# Ideal gas law calculator

I always have had difficulties in accepting chemistry in my life. The chemical equations, the different chemical phenomena, and the name of scientists and their contribution, of course, I had struggled with it. However, when I realized the importance and significance of this vast subject holds, I could not stop myself by giving it a shot. The chemistry has been there since the 17th century and helping us out in all the work we can do in terms of it or even more than it.

Thanks to my teacher who started this great chapter about gas laws. The laws act as those behind the scenes important personality which is essential for any movie to go blockbuster. Yes, that changed everything. I saw myself enjoying the subject eventually.

So for the chemistry nerds out there, there are 3 essential and fundamental gas laws of chemistry dealing with various constraints of the gases, such as temperature, pressure, volume, and mass of the gas. Those, when combined, give out what we are going to study below – Ideal gas law.

## Ideal gas law

You guys must be wondering what exactly the meaning of ideal is! We hear this word so much in our day to day life but one can relate more especially in chemistry. So ideal relates to the concept of perfection. Normally there is not a thing in this world that is perfect or in this case ideal. So we can figure out by now that ideal gas means perfect gas.

Now a perfect gas aka ideal gas is a theoretical gas which helps us establish the relations between the variables of the gases which we just say above. As per chemistry, there are 3 essential gas laws namely- Charles law, Boyle’s law, and last but not the least Avogadro’s law. When we combine all three of them the result obtained is known as the ideal gas law.

## Discovery of Ideal Gas Law

It was the year 1834 when ‘Benoît Paul Émile Clapeyron’ a physicist and an engineer birthed the ideal gas law. As we saw earlier that ideal gas law is the combination of the 3 fundamental gas laws, so according to Clapeyron an ideal gas consists of identical infinitesimally small particles of gas which only interact with each other like small elastic balls. While working on his research he found out that under certain conditions all the 3 fundamental laws od gases incorporated with each other thus forming a new equation which is true for ideal gases.

## Ideal gas law statement

The Ideal gas law gives us the relationship between pressure, volume, and temperature of the gas. It states that there is a relationship between the variables such that they all are equal to the ‘n’ gram moles of the gas.

**Ideal gas law equation –**

As all the laws have their converted mathematical form, let us have a look at the ideal gas laws’ equation which will be helpful in the calculations and stuff.

Mathematical relationship-

PV = nRT

P = pressure of the gas (atm)

V = volume of the gas (litres)

T = temperature of the gas (degree Kelvin)

N = moles of the gas (mol)

R = ideal gas law constant.

Here R is the constant for the relationship which has the value of R = 8.31 J/mole‐degree K in SI units.

When we compare the two ideal gases the general formula for it is given below-

P1V1/T1 = P2V2/T2

## Graph of Ideal Gas Law

Ideal gas law has 4 different variables which are pressure temperature, volume, and the number of moles. So it is difficult for us to draw and plot all the relationships between them in one graph only. So hence there are four graphs we can draw out for our easy. Those are

- PV graph

This graph gives the relationship between the pressure and volume, and how they are inversely proportional to each other. In other words, this is the graph of Boyles’s law. - VT graph

This graph gives the relationship between the volume and the temperature of the gas and how they are proportional to each other. The graph is a linear line with a positive slope. In other words, it is a graph for Charles’s law. - PT graph

This graph gives us the relationship between the pressure and temperature of the gas and how they are proportional to each other. The graph is a linear line with a positive slope. In other words, this is the graph of Gay Lussac’s law. - Vn graph

This graph gives us the relationship with the volume of the gas and mole of the gas. The graph is a linear line with a positive slope. This is the graph of Avogadro’s law.

**Derivations and Calculation**

Since ideal gas law is the combination of all the three gases hence for the derivation of ideal gas law we need to look at all the other 3 laws of gases-

- Boyle’s law-

P1V1 = P2V2 ……(1) - Charles law-

V1/T1 = V2/T2 ……(2) - Avogadro’s Law-

V= kn

V/n = k ……(3)

V- the volume of gas

n= amount of gas

k = constant for a given temperature and pressure

For numerical and calculations we may consider this formula as well –

n=m/M

n= number of moles

m= mass

M= molecular mass

So incorporating the above laws and equations 1,2 and 3 we can get one expression, which is-

PV=nRT

There are two different conditions – initial and final. The value 1 corresponds to initial and 2 to final. 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 ideal gas law as,

The formula to be used when comparing the two ideal gases is-

**P1V1/T1=P2V2/T2**

**Applications**

▪ We all are aware of the fact that the temperature of the gas goes down as the gas expands into a larger volume. This concept helps us so much in our daily life because it helps to make refrigerators. In refrigerators, the coolant is compressed hence causing the temperature to increase. As the hot gas expands it cools off the interior of the fridge.

▪ Breathing is an essential part of our life where we breathe in oxygen to help us live as long as we can of course. So we breathe in the air due to low pressure inside our lungs and once the air enters the pressure is high and after utilizing the oxygen we exhale the carbon dioxide out.