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 conditions 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 solve the question regarding Avogadro's hypothesis, we need to understand what Avogadro's law states. Here’s a step-by-step breakdown:

### Step 1: Understand Avogadro's Hypothesis
Avogadro's hypothesis states that under the same conditions of temperature and pressure, equal volumes of all gases contain an equal 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.

### Step 2: Analyze the Options
Now, let's analyze the options provided in the question to determine which one correctly represents Avogadro's hypothesis.

1. **Option A**: "Gases react together in volume which bear a simple ratio to the number."
- This statement is related to the law of combining volumes but does not directly represent Avogadro's hypothesis.

2. **Option B**: "Equal volume of all gases under the same conditions of temperature and pressure contain equal number of molecules."
- This statement accurately reflects Avogadro's hypothesis.

3. **Option C**: "Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of atoms."
- This statement is incorrect because Avogadro's hypothesis refers to molecules, not atoms.

4. **Option D**: "The rate of diffusion of gases is inversely proportional to the square root of their density."
- This statement refers to Graham's law of effusion and diffusion, not Avogadro's hypothesis.

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

### Final Answer
**The correct option is B.**

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