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

© 2019, L.S. Brown 3

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

© 2019, L.S. Brown 4

• 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

© 2019, L.S. Brown 5

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

© 2019, L.S. Brown 8

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

© 2019, L.S. Brown 10

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

© 2019, L.S. Brown 11

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