Gay Lussac’s Law

Gas is one of the three form of substances and it is an inseparable part of chemical studies. The
properties of an ideal gas depend on the structure of its molecules and more as well its behavior. As to
apprehend and analyze the behavior of gases, synthesized matrix of principles and understandable
information are proposed to study gases through these various laws known as the Gas laws. Particularly,
the French chemist Joseph Gay-Lussac (1778 - 1850) discovered the relationship between the pressure
of a gas and its absolute temperature. Gay-Lussac's Law states that the pressure of a given mass of gas
varies directly with the absolute temperature of the gas, when the volume is kept constant. Gay-Lussac's
law regarding the composition of gases by volume was made known about a hundred years ago. Gay-
Lussac's Law directly influenced the work of Amedeo Avogadro in the formation of his law: Avogadro’s
Law. Gay-Lussac's Law was relied upon heavily by Berzelius in the formation of his Theory of Volumes.
Gay-Lussac's Law contributed to the determination of the molecular formulae of water, hydrogen
chloride, and ammonia. Interestingly, Dalton rejected the validity of Gay-Lussac's Law, even though he
readily applied its implications. Gay-Lussac's Law can also be applied to osmosis, which, in turn, allows
the determination of molecular weights by osmotic pressure. More profoundly, the paper in which he
elaborated it, having been read to the Societe philomatique on December 31, 1808, was published in the
Memoires de la Societe d'Arceuil in the following year. Since then, the law has come to have a history of
its own. Chemists were at a loss and made many efforts to get it and other theories to suit one another,
and the place of the law in science, though not now likely to change, was for long settled and
contributed (Meldrum, 1909). Bullets and cannons are based on these principles: gas super-heated by
the burning of gun powder is trapped behind the bullet and expands until the bullet leaves the barrel.
Concerning this, it is prominently pertained as another exemplar that when the temperature of a sample
of gas in a rigid container is increased, the pressure of the gas increases as well (LibreTexts, 2021). The
increase in kinetic energy results in the molecules of gas striking the walls of the container with more
force, resulting in a greater pressure. This is obtained through the following equation:

P 1 P2
=
T1 T 2
This describes the isochoric process: Gay-Lussac’s Law. Concernedly Where:

 P1 is the initial pressure

 T1 is the initial temperature
 P2 is the final pressure
 T2 is the final temperature
Thus, respecting this form if constant volume is remained.

Problem

At a temperature of 300 K, the pressure of the gas in a deodorant can is 3 atm. Calculate the pressure of
the gas when it is heated to 900 K.
Solution
Initial pressure, P1 = 3 atm
Initial temperature, T1 = 300K
Final temperature, T2 = 900 K
P1 × T 2
P 2=
T1
3 atm ×900 K
P 2= =9 atm
300 K

Therefore, final pressure (P2) is 9 atm.

Circumstance is when someone is opening an oven may feel a quick flow of hot air; the air inside the
oven is heated, therefore pressurized. The same is true when heating food in closed containers; often, a
container will open to release the pressure. If it does not, opening the container will quickly release all
the pent-up pressure, which can be very dangerous because the gases inside the hot container may be
super-heated. This is why it is always best to open hot containers away from your body and face
(ChemTeacher, 2010).

References

Meldrum, A. N. (1909). Gay-Lussac's Law—Its Centenary. https://doi.org/10.1038/081519b0

LibreTexts. (2021, March 5). Gay-Lussac’s Law. https://chem.libretexts.org/@go/page/53824

ChemTeacher. (2010, December 29). Gay-Lussac’s Law.

http://chemteacher.chemeddl.org/joomla/index.php?
view=article&catid=1%3Agaslaws&id=8%3Agaylussaclaw&format=pdf&option=com_content
Combined Gas Law
Combined Gas Law is an amalgamation of the three past discovered laws: Gay-Lussac's gas law, Charles'
law and Boyle's law. These laws relate one thermodynamic variable to another holding everything else
constant. The interdependence of these variables represents combined gas law which states that the
ratio between the product of pressure-volume and temperature of a system remains constant. The
Combined gas law is so named as it is a combination of three laws mentioned. It mostly applies when
there is a closed container or compartment with a fixed amount of gas. Collectively, these laws explain
that the ratio of an element with pressure and volume to temperature remains fixed for a given amount
of gas in different conditions. Most noteworthy, when the addition of Avogadro’s law happens to
combined gas law, the ideal gas law results. Unlike the named gas laws, it is said that the combined gas
law doesn't have an official discoverer. It is simply a combination of the other gas laws that works when
everything except temperature, pressure, and volume are held constant (Helmenstine, 2020). The only
way to combine these laws was if the respective formula was observed:

P1V 1 P2V 2
=
T1 T2

This is the common formation of this equation as with respect with the previous proposed formulas of
the three laws whereas:

 P1 is the first pressure

 P2 is the second pressure
 V1 is the first volume
 V2 is the second volume
 T1 is the first temperature
 T2 is the second temperature
In order to understand the combined gas law properly, imagine that there is a diver and his lungs are full
of air when he begins the dive. Furthermore, as he goes deeper underwater, the pressure in the lungs
escalates. When this pressure escalates, the air inside the lungs gets squished. Consequently, the
volume decreases. This is where Boyle’s law is in action, which states that the higher the pressure
consequently means lower the volume. Another happening can be that of a balloon in the refrigerator.
As the temperature of the balloon in the refrigerator decreases, then consequently the gas volume
inside the balloon also decreases. Also, the balloon reverts to the original size once it is out. Similarly,
when temperature increases then consequently there is an increase in volume as well. This shows
Charles law in action. Take another episode in which a driver is driving down the road. Gradually, the
temperature inside the tire increases. So, as the air expands inside the tire then consequently the
pressure also increases. This example represents the Gay-Lussac’s law (FlexBooks, 2019).

Problem

2.00L of a gas at 35 °C and 0.833atm is brought to standard temperature and pressure (STP). What will
be the new gas volume?
Solution

Step 1: List the known quantities and plan the problem.

Known

 P1=0.833atm
 V1=2.00L
 T1=35 °C=308K
 P2=1.00atm
 T2=0 °C=273K

Unknown

 V2=?L

Use the combined gas law to solve for the unknown volume (V2). STP is 273K and 1atm. The
temperatures have been converted to Kelvin.

Step 2: Solve.

First, rearrange the equation algebraically to solve for V2.

P1 × V 1 × T 2
V 2=
P2 ×T 1

Now substitute the known quantities into the equation and solve.

0.833 atm ×2.00 L× 273 K

V 2= =1.48 L
1.00 atm ×308 K

Step 3: Think about your result.

Both the increase in pressure and the decrease in temperature cause the volume of the gas sample to
decrease. Since both changes are relatively small, the volume does not decrease dramatically.

References

Helmenstine, Anne Marie, Ph.D. (2020, August 25). The combined gas law.
https://www.thoughtco.com/definition-of-combined-gas-law-604936

Reference. (2020, April 13). How is the combined gas law used in everyday life?
https://www.reference.com/science/combined-gas-law-used-everyday-life-d109c2ff10010bb6

FlexBooks. (2019, January 28). Combined gas law. https://flexbooks.ck12.org/cbook/ck-12-physics-

flexbook-2.0/section/10.4/primary/lesson/combined-gas-law-phys