The translational kinetic energy of gas molecules for `1` mol of gas is equal to

Options

A. `(3)/(2)RT`
B. `(2KT)/(3)`
C. `(RT)/(2)`
D. `(3KT)/(2)`

Answer

To find the translational kinetic energy of gas molecules for 1 mole of gas, we can use the formula derived from the kinetic theory of gases. The translational kinetic energy (TKE) of gas molecules can be expressed as follows:

### Step-by-Step Solution:

1. **Understand the Concept**: The translational kinetic energy of a gas is related to the temperature and the number of degrees of freedom of the gas molecules. For a monoatomic ideal gas, the translational kinetic energy can be calculated using the formula derived from kinetic theory.

2. **Formula for Kinetic Energy**: The translational kinetic energy (TKE) for one mole of an ideal gas is given by:
\[ \text{TKE} = \frac{3}{2} nRT \]
where:
- \( n \) is the number of moles of the gas,
- \( R \) is the universal gas constant (approximately \( 8.314 \, \text{J/mol·K} \)),
- \( T \) is the absolute temperature in Kelvin.

3. **Substituting Values**: For 1 mole of gas, we set \( n = 1 \):
\[ \text{TKE} = \frac{3}{2} \times 1 \times RT \]
This simplifies to:
\[ \text{TKE} = \frac{3}{2} RT \]

4. **Conclusion**: Therefore, the translational kinetic energy of gas molecules for 1 mole of gas is:
\[ \text{TKE} = \frac{3}{2} RT \]

### Final Answer:
The translational kinetic energy of gas molecules for 1 mole of gas is equal to \( \frac{3}{2} RT \).

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