The kinetic energy of 1 mole of gas is equal to -

Options

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

Answer

To find the kinetic energy of 1 mole of gas, we can use the formula for the kinetic energy of an ideal gas.

### Step-by-Step Solution:

1. **Identify the Formula**: The kinetic energy (KE) of 1 mole of an ideal gas is given by the equation:
\[ KE = \frac{3}{2} nRT \]
where:
- \( n \) = number of moles of gas
- \( R \) = universal gas constant (8.314 J/mol·K)
- \( T \) = temperature in Kelvin

2. **Substitute for 1 Mole**: Since we are asked for the kinetic energy of 1 mole of gas, we set \( n = 1 \):
\[ KE = \frac{3}{2} (1) RT = \frac{3}{2} RT \]

3. **Understanding the Components**: The value of \( R \) is known (8.314 J/mol·K). Thus, the kinetic energy can be expressed as:
\[ KE = \frac{3}{2} (8.314) T \]

4. **Final Expression**: Therefore, the kinetic energy of 1 mole of gas can be simplified to:
\[ KE = \frac{3}{2} RT \]

5. **Conclusion**: The answer to the question is:
\[ \text{The kinetic energy of 1 mole of gas is } \frac{3}{2} RT. \]