A.P. Chapter Ten Outline: Gases
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The Kinetic Molecular Theory of Matter
Matter is composed of particles that are constantly in motion.
The particles composing a solid are tightly packed and only vibrate, the
particles composing a liquid are able to glide fluidly past each other are, and
the particles in a gas are in rapid motion and are distant from each other.
Kinetic energy is the energy of motion.
Kinetic Energy = K.E. = ½ (mass)(velocity)2
A. Ideal Gases: imaginary gases that behave perfectly, meeting all the
following requirements:
1) Gases consist of large numbers of tiny particles that are far apart
relative to their size.
2) Collisions between gas particles and between particles and
containers are elastic collisions. An elastic collision is one in
which there is no net loss of kinetic energy.
3) Gas particles are in constant, rapid, random motion.
4) There are no forces of attraction or repulsion between gas
particles.
5) The average kinetic energy of gas particles depend on the
temperature, in other words gas particles move faster as the
temperature increases.
 A real gas is a gas that does not behave according to the
above assumptions
** At room temp. most gases behave ideally. At pressures greater than 1 atm and
temperatures close to boiling points (low temperatures) gases deviate substantially**
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III.
The Kinetic-Molecular Theory and the Nature of Gases
 The kinetic molecular theory only applies to ideal gases
Expansion: gases do not have a definite shape or volume and thus expand to fill
any container
Fluidity: because the attractive force between gas particles are insignificant, gas
particles glide easily past each other. Because liquids and gases flow, they are
called fluids.
Low Density: the density of a substance in the gaseous state is about 1/1000 the
density of the same substance in the liquid or solid state.
Compressibility: because gas particles are very far apart they are easily
compressed.
Diffusion: gases spread out and mix with each other spontaneously due to their
random motion.
Effusion: a process by which gas particles under pressure pass through a tiny
opening.
Pressure
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Pressure, P, is defined as the force per unit area on a surface
The SI unit for force is the Newton, N. It is the force that will increase the
speed of a one kilogram mass by one meter per second each second it is
applied.
Gas molecules exert pressure on any surface with which they collide. The
pressure exerted by a gas depends on volume, temperature, and the
number of gas molecules present.
A. Measuring Pressure
1. A barometer is a device used to measure
atmospheric pressure
B. Units of Pressure
1. millimeters of mercury, mm Hg.
Average atmospheric pressure=760 mm Hg
2. 760 mm Hg = one atmosphere = 1 atm
3. One pascal, Pa, is the pressure exerted by a force of
one Newton acting on an area of one square meter.
4. One torr = 1 mm Hg so 1 atm = 760 torr
C. Standard Temperature and Pressure, abbreviated STP: 1 atm and 0C.
IV.
The Gas Laws
A. Boyles Law: The Pressure-Volume relationship
 At constant temperature, pressure and volume are inversely proportional (as one
increases the other decreases)
 P1V1= P2V2
B. Charles Law: The Volume – Temperature relationship
 Absolute zero = -273.15C = 0 Kelvins
 Kelvin temperature, K, = 273.15 + C
 At constant pressure, volume varies directly with the Kelvin temperature
(as one increases so does the other)
 V1/T1 = V2/T2
 This can be re-written as V1T2 = V2T1
C. Avagadro’s Law: The Amount – Volume Relationship
 Avagadro’s law states that the volume (V) of an ideal gas varies directly with
amount (n) when temperature and pressure are constant,
 V1/n1 = V2/n2
 This can be re-written as V1n2= V2n1
D. The Law of Combining Volumes: at constant temperature and pressure, the
volumes of reacting gases are always in the ratios of small whole numbers.
E. Gay-Lussac’s Law: the Pressure – Temperature Relationship
 At constant volume, pressure varies directly with Kelvin temperature
 P1/T1 = P2/T2
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This can be re-written as P1T2 = P2T1
F. The Combined Gas Law: the relationship between pressure, volume, and
temperature of a fixed amount of gas.
 P1V1/T1 = P2V2/T2
 This can be re-written as P1V1T2 = P2V2T1
G. The Ideal Gas Law: this combines Boyles, Charles, and Avagadro’s in one
formula, but requires the use of R, a proportionality constant called the ideal gas
constant.
 PV = n RT
 R can be written id different units (this is so that different pressure units can
be cancelled out)
 R = 0.08206 L atm/K mol
 R = 62.36 torr L/K mol
 R = 8.314 kPa dm3/K mol
 R = 8.314 J/K mol
H. Dalton’s Law of Partial Pressures
 If there is no chemical reaction, then the total pressure of a gas mixture is
the sum of the individual gases pressures.
 PT= P1 + P2 + P3 …
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Mole fraction of gas A = XA = moles of gas A/total moles of gas
 PA = XAPTotal
I. Gases collected by water displacement
 Gases produced in the laboratory are often collected over water
 A gas collected by water displacement is not pure but iw always mixed with
water vapor
 Patm = Pgas + PH2O
J. Real Gases
 Deviate at high pressures and low temperatures
 Real Volume < ideal volume at medium pressures
 Real Volume > ideal volume at high pressures
 Real Pressures < ideal pressures due to intermolecular attractions
 Real Volume > ideal volume
Van der Waals Equation
(Pmeasured + n2a/V2measured) (Vmeasured – nb) = nRT
P = (nRT/V-nb) – (n2a/V2)
K. Grahams Law
 At a given temperature, lighter molecules move faster than heavier molecules
R1/R2 = (M2/M1)1/2
Where R = rate of effusion and M is molar mass
μrms = (3kT/m)1/2 = (3RT/M)1/2
where μrms is the average speed of molecule (m/s) and m = mass (kg) and M =
molar mass and k = Boltzmann’s constant = 1.38 x 10-23 joule/K mole and T =
Kelvin temperature