Daltons Law of Partial Pressure

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Daltons Law of Partial Pressure
Pressure of each gas is proportional to the
number of moles of each gas. Total pressure is
the sum of the partial pressures.
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A useful equation
Ptot PA PB
Ptot (NaNb)RT/V
Ptot/(NaNb) RT/V Pa/Na
Na/(NaNb) Pa/Ptot
(independent on V and T)
Molar fraction (Xa)
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Partial Pressure
Ptot Pbar Pgas PH2O
Quantifying Gases by Collecting over Water Only
works if the gas is not water soluble!
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KINETIC MOLECULAR THEORY(KMT)

• Theory used to explain gas laws. Puts a molecular
  perspective to the empirical ideal gas law.
• KMT assumptions are
• Gases consist of molecules in constant, random
  motion.
• P arises from collisions with container walls.
• No attractive or repulsive forces between
  molecules. Collisions elastic.
• Volume of molecules is negligible.

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Kinetic Molecular Theory Pressure Assessing
Collision Forces

• Translational kinetic energy,
• Frequency of collisions, (number/volume)
• Impulse or momentum transfer,
• Pressure proportional to impulse times frequency

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Kinetic Molecular Theory Temperature
Modify (for one mole)
PVRT so
Solve for ek
Average kinetic energy is directly proportional
to temperature!
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Velocity of Gas Molecules

• Molecules of a given gas have a range of speeds.

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GAS DIFFUSION AND EFFUSION

• An application of KMT
• diffusion is the gradual mixing of molecules of
  different gases.
• effusion is the movement of molecules through a
  small hole into an empty container.

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GAS DIFFUSION AND EFFUSION

• Molecules effuse through holes in a rubber
  balloon, for example, at a rate ( moles/time)
  that is
• proportional to T
• inversely proportional to M.
• Therefore, He effuses more rapidly than O2 at
  same T.

He
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GAS DIFFUSION AND EFFUSION

• Grahams law governs effusion of gas molecules.

Thomas Graham, 1805-1869. Professor in Glasgow
and London.
Rate of effusion is inversely proportional to
species molar mass.
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Gas Diffusionrelation of mass to rate of
diffusion

• Molar mass of NH3 17.04 g/mol
• Molar mass of HCl 36.46 g/mol
• On which side of the tube will one observe the
  formation of NH4Cl?

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Gas Diffusionrelation of mass to rate of
diffusion

• HCl and NH3 diffuse from opposite ends of tube.
• Gases meet to form NH4Cl
• HCl heavier than NH3
• Therefore, NH4Cl forms closer to HCl end of tube.

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Using KMT to Understand Gas Laws

• Recall that KMT assumptions are
• Gases consist of molecules in constant, random
  motion.
• P arises from collisions with container walls.
• No attractive or repulsive forces between
  molecules. Collisions elastic.
• Volume of molecules is negligible.

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Deviations from Ideal Gas Law

• Real molecules have volume.
• There are intermolecular forces.
• Otherwise a gas could not become a liquid.

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Deviations from Ideal Gas Law Real Gases
One way to show the behavior of Real Gases

• Compressibility factor PV/RT 1 for 1 mole Ideal
• Deviations occur for real gases.
• PV/nRT gt 1 - molecular volume is significant.
• PV/nRT lt 1 intermolecular forces of attraction.

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Deviations from Ideal Gas Law

• Account for volume of molecules and
  intermolecular forces with VAN DER WAALS
  EQUATION.

J. van der Waals, 1837-1923, Professor of
Physics, Amsterdam. Nobel Prize 1910.
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Deviations from Ideal Gas Law

• Account for volume of molecules and
  intermolecular forces with the VAN DER WAALS
  EQUATION.

J. van der Waals, 1837-1923, Professor of
Physics, Amsterdam. Nobel Prize 1910.
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Deviations from Ideal Gas Law

• Cl2 gas has a 6.49, b 0.0562
• For 8.0 mol Cl2 in a 4.0 L tank at 27 oC.
• P (ideal) nRT/V 49.3 atm
• P (van der Waals) 29.5 atm