Here is the complete information about **Gas Laws**. The three fundamental gas laws discover the relationship of pressure, temperature, volume and amount of gas. Boyle’s Law tells us that the volume of gas increases as the pressure decreases. Charles’ Law tells us that the volume of gas increases as the temperature increases. And Avogadro’s Law tell us that the volume of gas increases as the amount of gas increases. The ideal gas law is the combination of the three simple gas laws.

Table of Contents

## Gas Laws

All gases generally show similar behaviour when the conditions are normal. But with a slight change in physical conditions like pressure, temperature or volume these show a deviation. Gas laws are an analysis of this behaviour of gases. The variables of state like the **Pressure, Volume** and **Temperature **of a gas depict its true nature. hence gas laws are relations between these variables. Let us study more about the important gas laws.

## Boyle’s Law

In 1662, Robert Boyle discovered the correlation between Pressure (P)and Volume (V)(assuming Temperature(T) and Amount of Gas(n) remain constant):

**P∝1V→PV=x**

where x is a constant depending on amount of gas at a given temperature.

- Pressure is inversely proportional to Volume

Another form of the equation (assuming there are 2 sets of conditions, and setting both constants to eachother) that might help solve problems is:

**P1V1=x=P2V2**

**Example of Boyle’s Law**

A 17.50mL sample of gas is at 4.500 atm. What will be the volume if the pressure becomes 1.500 atm, with a fixed amount of gas and temperature?

**Solution**

*V*2=*P*1⋅*V*1/*P*2

=4.500*atm*⋅17.50*mL*1.500*atm*

=52.50*mL*

## Charles’ Law

Jacques Charles in 1787 analyzed the effect of temperature on the volume of a gaseous substance at a constant pressure. He did this analysis to understand the technology behind the hot air balloon flight. According to his findings, at constant pressure and for constant mass, the volume of a gas is directly proportional to the temperature.

This means that with the increase in temperature the volume shall increase while with decreasing temperature the volume decreases. In his experiment, he calculated that the increase in volume with every degree equals 1/273.15 times of the original volume. Therefore, if the volume is V_{0 }at 0° C and V_{t }is the volume at t° C then,

V_{t }= V_{0 }+t/273.15 V_{0 }⇒ V_{t }= V_{0 }(1+ t/273.15 )

⇒ V_{t }= V_{0 }(273.15+ t/273.15 )

For the purpose of measuring the observations of gaseous substance at temperature 273.15 K, we use a special scale called the Kelvin Temperature Scale. The observations of temperature (T) on this scale is 273.15 greater than the temperature (t) of the normal scale.

T= 273.15+t

while, when T = 0° c then the reading on the Celsius scale is 273.15. The Kelvin Scale is also called Absolute Temperature Scale or Thermodynamic Scale. This scale is used in all scientific experiments and works. In the equation [ V_{t }= V_{0 }(273.15+ t/273.15 ) ] if we take the values T_{t }= 273.15+t and T_{0 }= 273.15 then:

V_{t }= V_{0 }( T_{t }/ T_{0 })

which implies V_{t}/V_{0}= ( T_{t }/ T_{0 }), which can also be written as:

V_{2}/V_{1}= T2/ T_{1}

or V_{1 }/T_{1 }= V_{2 }/ T_{2}

V/T = constant = k_{2 }

Therefore, V= k_{2} T

The graphical representation of Charles law is shown in the figure above. Its an isobar graph as the pressure is constant with volume and temperature changes under observation.

## Gay-Lussac’s law

Also referred to as Pressure-Temperature Law, Gay Lussac’s Law was discovered in 1802 by a French scientist Joseph Louis Gay Lussac. While building an air thermometer, Gay-Lussac accidentally discovered that at fixed volume and mass of a gas, the pressure of that gas is directly proportional to the temperature. This mathematically can be written as: p ∝\propto∝ T

⇒ p/T = constant= k_{3 }

The temperature here is measured on the Kelvin scale. The graph for the Gay- Lussac’s Law is called as an isochore because the volume here is constant.

## Avogadro’s Law

Amedeo Avogadro in 1811 combined the conclusions of Dalton’s Atomic Theory and Gay Lussac’s Law to give another important Gas law called the Avogadro’s Law. According to Avogadro’s law, at constant temperature and pressure, the volume of all gases constitutes an equal number of molecules. In other words, this implies that in unchanged conditions of temperature and pressure the volume of any gas is directly proportional to the number of molecules of that gas.

Mathematically, V ∝\propto∝ n

Here, n is the number of moles of the gas. Hence, V= k_{4}n

The number of molecules in a mole of any gas is known as the Avogadro’s constant and is calculated to be 6.022 * 10^{23}. The values for temperature and pressure here are the standard values. For temperature, we take it to be 273.15 K while for the pressure it equals 1 bar or 10^{5} pascals. At these Standard Temperature Pressure (STP) values, one mole of a gas is supposed to have the same volume. Now, n = m/M

According to Avogadro’s equation: V= k_{4} (m/M)

M=k_{4}(m/V)

m/V= d (density); Therefore M=k_{4}D

This means that at an unchanged temperature and pressure conditions, the molar mass of every gas is directly proportional to its density.

The above gas laws provide us with an indication of the various properties of gases at changed conditions of temperature, pressure volume and mass. These laws seem trivial but these find great importance in our day to day lives. From breathing to hot air balloons and vehicle tyres the deviation in gaseous behaviour in changed conditions may affect all. So the next time you are travelling just remember the effect change in physical conditions can have!

## Ideal Gas Law

The ideal gas law is the combination of the three simple gas laws. By setting all three laws directly or inversely proportional to Volume, you get:

**V∝nTP**

Next replacing the directly proportional to sign with a constant(R) you get:

**V=RnTP**

And finally get the equation:

**PV=nRT**

where P= the absolute pressure of ideal gas

- V= the volume of ideal gas
- n = the amount of gas
- T = the absolute temperature
- R = the gas constant

Here, R is the called the gas constant. The value of R is determined by experimental results. Its numerical value changes with units.

**R = gas constant = 8.3145 Joules · mol ^{-1 }· K^{-1 }(SI Unit)**

= 0.082057 L · atm·K^{–}^{1 }· mol^{–}^{1}