# Combined Gas Law

I want to calculate
Pressure 1
Volume 1
Temperature 1
Pressure 2
Volume 2
Temperature 2 Volume 1
Pressure 1
Temperature 1
Temperature 2
Volume 2
Pressure 2

At a certain point in childhood we all had this thought crossing our mind – ‘I wish I could learn everything’. Well, lesser we did know that is impossible. What if I tell you now that it might happen in a certain way? Sounds astonishing right! A simple trick: learn Chemistry. Yes, I say that because ultimately Chemistry is the study of everything. What we eat or drink, when we sit or breathe, it is all around. Even our body is made of chemistry, I mean chemicals of course. I know it gets complicated and perplex at times but you cannot ignore its significance.
For those who are not fond of Chemistry, why not think about it in this way, ‘chemistry is capable of doing wonders because when we combine basic of basic elements and particles, we always get something unique and rare.’ Who doesn’t wants to learn this art?
Well, now if you want to let me tell you the interesting part of Chemistry which at least I enjoyed every time I studied it- the Chemistry Laws. They are always so fun to learn because every statement is inferred by an experiment. You don’t have to memorize long equations. If you know the experiment you will know the law. As simple as a piece of cake.

## Discovery of the Combined Gas law Formula

Like any other law, even this law should be discovered by some great scientists or experts. Well, even I expected that and was curious to know whose brain is behind the combined gas law. However, the case isn’t obvious here unlike other gas laws. The combined gas law has no official discoverer or inventor. There is no one particular name that gets the credit.

Let’s see then how did we have the existence of the combined gas law.

## Combined gas law

Unlike other named laws that have their names in memory of the inventor, the combined gas law is a simple deal. You can remember and understand it just by its name. I say so because the name is self-explanatory- the combined gas law which surely has some gas laws combined. If you have been a sincere chemistry student, you must be familiar with the three named gas laws – Boyle’s law, Charles’ law, and Gay-Lussac’s law. Right? Just recall them and you will be good to go with the combined gas law.

Therefore, the combined gas law is a combination of the three famous gas laws that you must have come across- Boyle’s law, Charles’ law, and Gay-Lussac’s law.

### Boyle’s law

• The popular gas law discovered by Robert Boyle, also at times known as Boyle-Mariotte law states that the pressure is inversely proportional to the volume for a fixed amount of ideal gas at a constant temperature.

The formula is –
P α (1/V)
P = k (1/V)

PV = k
where k = constant,
P = pressure exerted by the gas
V = Volume occupied by gas

• Applications of Boyle’s law – Balloon, human lungs, and soda bottle, etc.

### Charles’ law

• The popular law discovered by Jacques Charles and proved by Gay-Lussac; hence got the name Lussac-Charles law states that the volume and temperature of gas vary proportionally when the pressure and amount of gas are kept constant.

The formula is –
V α T
V/T = k

V = KT

where k is the constant of proportionality
V = volume of the gas
T = temperature of the gas in Kelvin

• Application of Charles’ law- Ping pong balls, hot air balloon, tyres, etc.

### Gay-Lussac’s law

• The popular law discovered by Gay-Lussac, known as Gay-Lussac’s law in his honor states that the pressure varies proportionally with the absolute temperature of a dry gas given the volume of gas is kept constant with the fixed amount.

The formula is-
P α T
P/T = k,
P = kT
Where k = constant
P = pressure of the gas
T = absolute temperature of the gas

• Applications of Gay-Lussac’s law- Pressure cooker, car tyres in summer, water heater, etc.

## Combined gas law equation

The combined gas law is important as it gives a collective relationship between pressure, volume, and temperature of a fixed amount of gas. With combined gas law, one can easily relate and understand the three entities.

Let’s see how we can represent the combined gas law mathematically,

PV/T = k (constant)
Where P = pressure of the gas
V = Volume of gas
T = Temperature of gas
k = constant

## Derivation and formula of Combined Gas Law

The above equation of combined gas law enables us to find a relationship between pressure, temperature, and volume. It is a simple equation that can be used to solve various problems.

Let’s understand the formula for initial and final conditions,

The combined gas law can work under different conditions or states of gas which are usually referred to as initial and final conditions. Here, the numerical value 1 against the representation of P, V, or T means the initial or first condition. Similarly, the numerical value 2 represents the final or second condition depending on the number of states.

This gives rise to the following terms that can be expressed as,
P1 = initial pressure of the gas
V1 = initial volume of gas
T1 = initial temperature of the gas
P2 = final pressure of the gas
V2 = final volume of gas
T2 = final temperature of the gas

Therefore, we can derive a mathematical formula of the combined gas law as,
P1V1/T1 = k ———————-1
P2V2/T2= k ———————–2

Combining both the equations we get the following final formula,

P1V1/T1 = P2V2/T2

One important thing to note is the use of units. For pressure or volume, you may use any unit but in combined gas law, the unit for temperature has to be Kelvin (K) always.

## Applications of the combined gas law

The combined gas law can be observed in our daily life. This law takes place when there is a fixed amount of gas or air in a container or compartment. In that case, according to combined gas law which is a combination of Boyle’s, Charles’ and Gay-Lussac’s law explains that the ratio of the element with pressure and volume to temperature will be constant or fixed(won’t change) for a definite amount of gas.

• The above process is observed in refrigeration when the heat is removed from the refrigerator’s system.
• It is observed in scuba diving where scuba divers apply combined gas law so that they easily adapt the underwater environments.