If different ideal gases are at the same temperature, pressure and have same volume, then all gases have same

Options

A. Density
B. Number of molecules
C. Most probable speed
D. Internal energy per mole

Answer

To solve the question, "If different ideal gases are at the same temperature, pressure, and have the same volume, then all gases have the same...", we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Law**:
The ideal gas law is given by the equation \( PV = nRT \), where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature

Since the problem states that pressure (\( P \)), volume (\( V \)), and temperature (\( T \)) are the same for different gases, we can conclude that the number of moles (\( n \)) must also be the same.

2. **Relating Moles to Number of Molecules**:
The number of molecules (\( N \)) in a gas is related to the number of moles by the equation:
\[ N = n \cdot N_A \]
where \( N_A \) is Avogadro's number. Since \( n \) is the same for all gases, it follows that the number of molecules (\( N \)) is also the same for different ideal gases under the same conditions of temperature, pressure, and volume.

3. **Average Kinetic Energy**:
The average kinetic energy (\( KE \)) of the gas molecules is given by:
\[ KE = \frac{3}{2} nRT \]
Since \( n \), \( R \), and \( T \) are the same for all gases, the average kinetic energy per mole will also be the same.

4. **Conclusion**:
Therefore, we can conclude that if different ideal gases are at the same temperature, pressure, and volume, then **all gases have the same number of molecules**.

### Final Answer:
All gases have the same number of molecules.

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