The average kinetic energy of a molecule of the gas is

Options

A. proportional to absolute temperature
B. proportional to volume
C. dependent on the nature of the gas
D. proportional to pressure

Answer

To find the average kinetic energy of a molecule of a gas, we can use the formula derived from the kinetic theory of gases. The average kinetic energy (KE) of a single molecule of an ideal gas is given by the equation:

\[ KE = \frac{3}{2} k T \]

where:
- \( k \) is the Boltzmann constant (\(1.38 \times 10^{-23} \, \text{J/K}\)),
- \( T \) is the absolute temperature of the gas in Kelvin.

### Step-by-Step Solution:

1. **Identify the Formula**:
The average kinetic energy of a molecule of an ideal gas is given by the formula \( KE = \frac{3}{2} k T \).

2. **Understand the Variables**:
- \( k \) (Boltzmann constant) is a physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas.
- \( T \) is the absolute temperature measured in Kelvin.

3. **Substituting Values**:
If you have a specific temperature \( T \) for the gas, you can substitute that value into the equation to find the average kinetic energy.

4. **Calculate**:
If \( T \) is provided, for example, if \( T = 300 \, K \):
\[ KE = \frac{3}{2} (1.38 \times 10^{-23} \, \text{J/K}) (300 \, K) \]
\[ KE = \frac{3}{2} (4.14 \times 10^{-21} \, J) \]
\[ KE = 6.21 \times 10^{-21} \, J \]

5. **Conclusion**:
The average kinetic energy of a molecule of the gas at \( 300 \, K \) is approximately \( 6.21 \times 10^{-21} \, J \).