Avogadro’s Law:-
In 1811, Avogadro established relationship between volume of gas and number of molecules, present in it at given temperature and pressure and which is known as Avogadro’s Law. According to this law, “equal volume of all gases under the same conditions of temperature and pressure contain equal number of molecules”.
Mathematically it is written as:
where V is the volume and n is number of moles of gas. The number of molecules in one mole of a gas has been determined to be 6.023 × 1023 and is known a Avogadro constant.
Since volume of a gas is directly proportional to the number of moles. Hence, at standard temperature and pressure (STP), one mole of each gas will have same volume. Standard temperature and pressure means 273.15 K and 1 bar (106 pascal).
At STP, molar volume of an ideal gas is 22.4 L mol-1. Molar volume of some gases is given in table.
Table: Molar volume in litres per mole of some gases at 273.15 K and 1 bar (STP).
|
Gas |
Molar Volume |
| 1. |
Argon(Ar) |
22.37 |
| 2. |
Carbon dioxide(CO2) |
22.54 |
| 3. |
Dinitrogen(N2) |
22.69 |
| 4. |
Dioxygen(O2) |
22.69 |
| 5. |
Dihydrogen(H2) |
22.72 |
| 6. |
Ideal gas |
22.71 |
Boyle’s Law:
In 1662, Boyle studied the effect of pressure on given mass of gas at constant temperature. This is known as Boyle’s law or pressure-volume Relation. According to this law “At constant temperature, the pressure of a fixed amount (i.e., number of moles, n) of gas varies inversely with its volume”.
Mathematically, Boyle’s law is written as
where, P = Pressure, V = Volume, k1 = proportionality constant.
The value of k1 depends upon the temperature and mass of gas.
viz “At constant temperature, product of pressure and volume of a fixed amount of gas is constant”.
Suppose, a gas has volume V1 at pressure P1. At constant temperature, if pressure extended to P2 and volume becomes V2, then according to Boyle’s law,
P1V1 = P2V2 = Constant
Charle’s Law:
The effect of temperature on volume of gas at constant pressure was studied by J. Charle. It was further explained by Gay Lussac and its conclusion was termed as Charle’s Law. Since it gave relation between temperature and volume therefore it is also known as temperature-volume relationship. According to this law, “At constant pressure, the volume of gas increases or decreases by \(\frac{1}{273}\) on increasing or decreasing each degree of temperature”.
Mathematically, Charle’s law can be written as :
Suppose, the volume of gas is V0 at temperature 0°C. If temperature is increased as t°C then volume becomes Vt, then according to Charle’s law,
we can calculate the volume of given mass of gas at different temperatures.
It is clear from graph, at – 273 or -273.15 > C, the volume of each gas is zero.
