The kinetic molecular theory of gases predicts that at a given temperature

Options

A. All the molecules in the gas do not have the same average energy
B. All the molecules in the gas have the same average energy
C. Light gas molecules have lower average energies than heavy gas molecules
D. Light gas molecules have higher average energies than heavy gas molecules

Explanation

**Step-by-Step Solution:**

1. **Understanding Kinetic Molecular Theory (KMT)**: The KMT describes the behavior of gases in terms of particles in motion. It states that gas molecules are in constant random motion and that this motion is related to the temperature of the gas.

2. **Kinetic Energy and Temperature**: According to KMT, the average kinetic energy of gas molecules is directly proportional to the absolute temperature (in Kelvin) of the gas. This can be expressed mathematically as:
\[ KE_{avg} = \frac{3}{2} kT \]
where \( KE_{avg} \) is the average kinetic energy, \( k \) is the Boltzmann constant, and \( T \) is the absolute temperature.

3. **Kinetic Energy of Individual Molecules**: While all gas molecules at a given temperature have the same average kinetic energy, individual molecules may have different kinetic energies. The distribution of kinetic energies among the molecules is described by the Maxwell-Boltzmann distribution.

4. **Effect of Molecular Mass**: Heavier molecules have more mass, which affects their speed. At a given temperature, heavier molecules will have a lower average speed compared to lighter molecules. This is because the kinetic energy is shared among the mass of the molecules:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the molecule and \( v \) is its velocity. For a given kinetic energy, an increase in mass results in a decrease in velocity.

5. **Conclusion**: Therefore, at a given temperature, while all gas molecules have the same average kinetic energy, heavier molecules move slower on average compared to lighter molecules.

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