# Ideal gas law

Everything in the universe is made up of matter, matter is in three states of aggregation or physical states such as: solid, liquid and gas. To understand the variants of the states in which matter is subjected, it is necessary to study the kinetic molecular theory of matter.The ideal gas law  indicates that these are formed through the division of the real gases that are found in a system that has each of the attractive forces between molecules.

## What is the ideal gas law?

An ideal gas is one where all the collisions between the atoms or molecules are perfectly elastic, and it lacks attractive forces at the intermolecular level. It can be seen as a set of perfectly rigid spheres that collide with each other, without having any interaction. The internal energy in these gases presents a form of kinetic energy , which means that any change in the internal energy will cause its thermal highs or lows (changes in temperature).

• What is the ideal gas law?
• Who proposed it
• History
• Statement of the ideal gas law
• features
• Formula
• Explanation
• Experiments
• Examples of the ideal gas law
• Conclution

## What is the ideal gas law?

The ideal gas law is a simplification of real gases is done to study them more easily and is based on the condensation of Boyle ‘s law , the law of Charles , the law of Ovogadro and the law of Gay-Lussac .

## Who proposed it

It was first proposed in 1834 by the French physicist and engineer Émile Clapeyron (1799-1864) . This emerged as a combination of the law of Boyle and Charles’s law .

## History

The first gas law was developed at the end of the seventeenth century, where it is presumed that it was independently by  August Krönig  in 1856 and  Rudolf Clausius  in 1857. This universal gas constant had its discovery and was first introduced in the ideal gas law, instead of a large number of specific gas constants described by  Dmitri Mendeleev  in 1874.

It was in this same century that scientists began to notice that in the relationships between the volume, pressure and temperature of a small sample of gas in a closed system, a formula could be acquired that would be highly valid for all gases. .

This is a behavior similar to a wide variety of favorable conditions due to the harmonic approximation of the more distal molecules; Today the equation of state for an ideal gas is fervently derived from  kinetic theory .

Currently the above gas laws are considered as special conditions of the ideal gas equation , with one or more of the variables held constant.

Empirically, a series of proportional relationships between pressure, temperature and volume are observed that give way to the ideal gas law.

It was then when it was officially deduced first by the physical  Émile Clapeyron  in 1834 as a result of a combination of the Boyle ‘s law and the law of Charles .

## Statement of the ideal gas law

The ideal gas law indicates that to assign a gaseous mass we must ensure the existence of a constant directly proportional to the pressure and volume of the gas and inversely proportional to its temperature.

## features

• The number of molecules is negligible compared to the total volume of a gas.
• There is no type of attractive force between the molecules.
• The collisions are perfectly elastic.
• They have a variable volume, great diffusion and comprehensibility at the molecular junction.

## Formula

Starting from the equation of state:

P V = n R T

We have to:

Where R is the universal constant of the ideal gases, then for two states of the same gas, 1 and 2:

Common way:

The equation usually describes the relationship between pressure, volume, temperature, and quantity (in moles) of an ideal gas and is expressed like this:

PV = nRT

Where:

• P =  absolute pressure
• V =  Volume
• n =  Moles  of  gas
• R =  Universal constant of the ideal gases
• T =  absolute temperature

## Explanation

An ideal gas is one in which the molecules or atoms do not attract each other, so its behavior can be explained in a fixed way and culminates in the relationship called the ideal gas law.

The pressure exerted by the gas is due to collisions of the molecules with the walls of the container, which causes random temperature changes.

## Experiments

Ideal Gas Law Experiments:

• The paper that does not get wet.
• How to make dry ice with a fire extinguisher?
• How does the drinking bird work?
• The zombie gloves.
• The water that does not fall.
• How to put an egg in a bottle?

## Examples of the ideal gas law

There are some prominent examples that express the physics of the ideal gas law :

#### Example 1

Example: Find the pressure of 8.8 g of CO 2 at 27  0 C in a container with volume 1230 cm 3 . (C = 12, O = 16)

Solution:

First, find the molar mass of CO 2 ;

CO 2 = 12 + 2.16 = 44

So, we find moles of CO 2 ;

n = 8.8 / 44 = 0.2 moles

Convert the temperature from 0 ° C to K and the volume from cm 3  to liter;

T = 27 + 273 = 300 K

V = 1230 cm 3 = 1.23 liters

Now, we use the ideal gas law to find the unknown quantity.
PV = nRT

P.1, 23 = 0.2.0, 08206.300

P = 4 atm .

#### Example 2

Find the molar mass of X (gas) in the box below with 896 cm 3  volume, temperature 273 ° C, and mass 0.96 g. (O = 16, and the atmospheric pressure is 1 atm).

Solution:

We do unit conversions first.

P = 38 cm Hg = 38/76 = 0.5 atm

V = 896/1000 = 0.896 liters

T = 273 + 273 = 546 K

Now, we use the ideal gas law to find n;

PV = nRT

0.5.0.896 = n. (22.4 / 273) .546

n = 0.03 moles

The molar mass of X;

X = m X / n = 0.96 / 0.03

X = 32 g / mol

A) Yes; X (gas) = ​​O 2

## Conclution

Compilation data on the study of the ideal gas law:

• At a constant pressure, the volume of a gas is able to expand when it reaches a high temperature and contracts in this expansion.
• The temperature and the number of moles must be persistent.
• The pressure to prove Charles’s law must be constant.
• If the pressure of a gas doubles, the volume decreases, and if the pressure decreases or decreases, the volume increases.