions
P1V1 = P2V2
5.3 Boyle’s Law Problems
• A 175 mL sample of methane is stored at
125 kPa. What pressure is needed to
compress the gas to a volume of 50.0 mL?
• P1V1 = P2V2
• (125 kPa) (175 mL) = P2 (50.0 mL)
• P2 = 438 kPa
• Try this one
• A sample of argon occupies 476 mL at 650 Torr.
Find the volume at 975 Torr.
5.3 Charles’ Law
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Also credited to Gay-Lussac
Volume is directly proportional to temperature
Hold pressure and amount of gas constant
VaT
V = kT
Linear relationship
Must use Kelvins!
V1
V2
--- = --T1
T2
5.3 Charles’ Law Problems
• A 5.00 L helium balloon is heated from 20oC to
75oC. Find its new volume.
• V1/T1 = V2/T2
• 5.00 L
V2
--------- = -------293 K
348 K
• V2 = 5.94 L
• Try this one
• A 670 mL sample of chlorine is stored at 50oC. At what
temperature will its volume be 450 mL?
5.3 More Gas Laws
• Another form of Charles’ Law
• Pressure is directly proportional to temperature
• P = kT
• P1/T1 = P2/T2
• Avogadro’s Law
• Volume is directly proportional to the amount of
gas present
• Van
• Volume relationships in chemical reactions
5.3 Avogadro’s Law Problems
• How many liters of hydrogen are needed
to completely react with 1 liter of oxygen?
• 2 H2 + O2  2 H2O
• 2 mol hydrogen react with 1 mol oxygen
• V a n, so….
• 2 L hydrogen react with 1 L oxygen
• Try this one
• How many liters of ammonia are formed when 1 L
of hydrogen reacts with excess nitrogen?
5.4 The Ideal Gas Equation
• Ideal Gas
• No intermolecular attraction forces
• Particles have no volume
• Combine Boyle’s, Charles, and Avogadro’s
Laws
• PV = nRT
• STP = 1 atm, 273 K
• Molar volume of a gas = 22.414 L at STP
• R = 0.0821 atm L / mol K
5.4 Ideal Gas Equation Problems
• A sample of fluorine occupies 3.65 L at
45oC and 2.50 atm. How many moles of
fluorine are present?
• PV = nRT
• (2.50 atm)(3.65 L) = n (0.0821)(318 K)
• n = 0.350 mol
• Try this one
• A 0.500 mol sample of propane occupies 2.15 L. If
the temperature is 28oC, find the pressure.
5.4 Gas Density
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Since n = m/M….
PV = (m/M) RT
MPV = mRT
Divide by V to get density (m/V)
MP = rRT
Gas density expressed in g/L
5.4 Gas Density Problems
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Find the density of nitrous oxide at STP.
First, find molecular mass of N2O
MP = rRT
(44.0 g/mol)(1.00 atm) = r (0.0821)(273 K)
r = 1.96 g/L
Try this one….
• A gas is found to have a density of 2.54 g/L at
15oC and 1.50 atm. Find its molecular mass.
5.5 Gas Stoichiometry
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Mass-Mass problems (review)
Volume-Volume problems
Volume is proportional to moles, so….
Mol relationship from reaction can be used
directly
• No conversions needed!
5.5 Volume-Volume Problem
• 2 H2 + O2  2 H2O
• If 3.25 L of oxygen react, how many liters
of water vapor are formed?
• 3.25 L O2 2 L H2O
------------- x ------------ = 6.50 L H2O
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1 L O2
• Volume-Volume is just Avogadro’s Law!
5.5 Mass-Volume Problems
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Key step – get to moles!
Mass conversion – use molecular mass
Volume conversion – use gas equation
Need to know temperature and pressure
conditions
5.5 Mass-Volume Problems
• 25.0 g of sodium react with excess water
at STP. How many liters of hydrogen are
produced?
• 2 Na + 2 H2O  2 NaOH + H2
• 25.0 g Na 1 mol Na 1 mol H2
------------ x ----------- x ----------- = 0.543 mol
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23.0 g Na 2 mol Na
• Now use ideal gas equation to get volume
5.5 Mass-Volume Problems
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PV = nRT
(1.00 atm) V = (0.543 mol)(0.0821)(273 K)
V = 12.2 L
Try this one
• Potassium chlorate decomposes into potassium
chloride and oxygen gas. How many grams of
KClO3 are needed to produce 5.00 L of oxygen at
0.750 atm and 18oC?
• Hint: This one is backwards!
5.6 Dalton’s Law
• Partial pressure – the pressure of an
individual gas in a mixture of gases
• Total pressure of a mixture equals the sum
of the partial pressures of each gas
• Pt = P1 + P2 + P3 + ...
• Partial pressure is proportional to
the mol fraction (X1 = n1 / nt)
• P1 = X1 Pt
5.6 Dalton’s Law
• 2.00 mol He is mixed with 1.00 mol Ar. Find the
partial pressure of each at 1.75 atm pressure.
• XHe = 2.00 mol / 3.00 mol = 0.667
• XAr = 1.00 mol / 3.00 mol = 0.333
• PHe = (0.667) (1.75 atm) = 1.17 atm
• PAr = (0.333) (1.75 atm) = 0.583 atm
• Try this...
• Find the partial pressure of oxygen in air if it makes up 21%
of the Earth’s atmosphere by volume. (Note: The volume
gives you the mole ratio because of Avogadro’s law.)
5.7 Kinetic Molecular Theory
• Explains gas behavior in terms of
molecular motion
• Energy
• Work done by a moving object
• Measured in SI unit Joule (J)
• Kinetic energy
• Energy due to motion
• K = ½ mv2
• KMT is a simplification of reality (ideal gas)
5.7 Kinetic Molecular Theory
• Gas molecules are separated by great
distances
• They can be treated as “point masses”
• Gas molecules are in constant random
motion
• Frequent elastic collisions (no energy lost)
• No attractive or repulsive forces
• Average K is proportional to Temperature
5.7 Distribution of Molecular
Speeds
• Maxwell-Boltzmann Distribution
• Molecular speeds distributed around average
• Peak velocity depends on temperature and on
molec. mass
• Root Mean
Square Speed
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vrms = √3RT/M
• Rate of
diffusion
5.8 Deviations from Ideal Behavior
• We made approximations!
• Point masses
• No intermolecular forces
• These approximations become bad at...
• High pressure
• Low temperature
• Liquefaction
• van der Waals Equation
• (P + an2/V2) (V – nb) = nRT