ideal gases vs. real gaseschem107.chem.tamu.edu/brown/slides/1023_2.pdf · real gases: van der...
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CHEM 107, Fall 2019
© 2019, L.S. Brown 1
Ideal Gases vs. Real Gases
• Most gases obey the ideal gas law under normal conditions…
• but most substances are not gases under normal conditions
• Limitations on use of ideal gas model?– check assumptions of model
Assumptions in Ideal Gas Model
• Of various assumptions, the two most questionable are:– The molecules themselves occupy zero volume (i.e., point
masses)– The molecules do not exert any attractive or repulsive
forces upon each other• When are these assumptions unreasonable?• High pressures and/or low temperatures
CHEM 107, Fall 2019
© 2019, L.S. Brown 2
Real Gases:Van der Waals Equation
•The a term corrects for non-zero forces between molecules•The b term corrects for molecular volume•Both a and b depend on identity of the gas!
𝑃 +𝑎𝑛%
𝑉%𝑉– 𝑛𝑏 = 𝑛𝑅𝑇
Still no need to memorize this equation!
CHEM 107, Fall 2019
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Gas a(atm L2 mol–2)
b(L mol-1)
He 0.034 0.0237H2 0.2444 0.02661Ar 1.345 0.03219N2 1.390 0.03913
CH4 2.253 0.04278H2O 5.464 0.03049HF 9.433 0.0739SF6 7.747 00879
van der Waals constants for some common gases
a accounts for intermolecular forces.
b accounts for excluded volume
Intermolecular Forces (IMFs)• Responsible for the existence of condensed phases
(solids & liquids)• Based on Coulomb forces• Much weaker than chemical bonds• Types to consider (all very similar, but strengths vary):
– dipole forces– dispersion forces– hydrogen bonding
CHEM 107, Fall 2019
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• In a collection of dipoles, oppositely charged ends of the dipoles will attract each other. Similarly charged ends will repel.
• These forces will cause dipoles to line up with one another and “stick together.”
Dipole Forces
+–+
–
–
+–+or
Polar Molecules
• Many molecules have a dipole moment due to polarity of bonds & shape of molecule
• These polar molecules will be influenced by dipolar forces.
CHEM 107, Fall 2019
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Dispersion Forces• Non-polar molecules also form condensed phases. H2
boils at20 K, and He boils at 4.2 K (at 1 atm pressure)• Forces?
→“Dispersion forces” due to induced dipoles• Arise because electron cloud is not static• Present in all molecules (and geckos…)
Transient Dipoles - H2 example
• H2 molecule: average e– density is symmetric• But at any given instant, the e– density may be bigger
on one “end” of the molecule than on the other, creating a transient dipole.
• The transient dipole in one molecule will influence other molecules, so that the induced dipoles will “line up” just like “real” or permanent dipoles.
CHEM 107, Fall 2019
© 2019, L.S. Brown 6
Transient Dipoles - H2 example
H2, one e– on each end H2, both e–’s on same end,producing temporary dipole
– +
– +
– +
Transient dipole sets up similar dipoles in nearby molecules,and molecules line up to maximize attractive forces.
Strength of Intermolecular Forces
• Strength of forces between molecules determines physical state (solid, liq., gas)
• Strength of dispersion forces increases as molecules become larger.– more e–’s ® more “polarizable”
• Stronger intermolecular forces lead to higher melting & boiling points.
CHEM 107, Fall 2019
© 2019, L.S. Brown 7
Intermolecular forces & physical state
F2: gas at 298 K
Br2: liquid at 298 K
Strength of Intermolecular Forces
• Big, heavy molecules tend to have high boiling points.• Polar molecules tend to have higher boiling points
than non-polar molecules with similar size & shape.
CHEM 107, Fall 2019
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Hydrogen Bonding
• Special case of dipole-dipole interaction• Stronger than usual due to small size of H-atom• Occurs only in molecules containing H bound to a very
electronegative atom (F, O, or N)• H “end” of one molecule is attracted to the
electronegative “end” of another molecule
CHEM 107, Fall 2019
© 2019, L.S. Brown 9
Hydrogen bonds and water
• H-bonds give water some special properties:– high melting & boiling points, essential for our existence– structure of ice is very “open” and very stable– density of water increases slightly on melting, so ice floats
• H-bonds also important in structure of bio-molecules like proteins, DNA, ...
Hydrogen Bonding in Ice
Open structure leads to low density, so ice floats in liquid water.
CHEM 107, Fall 2019
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141.5 pm
154 pm
335 pmbetween layers
Graphite Diamond
Vapor Pressure and Boiling Point• Strength of intermolecular
forces governs boiling (and melting) points.
• Vapor pressure is gas pressure above a liquid in a closed container.
• “Normal boiling point”: boiling point at P = 1 atm, or T at which vapor pressure = 1 atm
CHEM 107, Fall 2019
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Phase Diagrams• Graphical representation
of most stable phase (or phases) under different conditions.
• Shown here for water.• These get much more
complicated for alloys, andmany of you will see them again in a future course.
H2O CO2