Lesson 5.2 The Empirical Gas Laws
Suggested Reading

Zumdahl Chapter 5 Sections 5.2
Essential Questions

What are the laws governing the behavior of gases?
Learning Objectives



Solve problems involving the relationship between temperature,
pressure & volume for a fixed mass of an ideal gas.
Apply Avogadro's law to calculate reacting volumes of gases.
Describe the conditions under which gases deviate from ideal behavior.
Introduction
All gases under moderate conditions behave simply with respect to pressure,
temperature, volume, and molar amount. By holding any two of these physical
properties constant, it is possible to show the relationship between the other
two. The discovery of these quantitative relationships, the empirical gas laws,
occurred from the mid-17th to mid-19th centuries. In this lesson we will look at
Boyle's law, Charles's law, the combined gas law, and Avogadro's law.
Boyle's Law
Recall that one of the characteristic properties of a gas is its compressibility-its
ability to be squeezed into a smaller volume by the application of pressure. By
comparison, liquids and solids are relatively incompressible. The
compressibility of gases was first studied quantitatively by Robert Boyle in
1661.
Boyle's most famous experiments with gases dealt with what he called the
"spring of air." These experiments were based on the observation that gases
are elastic. (They return to their original size and shape after being stretched
or squeezed.)
Boyle studied the elasticity of gases in a J-tube similar to the apparatus
shown in the figure. By adding mercury to the open end of the tube, he
trapped a small volume of air in the sealed end. Boyle studied what
happened to the volume of the gas in the sealed end of the tube as he
added mercury to the open end. Boyle noticed that the product of the
pressure times the volume for any measurement was equal to the product
of the pressure times the volume for any other measurement, within
experimental error.
P1V1 = P2V2
This expression, or its equivalent,
V ∝ 1/P or P ∝ 1/V
is now known as Boyle's Law. According to Boyle's law, the volume of a
sample of a gas at a given temperatures varies inversely with the applied
pressure. Thus, if you decrease the volume by half, the pressure doubles
and vice versa. This gas pressure-volume relationship can be expressed
graphically as follows (note the temperature is constant):
Charles' Law
On 5 June 1783, Joseph and Etienne Montgolfier used a fire to inflate a
spherical balloon about 30 feet in diameter that traveled about a mile and onehalf before it came back to earth. News of this remarkable achievement
spread throughout France, and Jacques-Alexandre-Cesar Charles
immediately tried to duplicate this performance. As a result of his work with
balloons, Charles noticed that the volume of a gas is directly proportional to its
temperature. This relationship between the temperature and volume of a gas,
which became known as Charles' law, can be stated as follows: the volume
occupied by any sample of gas at a constant pressure is directly proportional
to the absolute temperature. Although most gases follow Charles' law fairly
well, they deviate from it at high pressures and low temperatures.
Charles' law provides an explanation of how hot-air balloons work. If a gas
expands when heated, then a given weight of hot air occupies a larger volume
than the same weight of cold air. Hot air is therefore less dense than cold air.
Once the air in a balloon gets hot enough, the net weight of the balloon plus
this hot air is less than the weight of an equivalent volume of cold air, and the
balloon starts to rise. When the gas in the balloon is allowed to cool, the
balloon returns to the ground.
This gas volume-temperature relationship can be expressed graphically as
shown. A plot of the volume versus the temperature of a gas (when the
temperatures obtained are converted from Celsius to the Kelvin scale)
becomes a straight line that passes through the origin. Any two points
along this line can be used to construct the following variation of Charles'
law.
Before using this equation, it is important to remember that temperatures must
be converted from ºC to K!
Example: Using Charles' Law
Assume that the volume of a balloon filled with H2 is 1.00 L at 25°C. Calculate
the volume of the balloon when it is cooled to -78°C in a low-temperature bath
made by adding dry ice to acetone.
Solution:
First, you must convert temperatures to the Kelvin scale:
T1 = 25 + 273 = 298K
T2= -78 + 273 = 195K
Again, putting the data in tabular form, you help you to see what data you
have and what you must find
V1 = 1.00 L T1 = 298K
V2 = ? T2 = 195K
Rearranging V1T2 = V2T1 for V2 gives V2 = V1T2 ÷ T1 = (1.00L)(195K) ÷
(298K) = 0.653L
The Combined Gas Law
Boyle's law and Charles' law can be combined into a single statement: The
volume occupied by a given amount of gas is proportional to the absolute
temperature divided by the pressure (V ∝ T/P). The most commonly used
variation of this relationship is:
or P1V1T2 = P2V2T1
Example: Using the Combined Gas Law
Modern determination of %N in an organic compound is an automated version
of the Dumas method developed by French chemists Jean-Baptiste Dumas in
1830. The Dumas method uses hot copper(II) oxide to oxidize C and H in the
compound to CO2 and H2O while converting N in the compound to N2 gas.
Using the Dumas method, 39.8 mg of caffeine gives 10.1 cm3 of N2(g) at 23∘C
and 746mmHg. What is the volume of nitrogen at 0∘C and 760mmHg?
Solution:
First, you must convert temperatures to the Kelvin scale:
T1 = 23 + 273 = 296K
T2= 0 + 273 = 273K
Now, put the data for the problem into tabular form:
V1 = 10.1 cm3 P1 = 746mmHg T1 = 296K
V2 = ? P2 = 760mmHg T2 = 273K
From the data you see that you need to use the combined gas laws,
because V, P, and T are all involved. The unknown is V2, so rearranging
gives
P1V1T2 = P2V2T1 = V2 = P1V1T2 ÷ P2T1 = (746mmHg)(10.1cm3)(273K ) ÷
(760mmHg)(296K) = 9.1cm3
Watch this You Tube video:
https://www.youtube.com/watch?v=JdAg9vGKqi0
Avogadro's Law
In 1808 the French chemist Joseph Louis Gay-Lussac (1778 - 1850)
concluded from experiments on gas reactions that the volumes of reactant
gases at the same pressure and temperature are in rations of small whole
numbers (the law of combining volumes). Three years later, the Italian
chemist Amedeo Avogadro interpreted the law of combining volumes in
terms of what we now call Avogadro's law: equal volumes of any two gases
at the same temperature and pressure contain the same number of
molecules. Thus, two volumes of hydrogen contain twice the number of
molecules as one volume of oxygen.
One mole of any gas contains the same number of molecules (Avogadro's
number = 6.02 x 1023) and by Avogadro's law must occupy the same
volume at a given temperature and pressure. This volume of one mole of
gas is called the molar volume. Volumes of gases are often compared at
standard temperature and pressure (STP), the reference conditions for
gases chosen by convention to be 0∘C and 1atm (760mmHg, 1 torr,
1.01x105 Pa) pressure. At STP the molar volume is found to be 22.4
L/mol (22.4 dm3 mol -1). Remember this! This is a conversion factor that we
use in gas stoichiometry.
We can express Avogadro's law as follows: the molar volume at STP is a
specific constant independent of the type of gas.
Molar volume = 22.4 L/mol at STP
HOMEWORK: Practice exercises 10.4 - 10.8