gases. highly compressible. occupy the full volume of their containers. when gas is subjected to...
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GasesGases
P V T nEm pirical Gas Law sIdeal G as LawM ixtures
M athem atical Descriptions
Kinetic EnergyM olecular SpeedReal GasesApplications
KM - M odel of Gases
Behavior & Properties
• Highly compressible.• Occupy the full volume of their containers.• When gas is subjected to pressure, its volume decreases.• Gases always form homogeneous mixtures with other
gases.• Gases only occupy about 0.1 % of the volume of their
containers.
General Characteristics of GasesGeneral Characteristics of Gases
Four Physical Quantities for GasesFour Physical Quantities for Gases
Phys. Qty. Symbol SI unit Other common units
pressure PPascal (Pa)
atm, mm Hg, torr, psi
volume V m3 dm3, L, mL, cm3
temp. T K °C, °F
moles n mol
Atmosphere Pressure and the Barometer
Figure 10.2: PressureFigure 10.2: Pressure
A
FP
•Standard atmospheric pressure = 760 mm of Hg
•1 atm = 760 mmHg = 760 torr = 101.325 kPa.
Figure 10.7: The Pressure-Volume Relationship: Boyle’s Law
The Empirical Gas LawsThe Empirical Gas Laws
The Pressure-Volume Relationship: Boyle’s Law
• Mathematically:
• A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6x103 Pa. If the pressure is changed to 1.5x104 Pa at constant temperature, what will be the new volume?
PV
1constant constantPV
2211 VPVP
The Empirical Gas LawsThe Empirical Gas Laws
•A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6x103 Pa. If the pressure is changed to 1.5x104 Pa at constant temperature, what will be the new volume?
2211 VPVP
The Temperature-Volume Relationship: Charles’s Law• Charles’s Law: the volume of a fixed quantity of gas at constant
pressure increases as the temperature increases.• Mathematically:
• A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What will be the new volume if temp. is increased to 38°C at constant pressure?
TV constant2
2
1
1
T
V constant
T
V
T
V
The Empirical Gas LawsThe Empirical Gas Laws
Example CalculationExample Calculation
•A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What will be the new volume if temp. is increased to 38°C at constant pressure?
2
2
1
1
T
V
T
V
The Quantity-Volume Relationship: Avogadro’s Law
• Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas.
• Mathematically:
nV constant
2
2
1
1
n
V
n
V
2
2
1
1
n
V
n
V
The Empirical Gas LawsThe Empirical Gas Laws
• We can combine these into a general gas law:
The Ideal Gas EquationThe Ideal Gas Equation
), (constant 1
TnP
V
), (constant PnTV
),(constant TPnV
• Boyle’s Law:
• Charles’s Law:
• Avogadro’s Law:
PnT
V
• R = gas constant, then
• The ideal gas equation is:
• R = 0.08206 L·atm/mol·K = 8.3145 J/mol·K• J = kPa·L = kPa·dm3 = Pa·m3
• Real Gases behave ideally at low P and high T.
The Ideal Gas EquationThe Ideal Gas Equation
P
nTRV
nRTPV
Gas ExamplesGas Examples
• A sample of H2 gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 present.
• At a constant temperature of 25°C and a pressure of 1 atm, a 12.2 L sample containing 0.50 moles of O2 gas was converted to ozone ( O3 ). What would be the volume of ozone?
• A sample of diborane gas ( B2H6 ), a substance that bursts into flames when exposed to air, has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L. If temp. and pressure are changed to 36°C and 468 torr; what will be the new volume of the gas?
• What is the molar volume of an ideal gas at STP? [STP stands for Standard Temperature and Pressure: 0°C and 1 atm. STP is only applied to gases.]
• A sample of H2 gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 present.
nRTPV
At a constant temperature of 25°C and a pressure of 1 atm, a 12.2 L sample containing 0.50 moles of O2 gas was converted to ozone ( O3 ). What would be the volume of ozone?
nRTPV 2
2
1
1
n
V
n
V
2
2
1
1
n
V
n
V
• A sample of diborane gas ( B2H6 ), a substance that bursts into flames when exposed to air, has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L. If temp. and pressure are changed to 36°C and 468 torr; what will be the new volume of the gas?
nRTPV
V2 = 3.07 L
n = 0.07457 mol
What is the molar volume of an ideal gas at STP? [STP stands for Standard Temperature and Pressure: 0°C and 1 atm. STP is only applied to gases.]
nRTPV
Key – F14
Gas Densities and Molar Mass• The molar mass of a gas can be determined as follows:
• The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas?
Density of an Ideal-GasDensity of an Ideal-Gas
PdRTM
Density CalculationDensity Calculation
•The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas?
PdRTM
HW 11-9-11 - Key
• Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component:
• Each gas obeys the ideal gas equation:
Gas Mixtures and Partial PressuresGas Mixtures and Partial Pressures
321total PPPP
VRT
nP ii
• Partial Pressures and Mole Fractions
• Let ni be the number of moles of gas i exerting a partial pressure Pi, then
where i is the mole fraction (ni/nt).
Gas Mixtures and Partial PressuresGas Mixtures and Partial Pressures
totalPP ii
CyberChem Diving video
Assumptions:– Gases consist of a large number of molecules in constant
random motion.
– Volume of individual molecules negligible compared to volume of container.
– Intermolecular forces (forces between gas molecules) negligible.
Kinetic Molecular TheoryKinetic Molecular Theory
MTR
u
3
TR2
3Energy Kinetic
Kinetic Molecular TheoryKinetic Molecular Theory
Graham’s Law of Effusion• Effusion is the escape of a gas
through a tiny hole (a balloon will deflate over time due to effusion).
Figure 10.20
Diffusion• Diffusion of a gas is the spread of the gas through space
and the mixing through other gases.
• Diffusion is faster for light gas molecules.
• Diffusion is slowed by gas molecules colliding with each other.
Kinetic Molecular TheoryKinetic Molecular Theory
Graham’s Law of Effusion
• Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by:
Kinetic Molecular TheoryKinetic Molecular Theory
1
2
2
1
2
1
2
13
3
MM
M
M RT
RT
uu
rr
Also works for Comparison of Diffusion rates
Figure 10.19: Molecular Effusion and Diffusion• The lower the molar mass, M, the higher the rms.
Kinetic Molecular TheoryKinetic Molecular Theory
The van der Waals Equation
• General form of the van der Waals equation:
Real Gases: Deviations from Ideal BehaviorReal Gases: Deviations from Ideal Behavior
2
2
V
annbV
nRTP
nRTnbVV
anP
2
2
Corrects for molecular volume
Corrects for molecular attraction