Robert Boyle in 1662, studied the effect of change of pressure on the volume of a given mass of gas at constant temperature. According to Boyle's law, for given mass of a gas at constant temperature, the pressure (P) is inversely proportional to its volume (V).

**The gas laws**

**Boyle's law**

Robert Boyle in 1662, studied the effect of change of pressure on the volume of a given mass of gas at constant temperature. According to Boyle's law, for given mass of a gas at constant temperature, the pressure (P) is inversely proportional to its volume (V).

P a 1 / V

(at constant temperature)

V

(or)

PV = constant.

Thus if V_{1} is the volume occupied by
a given mass of a gas at pressure P_{1} and V_{2} is the volume
when pressure changes to P_{2}, then as the temperature remains
constant, according to Boyle's law

P1 V1 = P2 V2 = Constant

**Charle's Law**

The variation in the volume of a gas with
temperature at constant pressure is given by charle's law. The law may be
stated as,

For a
given mass of gas, at constant pressure, its volume (V) varies directly as its
absolute temperature (T).

V a T

or

V / T = Constant

Based on charle's law, the pressure - temperature relation is deduced
as, for a given quantity of a gas, at constant volume, the pressure (P) varies
directly as its absolute temperature (T)

P a T

or

P / T = Constant

where T is
temperature in kelvin.

**The equation of state for an ideal gas**

Gases which obey Boyle's law and Charle's law are known as ideal gases.
By combining these two laws, an equation of state of an ideal gas can be
derived.

According
to Boyle's law at constant temperature,

P a 1 / V

From
Charle's law

P a T (at
constant volume)

By
combining these proportionalities,

P a T/V

Or

PV a T

PV = RT

where `R' is a proportionality constant, commonly called as the **gas** **constant. **Generally, the ideal gas equation is written as

PV = n RT

where `n'
is the number of moles of the gas.

_{No. of moles
= Mass of the gas in gram }/ Molecular mass of the gas = m /
M = mol

PV = ( m / M ) RT

m = mass of the gas.

The ideal
gas equation can be written for a constant mass of a gas as,

P1 V1 / T_{1 = }P2
V2 / T_{2}

**Standard temperature
and Pressure (S.T.P)**

The
conditions of a gas system present at standard temperature and standard
pressure are its temperature at 273K and its pressure being at normal
atmospheric pressure namely 1.013 x 10^{5} Nm^{-2} (1 atm).
Value of R (Gas constant) depends on the different units of pressure and
volume.

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11th 12th std standard Class Organic Inorganic Physical Chemistry Higher secondary school College Notes : The gas laws: Boyle's law and Charle's Law |

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