Class 11 Physics Kinetic Theory | Justification of the Avogadros hypothesis |

**Justification of the Avogadro’s hypothesis from equation of gas**

- Avogadro’s hypothesis states that equal volumes of all gases at equal temperature and pressure have the same number of molecules.
- Consider the equation PV/NT = constant and if P,V and T are same for 2 gases then N(number of molecules) is also same.
- According to Avogadro’s hypothesis number of molecules per unit volume is same for all gasesat a fixed P and T.
- Avogadro number is denoted by N
_{A}. Where_{A}denotes Avogadro number. **N**. It is universal value._{A}= 6.02x10^{23}- Experimentally it has been found that the mass of 22.4 litres of any gas is equal to molecular weight in grams at standard temperature and pressure.

**Problem:- **Molar volume is the volume occupied by 1 mole of any (ideal) gas at standard temperatureand pressure (STP: 1 atmospheric pressure, 0 °C). Show that it is 22.4 litres.

**Answer:- **The ideal gas equation relating pressure (P), volume (V), and absolute temperature (T) is given as:PV = nRT

Where,R is the universal gas constant = 8.314 J mol^{–1} K^{–1}

n = Number of moles = 1

T = Standard temperature = 273 K

P = Standard pressure = 1 atm = 1.013 × 10^{5} Nm^{–2}

= 0.0224 m^{3}

= 22.4 litres

Hence, the molar volume of a gas at STP is 22.4 litres.

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