Boyle's Law
Lesson Objectives
The student will:
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State Boyle's law
Solve problems using Boyle's law
Vocabulary
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Boyle's law: the pressure of a given amount of a gas is inversely proportional to its
volume at a constant temperature
inverse proportionality: a relationship between two variables where, when one of the
variables is increased, the other variable will decrease by exactly the same factor
The gas laws are mathematical expressions that relate the volume, pressure, temperature, and
quantity of gas present. They were determined from the results of over 100 years of
experimentation. They can also be derived logically by examining the present day definitions of
pressure, volume, and temperature.
Boyle's Law
Gases are often characterized by their volume, temperature, and pressure. These
characteristics, however, are not independent of each other. Gas pressure is dependent on the
force exerted by the molecular collisions and the area over which the force is exerted. In turn,
the force exerted by these molecular collisions is dependent on the absolute temperature. The
relationships between these characteristics can be determined both experimentally and logically
from their mathematical definitions.
The relationship between the pressure and volume of a gas was first determined experimentally
by an Irish chemist named Robert Boyle (1627-1691). The relationship between the pressure
and volume of a gas is commonly referred to as Boyle's law.
When we want to observe the relationship between two variables, we must keep all other
variables constant so that the change in one variable can be directly related to the change in the
other. Therefore, when the relationship between the volume and pressure of a gas is
investigated, the quantity and temperature of the gas must be held constant so that these
factors do not contribute to any observed changes.
You may have noticed that when you try to squeeze a balloon, the resistance to squeezing
becomes greater as the balloon becomes smaller. That is, the pressure inside the balloon
becomes greater when the volume is reduced. This phenomenon can be studied more carefully
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with an apparatus like the one shown below. This device is a cylinder with a tightly fitted piston
that can be raised or lowered. There is also a pressure gauge fitted to the cylinder so that the
gas pressure inside the cylinder can be measured. The amount of gas of gas inside the cylinder
cannot change, and the temperature of the gas is not allowed to change.
In the picture on the left, a 4.0 liter volume of gas is exerts a pressure of 2.00 atm. If the piston
is pushed down to decrease the volume of the gas to 2.00 liters , the pressure of the gas is
found to be 4.00 atm. The piston can be moved up and down to positions for several different
volumes, and the pressure of the gas can be for each of the volumes. Several trials would
generate a data set like that shown below.
Trial
PV Data
Volume
Pressure
1
2
3
4
We might note from casual observation of the data that doubling volume is associated with the
pressure being reduced by half. Likewise, if we move the piston to cause the pressure to
double, the volume is halved. We can analyze this data mathematically by adding a fourth
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column to our table - namely, a column showing the product of multiplying pressure times
volume for each trial.
PV Data
Trial Volume Pressure Pressure
1
2
3
4
Volume
The data in the last column show that with constant temperature and quantity of gas, the
pressure times the volume for this sample of gas yields a constant. A mathematical constant
(often represented by ) is a number that does not change even when other quantities in the
formula do change. The value of
will change if a different quantity of gas is used or if the
trials are carried out at a different temperature, but for a particular mass of a particular gas at a
particular temperature, the value of
will always be the same. A subscript 1 is used to
distinguish this constant from the constants of other gas laws. This relationship can be shown in
a mathematical equation.
This equation is a mathematical statement of Boyle's law. This particular equation demonstrates
what is called an inverse proportionality. When one of the variables is increased, the other
variable will decrease by exactly the same factor. This relationship can be easily seen in a
graph like the one shown below.
This result matches our logic intuition. If the pressure a gas exerts is equal to the force divided
by the area over which it is exerted, we would expect the pressure to increase when we
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decrease the area but keep the force constant. Similarly, if we maintain the same number of
molecules of gas and we keep the same temperature, we expect the total force exerted by the
molecules to be the same. As a result, if we expand the volume of the gas, which increases the
area over which the force is exerted, we would expect the pressure to decrease.
Using Boyle's Law
Boyle's law states that for a sample of gas at constant temperature, every volume times
pressure trial will yield the same constant. Therefore, if you know the volume of a gas at one
pressure, you can use this information to find either the pressure of the gas sample at another
volume, or the volume of the gas at another pressure. We use the subscript 1 to represent one
set of conditions, and the subscript 2 to represent a second set of conditions after pressure and
volume of a closed system have been changed.
If P1V1 = k
and P2V2 = k
then P1V1 = P2V2
P1V1 = P2V2
Example:
A gas occupies 12.3 liters at a pressure of 40.0 mmHg. What is the volume when the pressure
is increased to 60.0 mmHg?
Step 1 : Assign known values to the appropriate variable.
P1 = 40.0 mmHg
V1 = 12.3 L
P2 = 60.0 mmHg
V2 = ??
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Step 2 : Solve the Boyle's law equation for the unknown variable.
Step 3 : Substitute the known values into the formula and solve for the unknown.
Lesson Summary
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Boyle's law states that for a gas at constant temperature, volume is inversely
proportional to pressure.
The volume of a mass of gas is dependent on the temperature and pressure. Therefore,
these conditions must be given along with the volume of a gas.
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