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Equal number of molecules of different gases under identical conditions of temperature and pressure occupy the same volume.

Hence, the volume occupied by one mole of an ideal gas at standard temperature (273.15 K) and pressure (101.325 K Pa) has a fixed volume (22.414 dm³). This indicates that the number of molecules contained in one mole of any real gas should be a constant quantity. This number is found to be 6.023 × 10²³ and is known as Avogadro number.

Important

Ideal gas is a gas which follows all the above gas laws under all conditions of temperature and pressure.

Real gases generally do not obey the gas laws, exactly, under all conditions of temperature and pressure.

The Ideal Gas Equation

Combination of Boyle’s and Charle’s laws. When temp. (T1) is kept constant and pressure is changed from p1 to p2, Let the new volume be V ^‘.

Important

Value of the proportionality constant k depends on:

(a)      Quantity of gas and

(b)         Units, in which p, V and T, are expressed.

On the basis of Avogadro’s hypothesis, 1 mole of all gases under similar conditions of temp. and  pressure occupies the same volume. Hence k will have the same value for 1 mole of any gas taken.

pV = kT. …(5)

(k is replaced by R called the molar gas constant).

For n moles of gas considered  (5) becomes

PV = nRT. …(6)

Eq. (6) is called the ideal gas equation showing the effect on the third variable when two of the three variables are changed simultaneously for a given amount of a gas. The units of R varies with the units of the other parameters (p, V, T).

e.g. R has the following values

0.0821 litre atm/ K /mole

5.28 × 10¹⁹ ev / K / mole

8.314 Joules / K / mole

1.99 cal / K / mole

0.002 k cal / K / mole

8.314 × 10⁷ erg / K / mole

Illustrations

1.   A two litre flask, containing O2 at 1 atm pressure is at a constant temperature at 27°C. The gas pressure is reduced to 10^–6 atm by attaching the flask to a vacuum pump. Assuming ideal behaviour, answer the following:

(a) What will be the volume of the gas which is left behind?

(b) What will be the no of molecule given in the problem?

Sol. Given that V₁ = 2 l, p₁ = 1 atm, T = 27°C = 300 K

We have the following results

(a)         The volume of oxygen left behind will be the same i.e. 2 l.

(b)         The number of moles of oxygen left behind is given by