Which of the following represents Avogadro's hypothesis ?

Options

A. Gases react together in volumes which bear a simple ratio to one another
B. Equal volumes of all gases under same conditions of temperature and pressure contain equal number of molecules
C. Equal volumes of all gases under same condition of temperature and pressure contain equal number of atoms
D. The rates of diffusion of gases are inversely proportional to the square root of their densities

Answer

To determine which statement represents Avogadro's hypothesis, we need to first understand what Avogadro's hypothesis states.

### Step-by-Step Solution:

1. **Understanding Avogadro's Hypothesis**:
Avogadro's hypothesis states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This means that if you have two containers of gas that are the same size and are kept at the same temperature and pressure, they will have the same number of gas molecules.

2. **Analyzing the Options**:
- **Option 1**: "Gases react together in volumes which bear a simple ratio to one another."
- This statement refers to the law of combining volumes and is not Avogadro's hypothesis.
- **Option 2**: "Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of gaseous molecules."
- This statement directly reflects Avogadro's hypothesis and is correct.
- **Option 3**: "Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of atoms."
- This is incorrect because Avogadro's hypothesis refers to molecules, not atoms.
- **Option 4**: "The rates of diffusion of gases are inversely proportional to the square root of their density."
- This statement describes Graham's law of diffusion and is not related to Avogadro's hypothesis.

3. **Conclusion**:
Based on the analysis of the options, the correct representation of Avogadro's hypothesis is **Option 2**: "Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of gaseous molecules."

### Final Answer:
**Option 2** is the correct representation of Avogadro's hypothesis.