Kinetic energy of one of an ideal gas at 300 K in kJ is

Options

A. 34.8
B. 3.48
C. 3.74
D. 384

Explanation

To find the kinetic energy of one mole of an ideal gas at 300 K, 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 one mole of an ideal gas is given by the formula:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the gas constant and \( T \) is the temperature in Kelvin.

2. **Substitute the Values**:
- The value of \( R \) (gas constant) is \( 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \).
- The temperature \( T \) is given as \( 300 \, \text{K} \).

Plugging in these values:
\[ KE = \frac{3}{2} \times 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \times 300 \, \text{K} \]

3. **Calculate the Kinetic Energy**:
- First, calculate \( 8.314 \times 300 \):
\[ 8.314 \times 300 = 2494.2 \, \text{J} \]
- Now, multiply by \( \frac{3}{2} \):
\[ KE = \frac{3}{2} \times 2494.2 = 3741.3 \, \text{J} \]

4. **Convert Joules to Kilojoules**:
Since 1 kJ = 1000 J, we convert the energy from Joules to Kilojoules:
\[ KE = \frac{3741.3 \, \text{J}}{1000} = 3.7413 \, \text{kJ} \]

5. **Final Answer**:
Rounding to two decimal places, the kinetic energy of one mole of an ideal gas at 300 K is approximately:
\[ KE \approx 3.74 \, \text{kJ} \]