# Behaviour Of Gases

## Gas Laws

Gas laws are study of any two of quantities like pressure, volume and temperature, when the third is kept constant

**A. Boyle's law**

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

V ∝ 1/P

Or, PV = constant(1)

- If P
_{1}, V_{1}are initial pressure and volumes and P_{2}, V_{2}be final values then,

P_{1}V_{1}= P_{2}V_{2}

- Graph between P and V at temperature T
_{1} and T_{2} such that T_{1}<T_{2} are shown below,

- Graph above shows that Boyle's law is strictly not obeyed by gases at all values of P and T but it obeys this law only at low pressure and high temperature i.e., at law density

**B. Charle's Law **
- Charle's Law is stated as follows :

"When pressure of a gas is constant the volume of a given mass of gas is directly proportional to its absolute temperature".

V/T = Constant(2)

- Graph between V and T is

This graph shows that experimental graph deviates from straight line. Theoretical and experimental graphs are in agreement at high temperature.

## Ideal gas equation

- We can combine Boyle' law eqn (1) and Charle's' law eqn (2) in to a single eqn i.e.,

PV/T = Constant(3)

If n moles is the mass of gas then we write

PV = nRT(4)

where, n is number of moles of gas, R=N_{A}K_{B} is the universal constant known as gas constant and T is the absolute temperature.

- A gas satisfying eqn (4) at all values of pressures and temperatures is said to be an ideal gas

now no of moles of gas

n = m/M = N/N_{A}

where

m - mass of gas containing N molecules

M - molar mass

N_{A} - Avogadro' number.

From this,

P = ρRT/M

ρ - mass density of gas.

## Dalton law of partial pressures

- Consider a mixture of non-interacting ideal gases with n
_{1} moles of gas 1,n_{2} of gas 2 and so on

- Gases are enclosed in an enclosure with volume V, temperature T and pressure P.

- Equation of state of mixture

PV = (n_{1}+ n_{2})RT

orP = n_{1}RT/V + n_{2}RT/V + - - - -

= P_{1} + P_{2} + - - --

where,

P_{1} = n_{1}RT/V

is pressure the gas 1 would exert at same V and T if no other gases were present in the enclosure. This is know as law of partial pressure of the gases.

- The total pressure of mixture of ideal gases is sum of partial pressures of individual gases of which mixture is made of.

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