**Gases**

There are three physical states of matter i.e., gases, liquids and solids. Behavior of gases is simpler and there is uniformity in the properties of gases. When the external conditions of temperature and pressure are changed, then the volume of the gases are affected to some extent. That is why all the gases more or less follow the same principles and laws. Some of these laws are given briefly as follow.

## Boyle’s Law

According to this law, *“the volume of a given mass of a gas is inversely proportional to the pressure provided that the temperature remains constant.”*

V (when temperature ‘T’and number of moles ‘n’ are constant)

V

PV = k

Or P_{1}V_{1}= P_{2}V_{2 }= P_{3}V_{3 }= k ………(1)

When the ‘T’ and ‘n’ are constant.

## Charles Law

According to this law, *“the volume of a given mass of a gas increases or decreases by **of its volume at *0C, *for every one degree rise or fall of temperature provided that the pressure is constant.”*

From this law, we get the idea of absolute zero, which starts from 273.16C. this is the lowest temperature which is never attained. When the graph is plotted between temperature on x-axis and volume of gas on y-axis, it gives a straight line and when extrapolated meets the temperature axis at 273.16C.

## Combined Gas law

**
**Keeping in view, the Boyle’s law and the Charles’s law, we can prove that

V

Since V n, V T and V

So, V

Or PV = nRT ……… (2)

This is a general gas equation in which ‘R’ is general gas constant and ‘n’ is the number of moles of the gas. This gas equation has another shape as well.

P_{1}V_{1}**/ **T_{1}= P_{2}V_{2}**/** T_{2} ……… (3)

Or d = ……… (4)

In equation 4 ‘d’ is the density of the gas ‘P’ is pressure and ‘M’ is the molar mass. The density of gas is directly proportional to pressure and inversely proportional to the temperature.

**Gas Constant**

‘R’ is called universal gas constant. Its significance can be readily understood, if you examine the nature of the quantities which makes its values.

Since PV = nRT

So, R =

Or R =

Since, pressure is force per unit area

R =

Area = (length)^{2}

Volume = (length)^{3}

Temperature is in kelvin

So, R =

=

Force length = Energy or work

So, R= =Energy K^{-1} mol^{-1}

It means that the ‘R’ will be expressed in terms of energy per kelvin per mole. When we use the Avogadro’s principal, then the values and units of ‘R’ are as follows.

**Values and Units of ‘R’**

According to Avogadro’s law of gases, one mole of an ideal gas at standard temperature and pressure occupies the volume of 22.414 dm^{3}.

Since R = P = 1 atm., V = 22.414dm^{3}

Putting values

R = = 0.082 dm^{3}atmK^{-1} mol^{-1}

If the units of pressure and volume are taken in S.I system, then

P = 101325 Nm^{-2} (since 1 atm = 101325 Nm^{-2})

V = 0.0224 m^{3}(Since 1 dm^{3}= 10^{-3}m^{3})

Putting values R = =8.3143 Nm K^{-1} mol^{-1}

Since Nm = J

So, R = 8.3143 J.K^{-1} mol^{-1}

We know that, 1 calorie = 4.18 Joules

The value of R may be expressed in calories

R = JK^{-1} mol^{-1}= 1.987 calK^{-1} mol^{-1}.