BOYLE’S LAW
Robert Boyle, a British chemist who lived from 1627 to 1691 formulated the first gas law, now known
as Boyle’s law. This law describes the relationship between the pressure and volume of a sample of
gas confined in a container. Boyle found that gases compress, much like a spring, when the pressure
on the gas is increased. He also found that they “spring back” when the pressure is lowered. By
“springing back” he meant that the volume increases when pressure is low- ered. It’s important to
note that Boyle’s law is true only if the temperature of the gas does not change and no additional gas
is added to the container or leaks out of the container.
Boyle’s law states that the volume and pressure of a sample of gas are inversely proportional to each
other at constant temperature. This statement can be expressed as follows.
According to Boyle’s law, when the pressure on a gas is
increased, the volume of the gas decreases. For
example, if the pressure is doubled, the volume
decreases by half. If the volume quadruples, the
pressure decreases to one-fourth of its original value.
The expression PV = k means that the product of the pressure and volume of any sample of gas is a
constant, k. If this is true, then P × V under one set of conditions is equal to P × V for the same
sample of gas under a second set of conditions, as long as the temperature remains constant.
Boyle’s law can be expressed by the following mathematical equation.
Calculate the unknown quantity in each of the following measurements of gases. Work must be shown.
Answers: a. 13 mL b. 200. kPa c. 80. L d. 100. kPa e. 63 L
All Temperatures MUST be calculated in Kelvin and then converted back to Celcius. °C+273=K
CHARLES’S LAW
The French physicist Jacques Charles carried out experiments in 1786 and 1787 that showed a
relationship between the temperature and volume of gases at constant pressure. You know that most
matter expands as its temperature rises. Gases are no different. When Benjamin Thomson and Lord
Kelvin proposed an absolute temperature scale in 1848, it was possible to set up the mathematical
expression of Charles’s law.
Charles’s law states that the volume of a sample of gas is directly proportional to the absolute
temperature when pressure remains constant. Charles’s law can be expressed as follows.
According to Charles’s law, when the temperature of a sample of gas increases, the volume of the gas
increases by the same factor. Therefore, doubling the Kelvin temperature of a gas will double its
volume. Reducing the Kelvin temperature by 25% will reduce the volume by 25%.
The expression V/T = k means that the result of volume divided by temperature is a constant, k, for
any sample of gas. If this is true, then V/T under one set of conditions is equal to V/T for the same
sample of gas under another set of conditions, as long as the pressure remains constant.
Charles’s law can be expressed by the following mathematical equation.
Volume under
the first set of
conditions
Temperature
under the first
set of conditions
Volume under
the second set
of conditions
Temperature
under the
second set of
conditions
Calculate the unknown quantity in each of the following measurements of gases. Work must be shown.
Answers: a. 50.0 mL b. 200. K c. 200. mL d. 244 K e. 0.0021 L
All Temperatures MUST be calculated in Kelvin and then converted back to Celcius. °C+273=K
GAY-LUSSAC’S LAW
You may have noticed a warning on an aerosol spray can that says something similar to Do not
incinerate! Do not expose to temperatures greater than 140°F! Warnings such as this appear because
the pressure of a confined gas increases with increasing temperature. If the temperature of the can
increases enough, the can will explode because of the pressure that builds up inside of it.
The relationship between the pressure and temperature of a gas is described by Gay-Lussac’s law.
Gay-Lussac’s law states that the pressure of a sample of gas is directly proportional to the absolute
temperature when volume remains constant. Gay-Lussac’s law can be expressed as follows.
According to Gay-Lussac’s law, when the temperature of a sample of gas increases, the pressure of the
gas increases by the same factor. Therefore, doubling the temperature of a gas will double its
pressure. Reducing the temperature of a gas to 75% of its original value will also reduce the pressure
to 75% of its original value.
The expression P/T = k means that the result of pressure divided by temperature is a constant, k, for
any sample of gas. If this is true, then P/T under one set of conditions is equal to P/T for the same
sample of gas under another set of conditions, as long as the volume remains constant.
Gay-Lussac’s law can be expressed by the following mathematical equation.
Pressure under
the first set of
conditions
Temperature
under the first
set of conditions
Pressure under
the second set
of conditions
Temperature
under the
second set of
conditions
Calculate the unknown quantity in each of the following measurements of gases. Work must be shown.
Answer: a. 2.25 atm b. 225 K c. 92.6 kPa d. 52°C d. 616°C
All Temperatures MUST be calculated in Kelvin and then converted back to Celcius. °C+273=K
THE COMBINED GAS LAW
Look at the relationships among temperature, volume, and pressure of a gas that you have studied so
far.
Notice in these proportions that while P and V are inversely proportional to each other, they are each
directly proportional to temperature. These three gas laws can be combined in one combined gas law.
This law can be expressed as follows.
If PV/T equals a constant, k, then PV/T for a sample of gas under one set of conditions equals PV/T
under another set of conditions, assuming the amount of gas remains the same.
Therefore, the combined gas law can be expressed by the following mathematical equation. This
equation can be used to solve problems in which pressure, volume, and temperature of a gas vary.
Only the molar quantity of the gas must be constant.
Calculate the unknown quantity in each of the following measurements of gases. Work must be shown.
Answers: a. 224 mL b. 0.884 atm c. 310 K d. 39.9 mL
All Temperatures MUST be calculated in Kelvin and then converted back to Celcius. °C+273=K
Directions: On a separate paper write down the given and goal for the question. Next show the
mathematical set up to solve the problem. Check your answer to the one given. Receive a stamp
/sticker when Q.1-8 are complete.
1. A sample of neon gas occupies a volume of 2.8 L at 1.8 atm. What will its volume be at 1.2
atm? ans: 4.2 L
2. To what pressure would you have to compress 48.0 L of oxygen gas at 99.3 kPa in order to
reduce its volume to 16.0 L? ans: 298 kPa
3. A balloon full of air has a volume of 2.75 L at a temperature of 18°C. What is the balloon’s
volume at 45°C? ans: 3.01 L
4. A sample of argon has a volume of 0.43 mL at 24°C. At what temperature in degrees Celsius
will it have a volume of 0.57 mL? ans: 121°C
5. A cylinder of compressed gas has a pressure of 4.882 atm on one day. The next day, the same
cylinder of gas has a pressure of 4.690 atm, and its temper- ature is 8°C. What was the
temperature on the previous day in °C? ans: 20.°C
6. A mylar balloon is filled with helium gas to a pressure of 107 kPa when the temperature is
22°C. If the temperature changes to 45°C, what will be the pressure of the helium in the
balloon? ans: 115 kPa
7. A student collects 450. mL of HCl( g) hydrogen chloride gas at a pressure of 100. kPa and a
temperature of 17°C. What is the volume of the HCl at 0°C and 101.3 kPa? ans: 418 mL
8. A weather balloon is inflated with 2.94 kL of helium at a location where the pressure is 1.06
atm and the temperature is 32°C. What will be the volume of the balloon at an altitude where
the pressure is 0.092 atm and the temperature is 35°C? ans: 26.4 kL
Bonus Question (Worth 4 points):
A 500 mL bottle is partially filled with water so that the total volume of gases (water vapor and
air) remaining in the bottle is 325 cm3, measured at 20.°C and 101.3 kPa. The bottle is sealed
and taken to a mountaintop where the pressure is 76.24 kPa and the temperature is 10°C. If
the bottle is upside down and the seal leaks, how much water will leak out? The key to this
problem is to determine the pressure in the 325 cm3 space when the bottle is at the top of the
mountain. ans: 89 cm3 The pressure in the bottle on top of the mountain is the sum of PO2 dry
at the temperature of the mountaintop and PH2O vapor at the temperature on top of the
mountain.
All Temperatures MUST be calculated in Kelvin and then converted back to Celcius. °C+273=K