Which of the following parameters is the same for molecules of all gases at a given temperature?

Options

A. mass
B. Speed
C. Momentum
D. Kinetic energy

Answer

To solve the question regarding which parameter is the same for molecules of all gases at a given temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Question**: We need to identify which parameter remains constant for all gas molecules when they are at the same temperature.

2. **Analyze the Options**:
- **Mass**: The mass of gas molecules varies between different gases. For example, oxygen (O2) has a different mass compared to nitrogen (N2). Therefore, mass is not the same for all gases.
- **Speed**: The speed of gas molecules depends on their mass and temperature. Different gases will have different molecular masses, which affects their speeds. Hence, speed is not constant across different gases.
- **Momentum**: Momentum is defined as the product of mass and velocity (p = mv). Since both mass and speed can vary between different gases, momentum will also vary. Thus, momentum is not the same for all gases.
- **Kinetic Energy**: The average kinetic energy of gas molecules is directly related to the temperature of the gas. According to the kinetic theory of gases, the average kinetic energy (KE) of gas molecules can be expressed as:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature. This means that at a given temperature, the average kinetic energy of all gas molecules will be the same.

3. **Conclusion**: Since the average kinetic energy is the only parameter that remains constant for all gas molecules at a given temperature, the correct answer is:
- **Kinetic Energy** (Option D).

### Final Answer:
The parameter that is the same for molecules of all gases at a given temperature is **Kinetic Energy** (Option D).