mixtures of gases dalton's law of partial pressure states: –the total pressure of a mixture...
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Mixtures of Gases
• Dalton's law of partial pressure states:– the total pressure
of a mixture of gases is equal to the sum of the partial pressures of the component gases.
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Dalton's Law of Partial PressurePT = P1 + P2 + P3 + …….
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Partial Pressure in terms of mole fraction
OR
XA Ptotal = PA
(XA = mole fraction of A and PA = partial
pressure of gas A)
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Mole fraction
• What is the mole Fraction of Gas A in mixture I?
• What is the mole fraction of Gas B in mixture II?
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Example: If there are 3 moles of gas A, 4 moles of gas B and 5 moles of gas C in a mixture of gases and the pressure of A is
found to be 2.5 atm, what is the total pressure of the sample of gases?
XA = 3 = 0.2
3+4+5
PA = 2.5 atm
PT = PA/ XA = 2.5/0.2 = 12.5 atm
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2KClO3 (s) 2KCl (s) + 3O2 (g)
Bottle full of oxygen gas and water vapor
PT = PO + PH O2 2
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Graham’s Law of Diffusion
• Graham’s law states that the rates of effusion of two gases are inversely proportional to the square roots of their molar masses at the same temperature and pressure:
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Graham’s Law of Effusion
• The velocity of effusion is also inversely proportional to the molar masses:
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Graham’s Law of Diffusion
• But the time required for effusion to take is directly proportional to the molar masses:
• The density of the gas is also directly proportional to the molar masses:
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Graham’s Law of Diffusion
• Compare the rate of effusion for hydrogen and oxygen gases.
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Deviations from Ideal Behavior of Gases
• Deviation from ideal behavior is large at high pressure and low temperature
• At lower pressures and high temperatures, the deviation from ideal behavior is typically small, and the ideal gas law can be used to predict behavior with little error.
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Deviation from ideal behavior as a function of temperature
• As temperature is decreased below a critical value, the deviation from ideal gas behavior becomes severe, because the gas CONDENSES to become a LIQUID.
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• J. D. van der Waals corrected the ideal gas equation in a simple, but useful, way
(a) In an ideal gas, molecules would travel in straight lines. (b) In a real gas, the paths would curve due to the attractions between molecules.
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Real Gases
• No such thing as an ideal gas
• Real gases begin to behave like ideal gases under ideal conditions.– at low pressures– At high temperatures
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Real Gases
• Look at real gas behavior– Graph of PV/nRT vs P– For ideal gases, PV / nRT = 1 at any pressure– For real gases, PV / nRT approaches 1 at
very low pressures (below 1 atm)
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Real Gases
• What is the effect of temperature when plotting PV / nRT vs. P?– PV / nRT approaches 1 at low pressure and at
high temperatures
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Real Gases
• Johannes van Der Waals– Developed an equation for real gases– Received a Nobel prize for his work
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Ideal Gases vs. Real Gases
• Volumeless• Do not interact with
each other
• Finite volumes• Particles do take up
space• Volume of the gas is
actually less than the volume of the container
• Particles do attract each other
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van der Waals Equation
• Correction factors for the ideal gas law
• Correct for the volume:– The actual volume of a real gas is
• V – nb• V = volume of the container• n = # moles of gas particles• b = constant, determined using experimental
results
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van der Waals Equation
• Correction factors for the ideal gas law
• Correct for the attractive forces between particles– Attractive forces would result in fewer, as well
as slightly weaker collisions, resulting in less pressure.
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van der Waals Equation
• Pobs = observed pressure
• P’ = pressure expected from the ideal
gas law
• Pobs = P’ – correction factor
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van der Waals Equation• The correction factor for the attractive
forces would also have to be experimentally determined.
• Depends on– concentration of gas molecules (moles/liter
or n/V)• more gas molecules, more interactions
• Correction factor: a(n/V)2
– a = proportionality constant
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van der Waals Equation
• Pobs = nRT – a (n/V)2
V – nb
Rearrange to get van der Waals equation:
[Pobs + a(n/V)2] x (V – nb) = nRT
( Pcorrected . Vcorrected = nRT)
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van der Waals Equation• A real gas becomes more like an ideal
gas at low pressure…– Low pressure implies a large volume for
the gas particles…the volume of the gas becomes the volume of the container as the gas particles (nb becomes very small) get farther apart
– note that b is smaller when gas particles are smaller (b for He is 0.0237 L/mol while b for Xe is 0.0511 L/mol)
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van der Waals Equation
• A real gas becomes more like an ideal gas at high temperature…
• High temperature means the gas particles have high kinetic energy and are moving past each other with greater speeds, giving the particles less of a chance to feel any attractive force. Pobs approaches Pideal
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Real Gases and Ideal Gases
• In summary, a real gas approaches the behavior of an ideal gas – at low pressure (large container)– at high temperature– when the gas experiences few attractive
forces (the more nonpolar the particle, the weaker the attractive forces)