Gases and gas laws
Chapter 12
Key concepts
1.
2.
Understand basic characteristics of gases.
Know the definition of pressure and measurement units commonly used
with pressure
3.
Know what a barometer measures.
4.
Know the relationships described by Boyle’s Law, Charles’ Law, and
Avogadro’s Law.
5.
Know the ideal gas equation and it’s derivation.
6.
Understand gas density and using molar masses in the ideal gas equation.
7.
Understand Dalton’s law of partial pressures and its applications.
8.
Know the basic principles of the kinetic theory of gases and how this
explains gas behavior described by the ideal gas laws.
9.
Know the terms effusion and diffusion; know Graham’s law of effusion.
10. Understand gas interactions that cause deviations from ideal gas law
behavior.
Common characteristics of gases
(uniquely different from liquids or solids)
•
All gas mixtures are homogeneous mixtures.
•
Gases expand to fill the container they occupy
–
•
the volume of EACH GAS in a mixture of gases in a
container = volume of the container.
The actual space occupied by the gas
molecules is small relative to the total volume.
Pressure
• Force applied per unit area
P = F/A
• The same force may result in much
different pressures…
Pressure units
•
•
•
•
•
pounds per square inch (psi)
inches of mercury (in Hg)
mm Hg
Pascals (SI units)
torr (from Torricelli, inventor of the barometer)
– 1 torr = 1 mm Hg
• standard atmospheric pressure
– 760 torr = 1 atmosphere (atm); typical pressure at
sea level.
• conversions:
– 1 atm = 760 torr = 1.01325  105 Pa = 14.7 psi
The barometer
• Mercury barometer:
– atmospheric pressure
 force applied on Hg
 the change in
height of mercury
column.
http://www.usatoday.com/weather/wbaromtr.htm
Basic Gas Laws
• Relationships between gas pressure,
temperature, volume, and amount (moles).
• Now, let’s have some fun….
Boyle’s Law
• Boyle’s law relates to changes in pressure
and volume.
• At constant temperature, the change in
pressure is ________ proportional to the
change in volume.
Charles’ Law
• Charles’ Law relates changes in volume
and temperature
• At constant pressure, the change in
volume is _______ proportional to the
change in temperature
Avogadro’s Law
• Identical volumes of a gas at the same
temperature and pressure have the same
number of gas particles.
Summary
• P  1/V (constant n and T) (Boyle)
• V  T (constant n and P) (Charles)
• V  n (constant T and P) (Avogadro)
• Combined, we get….
PV=nRT; the ideal gas equation
• Gases that can have their temperature, volume, and
pressure characteristics completely described by this
equation are called ideal gases.
• R = the gas constant. It’s units vary depending on the
units of P, V, and T.
• If
L  atm
• P is in atm,
R  0.08206
• V is in L,
mol  K
• T is in K,
• STP = standard temperature and pressure. Defined as
1 atm and 0 C (273.15 K).
• What is the molar volume of a gas at STP?
Using ideal gas equation to
represent gas laws.
1. Boyle’s Law.
– PV = nRT
– P and V will change, but n, R and T are
constant.
2. Charles’ Law
• PV = nRT
• V and T will change, but n, R, and P are
constant.
3. P, V, and T all change, but n is constant
– PV = nRT
More applications of the ideal gas
equation.
• Obtaining the density of a gas:
– from PV = nRT…
• d = PM/RT (where M is the molar mass)
volumes of gases in chemical
reactions.
• air bags.
– 2 NaN3(s)  2 Na (s) + 3 N2 (g)
– air bag volume: 36 L; pressure 1.15 atm;
temperature 26.0 C. How much NaN3, in g,
needed?
• 2 KClO3 (s) 2 KCl (s) + 3 O2 (g)
• volume of O2 produced when 1.50 g KClO3
decomposes?
Gas mixtures and partial pressures
• Dalton’s Law of partial pressures:
– from PV = nRT….
• Ptotal = P1 + P2 + P3 + ….
• collecting gases over water—the gas is
not alone….
Kinetic molecular theory of gases.
• An explanation of what happens at the
molecular level that causes the observations in
the ideal gas laws.
1. Gases consist of large numbers of molecules in
continuous random motion.
2. The volume of all the molecules of gas is
negligible compared to the total volume (i.e.,
each gas molecule is basically an infintessimally
small dot).
3. Attractive and repulsive forces between
molecules are negligible.
4. Energy transitions between molecules are
perfectly elastic. The average kinetic energy
of the molecules will not change over time as
long as the temperature stays constant.
5. The absolute temperature is proportional to the
average kinetic energy of the gas. At any
given temperature all gases in the mixture
have the same average kinetic energy.
• KE = ½ mu2. u = the root mean square (rms)
speed of the gas. (root mean square is an
averaging technique, though it is not the same
as the average)
The kinetic theory explains the gas
law
Important observations:
• volume increases at constant temperature
(Boyle’s law). Molecules must travel further to
reach the wall of a larger container. Thus,
collisions against the container wall are less
frequent, the pressure therefore drops.
• Temperature increases at constant volume
(Charles’ Law). when temperature (and kinetic
energy) increase, the speed of the molecules
increases. Faster molecules collide with the
container walls more often, so pressure
increases.
Effusion and diffusion
• effusion –
• diffusion –
• Lighter molecules move faster than
heavier molecules
3RT
u
M
Graham’s Law of effusion
• the rate of effusion is
twice as fast for r1 if
M1 is 4 times lighter
than M2.
M2
r1

r2
M1
Diffusion vs. effusion
• Diffusion is complicated by the presence
of other molecules. The mean free path is
a determining factor.
• Mean free path –
Real gases
• Assumptions in
kinetic theory of
gases not always
valid.
– Molecules are not
infinitely small
– Attractive and
repulsive forces are
not negligible.
– Collisions are not
always elastic.
Deviations from ideality
• for one mole of an ideal
gas (n=1). PV/RT always
= 1.
• For ANY amount of ideal
gas, PV/nRT = 1
• However, for real gases,
PV/nRT doesn’t always
= 1.
• Ideal gas equation is
better in some regions
than in others.
PV
n
RT
PV
1
RT
Deviations more likely to occur at…
• low temperature: Molecules moving slower,
intermolecular forces become a greater factor
(especially near liquid/gas interface).
• Higher pressure: Molecule size becomes an
greater factor; interfering with travel of
molecules.
• Corrections to ideal gas equation are made to
take this into account.
– Van der Waal’s equation is one example