Avogadro's hypothesis states that

Options

A. the ideal gas consists of a large number of small particles called molecules
B. under the same conditions of temperature and pressure equal volumes of gases contains the same number of molecules
C. volume of definite quantity of gas at constant pressure is directly
D. none of the above

Answer

### Step-by-Step Solution:

1. **Understanding Avogadro's Hypothesis**: Avogadro's hypothesis states that under the same conditions of temperature and pressure, equal volumes of gases contain the same number of molecules. This means that if you have two different gases at the same temperature and pressure, and they occupy the same volume, they will have the same number of molecules.

2. **Mathematical Representation**: The relationship can be expressed mathematically. If we denote the number of molecules as \( N \) and the volume as \( V \), Avogadro's hypothesis can be represented as:
\[ N \propto V \quad \text{(at constant temperature and pressure)} \]
This indicates that the number of molecules \( N \) is directly proportional to the volume \( V \).

3. **Ideal Gas Equation**: The ideal gas equation is given by:
\[ PV = nRT \]
where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is temperature.

4. **Relating Moles to Molecules**: The number of moles \( n \) can be related to the number of molecules \( N \) using Avogadro's number \( N_A \):
\[ N = n \times N_A \]
where \( N_A \) is Avogadro's constant (approximately \( 6.022 \times 10^{23} \) molecules/mol).

5. **Conclusion**: From the above relationships, we can conclude that under the same conditions of temperature and pressure, equal volumes of gases will contain the same number of molecules. Therefore, the correct option that describes Avogadro's hypothesis is:
- **Option B**: Under the same conditions of temperature and pressure, equal volumes of gases contain the same number of molecules.