boyle's law for a fixed amount of gas at constant temperature, pressure is inversely...
TRANSCRIPT
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Boyle's Law
For a fixed amount of gas at constant temperature,pressure is inversely proportional to volume.
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Boyle’s Law tells us that PV must be constant.
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Charles’s Law
For a fixed amount of gas at constant pressure,volume is directly proportional to temperature.
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Ideal Gas LawNote: Avogadro's Law: volume increases linearly with n (T, V constant)
Relation to molar mass (M):
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Partial Pressures
Gas component 1 in the mixture has a mole fraction (x):
The partial pressure of component 1 in the mixture (P) is:
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REMOVE PINS
Irreversible Expansion
pins
P = 2 atm
Pext = 1 atm
P = 1 atm
Pext = 1 atm
Expansion of an Ideal Gas
The work done is
12 VVPVPxAPxfw extextextext
• w is negative for expansion (the gas does work on the “surroundings”)• w is positive for compression (the “surroundings” does work on the gas)
Dx
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Kinetic Theory of Gases
• Volume of particles assumed negligible• Pressure caused by collisions on wall• Particles in constant motion• No intermolecular interactions• Kinetic energy proportional to temperature• Collisions are are elastic
Each particle has a velocity given by:
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Some Important Results
For rates of effusion
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Collisions
With container walls Intermolecular Mean free path
(learn the proof for this one)
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Real Gases
Molar volume is volume divided by moles, and is inversely related to density
• At low P particles attract so molar volume of real gas < molar volume of ideal gas• At high P particles repel so molar volume of real gas > molar volume of ideal gas
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Pote
ntial
Ene
rgy
attra
ction
repu
lsio
n
0 Intermolecular separation
Repulsion/attraction cancels outThe Lennard-Jones Potential
Short-range repulsion(positive)
Long-range attraction(negative)
Attractive interactions include dipole-dipole, dipole-induced dipole, and London dispersion interactions
The van der Waals equation of state takes into account excluded volume due to thefinite size of particles, and a weak intermolecular attraction interaction.
Intermolecular Interactions
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Equilibrium
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