Which of the following quantities is the same for all ideal gases at the same temperature?

Options

A. the kinetic energy of equal moles of gas
B. the kinetic energy of equal mass of gas
C. the number of molecules of equal moles of gas
D. the number of molecules of equal of gas

Answer

To solve the question "Which of the following quantities is the same for all ideal gases at the same temperature?", we will analyze the properties of ideal gases and their behavior at a given temperature.

### Step-by-Step Solution:

1. **Understanding Ideal Gases**:
Ideal gases are hypothetical gases that follow the ideal gas law (PV = nRT) perfectly under all conditions. They are characterized by their molecules having no volume and no intermolecular forces.

2. **Kinetic Energy of Gas Molecules**:
The kinetic energy (KE) of gas molecules is given by the formula:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature in Kelvin.

3. **Kinetic Energy at Constant Temperature**:
From the formula, we can see that the kinetic energy of the gas molecules depends only on the temperature \( T \). Therefore, if the temperature is the same for all ideal gases, the kinetic energy of the molecules will also be the same.

4. **Comparison with Other Quantities**:
- **Mass**: The mass of different gases varies depending on their molar mass. Thus, it is not the same for all gases at the same temperature.
- **Number of Molecules**: The number of molecules in a gas sample can vary depending on the number of moles and the molar mass of the gas. Therefore, this quantity is also not the same for all gases at the same temperature.

5. **Conclusion**:
Since the only quantity that remains the same for all ideal gases at the same temperature is the kinetic energy of the gas molecules, we conclude that the answer is the kinetic energy.

### Final Answer:
The kinetic energy of equal moles of gas is the same at the same temperature for all ideal gases.

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