*GAS LAWS*

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**Boyle’s Law**

This law was given by Boyle in 1662. According to this law,

At constant temperature, the volume of a given mass of a gas is inversely proportional to its pressure.

V 1/P (when T =Constt.)

PV = CONSTANT

Boyle’s law can be derived by Kinetic Gas Equation

PV =1/3(mNv2) (i)

PV =(2/3). (1/3)(mNv2) (ii)

= 2/3 Ek

Ek = Average kinetic energy.

1/2 mNv2 T

1/2 mNv2 =KT (iii)

K is proportionality constt.

Compare Eq. (2) & (3)

PV = 2/3 KT

PV = constt.

** V 1/P ****(At Constt. T) Boyle’s law**

**Charle’s Law**

This law was given by charles in 1787 According to this law,

At constant pressure, the volume of given mass of a gas is directly proportional to its absolute temperature (T).

V T ( at constt. Pressure)

V =KT

V/T = constt.

If the volumes of given mass of a gas are V_{1} & V_{2} at constt pressure & absolute temperatures T_{1} & T_{2}

According to Charle’s law-

V1/T1 = V2/T2

(Absolute Temperature = 273 + temperature in c)

**Avogadro’s Law**

Berzelius presented a hypothesis & Avogadro modified, well tested & verified & then gave a law i-e Avogadro’s law.

According to this law,

‘Equal volumes of all gases under similar conditions of temperature & pressure contain equal number of molecules’.

For two gases, kinetic gas equation can be written as,

P1V1 =1/3 (m1 .N1 .v12) =2/3.1/3 .(m1 .N1 .v12)

P2V2 =1/3 (m2 .N2 .v22) =2/3.1/3 .(m2 .N2 .v22)

because, P1.V1 =P2.V2

1/2 m1. N1.v12 =1/2 (m2 .N2 .v22)

If temperature is constt, the average kinetic energy per molecule must be the same.

1/2 m1.v12 =1/2 m2.v22

N1 = N2 (Avogadro’s law.)

**The important conclusions of this law-**

- The proportion of volumes of gases in the gaseous reaction is the same as the proportion of their molecules or moles.

**Ex. N2 + 3H _{2 —–.> 2NH3}**

one mole of N2 combines with 3 moles of H_{2} to produce 2 moles of NH_{3}

According to Avogadro’s Law,

proportion of volumes of N_{2}, H_{2} & NH_{3} in the reaction is 1:3:2

- The volume of 1 mole of gas at N.T.P. is 22.4 litres.
- Mass of 22.4 litre of any gas at N.T.P. is equal to its gram molecular weight.

Molecular weight = 2 × vapour density

Ex.- Mass of 22.4 litre of hydrogen at N.T.P. is 2 grams.