CHEMISTRY SEMESTER ONE
UNIT 10
UNIT 10: GASES
INTRODUCTION TO THIS UNIT:
Of the three states of matter, the properties of gases are the most easily predicted. In the laboratory,
gases can be studied with relatively simple apparatus. No doubt, our early fascination with the nature of
our atmosphere and the fact that we could study it easily meant that the properties of gases were first
studied more than 300 years ago. The theory presented in this section is not too difficult, but be careful
with your calculations. Earlier this semester, you learned how to convert from one set of units to
another. The need for this skill will become apparent in this section; when describing the pressure of a
gas, units of atm, bar, mmHg, Torr and Pa are all used frequently.
Gases can be quantified by their amount, temperature, volume and pressure. The pressure of a gas
results from collisions of molecules against the walls of the container. Recall that pressure represents a
force applied over an area. Early units of pressure included millimeters of mercury, inches of water and
atmospheres. In the SI metric system, the unit would be N/m2 which is known as the pascal. Later in
this unit you will encounter the ideal gas law and the ideal gas constant, R. The numerical value of R
depends on the units of pressure (kPa or atm) you use in your calculations. To avoid making errors,
always verify that units cancel in your calculations leaving the answer expressed in the proper units.
When looking at the properties of gases, note how volume of a gas sample varies with pressure (V α 1/P,
Boyle's Law), temperature (V α T, Charles' Law) and amount (V α n, Avogadro's Hypothesis). Note the
significance of Charles' Law. As the temperature of a gas decreases, the volume decreases. Since
volume cannot assume a negative value, this means that there must be a minimum on the temperature
scale. We call it 'absolute zero'. Charles' Law was used to estimate absolute zero with great accuracy
more than 100 years ago.
If you keep the three mathematical relationships above in mind, you will be able to derive the Ideal Gas
Law, PV = nRT. This law allows you to solve many gas problems, and the answers are more accurate at
low pressures and high temperatures. Under these conditions, gases behave more ideally. What this
really means is that intermolecular forces are small with respect to the amount of energy possessed by
the atoms or molecules. Later in this unit, we will learn of a way to predict properties of non-ideal gases
or gases under non-ideal conditions.
Through some simple substitutions, notice how the Ideal Gas Law allows us to calculate the density of a
gas or the molecular weight of a gas. Starting with PV = nRT, recall that amount equals mass/molecular
weight, so we get PV = (m/MW)RT. By making simple measurements in a first-year laboratory, we can
calculate the molecular weight of an unknown sample of gas. This can help us identify an unknown
sample of gas. Then, by making one more substitution (mass equals density times volume), we obtain
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CHEMISTRY SEMESTER ONE
UNIT 10
PV = (dV/MW)RT. This simplifies to P = (d/MW)RT. Through this equation we can calculate the density
of gas if we know the molecular weight of the gas.
Perhaps the more important point is that the larger the molecular weight, the more dense the gas
(assuming P and T are constant). This means that gases with low molecular masses such as hydrogen
rise in air, while gases with higher molecular weights such as the vapour of chloroform (CHCl3) sink in air.
These observations do not mean that gases stratify according to their molecular weights; they do mix
completely after a period of time.
Until now, we have looked at pure samples of gases, but looking at mixtures of gases is not too different.
Because of their close-to-ideal behaviour, Dalton's Law of Partial Pressures says that we can consider
different gases to behave independently even when mixed with other gases. As you read through
Dalton's Law of Partial Pressures, think of the components of Earth's atmosphere in a quantitative
sense. For example, if 78 % of our atmosphere, by volume, is N2, then 78 % of the total pressure we
experience is due to N2 and 78 % of the total atoms and molecules in our atmosphere are N2.
The gas laws preceded the theory, and now is time to discuss the Kinetic-Molecular Theory of gases.
This theory has three postulates pertaining to an ideal gas:
(1) the volume of the particles (molecules or atoms) is insignificant with respect to the volume of
the container,
(2) the particles are in constant, rapid, random motion and undergo elastic collisions and,
(3) the average kinetic energy of the particles is proportional to the temperature of the sample.
The speed of the particles is taken as the root-mean-square (rms) speed. If you look at the diagram in
your textbook, you will see that all molecules of a pure gas sample do not have the same speed; there is
a distribution of speeds. Because of this distribution, to state the speed of the particles, we need to
choose some kind of 'average speed', and this is the rms speed. Although, you could prove this through
mathematics, notice that lighter molecules have a faster rms speed than heavier ones, and as the
temperature of a gas sample increases, so does the average speed of the molecules. Since the speeds of
the particles are inversely proportional to the root of their molecular weights, we can compare rates of
diffusion and effusion if we know the molecular weights of the gases. Lighter gases diffuse and effuse
faster. A practical application of this fact is the separation of 235U from 238U where the uranium is in the
gas phase as uranium hexafluoride.
Now, we must consider non-ideal gases. To this point, we assumed that there were no attractive forces
between particles and the volume of the particles (molecules and atoms) was zero. Although the forces
between particles are weak, they are not zero. At low temperatures, these attractive forces become
significant with respect to the energy of the particles. This means we should expect non-ideal behaviour
at low temperatures. Further, the atoms and molecules of gases do have a finite volume. This means
we cannot compress a sample to zero volume no matter how much pressure is applied. At high
pressure, the volume of the particles becomes significant with respect to the volume of the container.
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CHEMISTRY SEMESTER ONE
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To treat gases under conditions of high pressure and low temperature, we use the Van der Waals
equation.
2


n


 P  a  V  bn   nRT

 V  

This equation has the approximate form of the Ideal Gas equation, but the pressure term is corrected
for attractive forces with the additional term, a(n/V)2, and the volume term is corrected for the finite
size of the molecules or atoms with the term, bn. The values of a and b are unique for each gas and can
be found in tables. When using this equation, be sure to note the units of a and b, and be certain that
they cancel to give the desired units of the answer.
READINGS:
(in Petrucci, 9th ed.) : Sections 11.1 – 11.9
OVERVIEW & STRUCTURE FOR YOUR NOTES:

Pressure concept, units

Boyles Law

Charles Law and the idea of an absolute temperature scale

Combined gas law and ideal gas law

Use of ideal gas law to determine the amount of sample and molar mass

Gas mixtures

Kinetic theory of gases and distribution of gas molecule velocities

Effusion, diffusion and molar mass determination
ASSIGNMENT:
(in Petrucci, 9th ed.): From Chapter 11: # 2, 8, 10, 16, 22, 26, 30, 34, 40 42, 50, 52
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CHEMISTRY SEMESTER ONE
UNIT 10
CONCLUDING REMARKS:
In this unit we have successfully used simple theories to predict the properties of gases. Of the three
forms of matter, gases have the weakest intermolecular forces, and therefore behave more ideally than
solids or liquids. For this reason, when studying matter, it is convenient to look at the relatively simple
examples of gases before looking at less ideal solutions of liquids and solids. We will encounter these in
the following units.
SUMMARY LEARNING OUTCOMES FROM THIS UNIT:

Understand the concept of gas pressure being due to gas phase molecules impinging on a surface

Understand the concept of pressure being force per unit area

Understand the proper units for pressure

Be able to convert between different pressure units

Understand Boyles Law and be able to use it in calculations

Understand Charles Law and the idea of extrapolating to hypothetical zero volume at a certain
temperature (-273.15C)

Understand the definition of Kelvin temperature as T(K) = T(C) + 273.15

Be able to use Charles Law in calculations

Be able to use the combined gas law in calculations

Understand Avagadro’s Hypothesis and the development of the ideal gas law

Understand that the above law allows determination of the number of moles of a gas and be able to
use such ideas in calculations

Be able to the calculate molar mass of a gas from its mass, temperature, volume and pressure

Be able to calculate molar masses from gas density

Be able to perform calculations relating to the gas laws, chemical reactions and stoichiometry

Understand the concept of gas mixtures and partial pressures

Be able to perform calculations relating to the pressures of gas mixtures
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CHEMISTRY SEMESTER ONE
UNIT 10

Understand the concept of kinetic theory of gases and the idea of a distribution of gas molecule
velocities

Understand the idea mean square velocity (mean square speed) and its connection to kinetic energy.

Be able to perform calculations which connect mean squared velocity, molar mass and temperature

Understand diffusion and effusion and their connection to molar mass

Be able to perform calculations which relate effusion to molar mass

Appreciate the fact that the ideal gas law is only valid as the pressure of a gas gets very low and
deviations can be considerable at high pressure and low temperature.
NANSLO Chemistry Core Units and Laboratory Experiments
by the North American Network of Science Labs Online,
a collaboration between WICHE, CCCS, and BCcampus
is licensed under a Creative Commons Attribution 3.0 Unported License;
based on a work at rwsl.nic.bc.ca.
Funded by a grant from EDUCAUSE through the Next Generation Learning Challenges.
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