AP Chemistry
th
Zumdahl Notes, 9 ed.
A Brief Collection of notes, Chapter 5
Feel free to open these files and annotate as you feel the need…this is
for your success.
Pressure
• What is pressure? The molecules hitting the inside walls of whatever
contains them; this is directly proportional to temperature, which is
nothing more than a measure of the kinetic energy of the particles of
whatever gas is being measured
• Barometer: device to measure barometric (atmospheric) pressure,
invented by Torricelli, 760mmHg, at sea level
• Barometers are manometers, devices to measure differences in
pressure
• Units
• 1 atm = 760 mmHg = 760 torr = 101.325 kPa (kilopascals)
• Yes, you will need to keep conversions in mind.
The gas laws of Boyle, Charles, Avogadro
• Boyle’s Law
• Pressure and volume are inversely proportional: PV = k, at constant temp.
• Reality check: a gas that strictly follows this is called an ideal gas
• This means that there are no intermolecular attractions, nor loss of energy during
collisions of particles of said gas
• Second reality check: at pressures near 1 atm, our calculations work very well
for real world gases
• Form of Boyle’s law that is used for calculations: P1V1 = P2V2
• Rearrange as needed to solve for unknown
The gas laws of Boyle, Charles, Avogadro
• Charles’ Law
• Volume and temperature are directly proportional, at constant pressure
• Reality check: must use kelvin temperatures…need to always be positive (K=°C + 273)
• V = bT
• Second reality check: we have never actually reached absolute zero…very, very close but
not quite there
• Form of Charles’ law that is used for calculations:V1/T1 = V2/T2
• Rearrange as needed to solve for unknown
Gay-Lussac’s Law and Combined gas law…not in
Zumdahl
• Another relationship: at constant volume, pressure is directly
proportional to temperature in Kelvins
• P/T = C
• This becomes another part of combined gas law:
P1V1/T1 = P2V2/T2
I wanted to include these, as you may run into them, even though the Zumdahls
chose to leave them out of the 9th edition
The gas laws of Boyle, Charles, Avogadro
• Avogadro’s Law
• The amount of a gas present is directly proportional to the volume it
occupies, at constant temperature and pressure
• V/n = C
• Works best at low pressures…as pressure increases, intermolecular attractions, etc., start
to affect real world gases…think liquification….
Ideal Gas Law
• If we combine Boyle’s, Charles’, and Avogadro’s, we can arrive at the
mathematical formula: V = R (Tn/P), where R is a proportionality
constant (universal gas constant, relating the units together)
• Rearranging, we get to the form we use: PV = nRT
• Normal reality check…we can solve for one unknown by algebraically rearranging this
equation. This is one of those times where I remind you of the importance of labelling
with units!
Gas Stoichiometry
• At STP, (standard temperature and pressure, O°C, 1 atm), one mole of
an ideal gas occupies a volume of 22.42 L. Yes, you will use this a lot
for these kinds of problems
• You will need to substitute this in some calculations which use one of
the gas laws
• Another fun calculation/formula
• Molar mass = dRT/P, where d = density in g/L
• Yes, it is likely you will need to mess with this formula
• Yes, you can derive it if you need to as the units will guide you to data location
Dalton’s Law of Partial Pressures
• “For a mixture of gases in a container, the total pressure exerted is
the sum of the pressures that each gas would exert if it were alone.”
Awesomely summarized…means that each one adds its part to the
final pressure
• Formula: Ptotal = P1 + P2 + P3 + …
• Each gas, therefore, exerts what is referred to as its “partial pressure”
• Reality check: you can substitute “n1RT/V” as needed for each gas so as to
calculate each gas’ contribution; this is dependent upon what information you
are given to solve a problem with, as usual
• Mole fraction: the ratio of one component to the total (see page 210-211)
• X1 = n1/ntotal
Kinetic Molecular Theory of Gases
• An attempt to explain the properties of ideal gases
• The particles are so small compared with the distances separating them that
we consider the individual volumes to be zero
• The particles are in continuous motion and their collisions with the walls of
their container create the pressure exerted by same particles
• The particles have no interactions with each other, as far as
attraction/repulsion…consider similar to billiard balls
• The average KE of a collection is considered to be in direct proportion to the
Kelvin temperature of the gas
• REALITY check: we know that real gases violate these, right?
But…these do help us explain much of gas behavior…it allows us to
develop the relationships we call the gas laws, which we have been
discussing
Kinetic Molecular Theory of Gases, continued
• Important expression: KEavg = 3/2 RT
• This allows for the calculation of the energy of the gas at a given temperature
• Also allows for velocity calculations of gas particles…be thoughtful about
units…need to be working in joules for energy
Effusion and Diffusion
• Effusion: movement into evacuated chamber
• Diffusion: movement into “occupied” chamber
• Graham’s Law of Effusion:
Rate of effusion of gas 1 = (mass of gas 2) 1/2
Rate of effusion of gas 2
(mass of gas 1) ½
This shows the inversely proportional relationship between relative
rates and the square roots of the masses of the gases involved
• Diffusion rates: yes, can be calculated similarly, but found
experimentally to be less…showing a much more complicated analysis
is necessary and beyond our needs to perform
Real gases
• Real gases behave most like ideal gases at low pressures and high
temperatures…why?
Chemistry in the atmosphere
• Components of atmosphere: mostly nitrogen and oxygen
• Pollutants: sources of acid rain!
• Nitrogen oxides
• Sulfur oxides