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CH 11 – Physical Characteristics of Gases: Objectives
• Describe how the kinetic-molecular theory of matter explains ideal gases
• Differentiate between ideal and real gases• Describe temperature & pressure and convert units.• State the conditions of STP• Explain and calculate the relationship between volume,
temperature and pressure of gases• Perform the calculations with the combined gas law• Calculate partial pressures from Dalton’s law.• Use the Ideal Gas Law to solve molar gas problems.• Use Graham’s Law to solve gas effusion problems.
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A. Kinetic-Molecular Theory of Ideal Gases
• Particles in an ideal gas…– are far apart relative to their size.– have elastic collisions (no loss of kinetic
energy). – are in constant, random, rapid motion.– don’t attract or repel each other.– have an avg. KE directly related to
temperature.
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A. Kinetic-Molecular Theory of Ideal Gases
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B. Real Gases
• Particles in a REAL gas…– have their own volume– attract each other
• Gas behavior is most ideal…– at low pressures– at high temperatures– in nonpolar atoms/molecules (He, Ne,
H2, N2, I2 etc.)
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C. Characteristics of gases
• Gases expand to fill any container.– random motion, no attraction
• Gases are fluids (like liquids).– no attraction
• Gases have very low densities.– no volume = lots of empty space
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C. Characteristics of gases
• Gases can be compressed.– no volume = lots of empty space
• Gases undergo diffusion & effusion.– random motion
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D. Temperature
ºF
ºC
K
-459 32 212
-273 0 100
0 273 373
32FC 95 K = ºC + 273
• Always use absolute temperature (Kelvin) when working with gases.
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E. Pressure
area
forcepressure
Which shoes create the most pressure?
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E. Pressure• Barometer
– measures atmospheric pressure
Mercury Barometer
Aneroid Barometer
Invented by Evangelista Torricelli
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E. Pressure
• KEY UNITS AT SEA LEVEL
– 101.325 kPa (kilopascal)
– 1 atm
– 760 mm Hg
– 760 torr
– 14.7 psi (pounds per square inch)
2
NPa
m
These are all equalities for conversion
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F. STP
Standard Temperature & Pressure
0°C 273 K
1 atm 101.325 kPa
-OR-
STP
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G. Dalton’s Law of Partial Pressures• The total pressure of a mixture of
gases equals the sum of the partial pressures of the individual gases.
Ptotal = P1 + P2 + ...When a H2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H2 and water vapor.
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L. Sample Problems - Dalton
GIVEN:
Pgas = ?
Ptotal = 742.0 torr
PH2O = 42.2 torr
WORK:
Ptotal = Pgas + PH2O
742.0 torr = Pgas + 42.2 torr
Pgas = 699.8 torr
• A gas is collected over water at a temp of 35.0°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas?
Look up water-vapor pressure on p.859 for 35.0°C.
The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.Go to 2nd to last page of
note packet!
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H. Boyle’s Law
V
P
PV = k
Volume (mL)
Pressure (torr)
P·V (mL·torr)
10.0 760.0 7.60 x 103
20.0 379.6 7.59 x 103
30.0 253.2 7.60 x 103
40.0 191.0 7.64 x 103
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H. Boyle’s Law
• The pressure and volume of a gas are inversely related – at constant mass & temp
P1V1 = P2V2
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I. Charles’ Law
kT
VV
T
Volume (mL)
Temperature (K)
V/T (mL/K)
40.0 273.2 0.146
44.0 298.2 0.148
47.7 323.2 0.148
51.3 348.2 0.147
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I. Charles’ Law
• The volume and absolute temperature (K) of a gas are directly related – at constant mass & pressure
ALL TEMPS INKELVIN1 2
1 2
V V
T T
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J. Gay-Lussac’s Law
kT
PP
T
Temperature (K)
Pressure (torr)
P/T (torr/K)
248 691.6 2.79
273 760.0 2.78
298 828.4 2.78
373 1,041.2 2.79
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J. Gay-Lussac’s Law
• The pressure and absolute temperature (K) of a gas are directly related – at constant mass & volume
1 2
1 2
P P
T T
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Concept Check – assuming other things constant
P decreases Volume
T increases Pressure
V increases Temperature
P decreases Temperature
T decreases volume
V increases pressure
IF… THEN…Increases
Decreases
IncreasesIncreases
DecreasesDecreases
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K. Combined Gas Law
= kPVPTVT
PVT
P1V1
T1
=P2V2
T2
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Sample Problems• A gas occupies 473 cm3 at 36°C. Find its
volume at 94°C.
GIVEN:V1 = 473 cm3
T1 = 36°C = 309K
T2 = 94°C = 367K
V2 = ?
WORK:T VCHARLES’
𝑉 1
𝑇 1
=𝑉 2
𝑇2
Law?:
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Sample Problems
GIVEN:V1 = 100. mL
P1 = 150. kPa
V2 = ?
P2 = 200. kPa
WORK:P1V1 = P2V2
• A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa.
BOYLE’S
P VLaw?:
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Sample Problems
GIVEN:V1 = 7.84 cm3
P1 = 71.8 kPa
T1 = 25°C = 298 K
P2 = 101.325 kPa
T2 = 273 K
V2 = ?
WORK:
• A gas occupies 7.84 cm3 at 71.8 kPa & 25°C. Find its volume at STP.
P T VCOMBINED GAS
LAW𝑃1𝑉 1
𝑇1
=𝑃2𝑉 2
𝑇2
Law?:
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L. Avogadro’s Law
Equal volumes of gases contain___________________.equal numbers of moles
- @ constant temperature and pressure
V
n
kn
V
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M. The Ideal Gas Law
PV=nRT
R=UNIVERSAL GAS CONSTANTR=0.0821 Latm/molKR=8.315 LkPa/molKn = number of moles
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Sample Problem 1
Calculate the pressure in atmospheres of 0.412 mol of He at 16°C & occupying 3.25L
GIVEN: WORK:
P = ? atmn = 0.412 molT = 16°C = 289 KV = 3.25 L R =
PV = nRT
P(3.25)=(0.412)(0.0821)(289) L mol Latm/molK K
P = 3.01 atm0.0821 L*atm/mol*K
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Sample Problem 2
Find the volume of 85 g of O2 at 25°C and 104.5 kPa.
GIVEN: WORK:V = ?
n = 85 g
T = 25°C = 298 K
P = 104.5 kPa
R = 8.315 L*kPa/mol*K
PV = nRT
( )= 2.7 mol85 g O2 32 g O2
1 mol O2
(104.5)V=(2.7)*(8.315)*(298)
V = 64L
n
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