What is average kinetic energy of `1` mole of `SO_(2)` at `300 K`?

Options

A. `4578` J/mol
B. `3134` J/mol
C. `3741` J/mol
D. `4173` J/mol

Explanation

To find the average kinetic energy of 1 mole of \( SO_2 \) at \( 300 \, K \), we can use the formula for the average kinetic energy of a gas:

\[ KE = \frac{3}{2} RT \]

Where:
- \( KE \) is the average kinetic energy,
- \( R \) is the gas constant,
- \( T \) is the temperature in Kelvin.

### Step 1: Identify the values needed
We need to identify the values for \( R \) and \( T \):
- \( R = 8.314 \, \text{J/(K mol)} \) (since we need the energy in Joules),
- \( T = 300 \, K \).

### Step 2: Substitute the values into the formula
Now, we substitute the values of \( R \) and \( T \) into the kinetic energy formula:

\[ KE = \frac{3}{2} \times 8.314 \, \text{J/(K mol)} \times 300 \, K \]

### Step 3: Calculate the average kinetic energy
Now, we perform the calculations:

1. Calculate \( 8.314 \times 300 \):
\[ 8.314 \times 300 = 2494.2 \, \text{J/mol} \]

2. Now, multiply by \( \frac{3}{2} \):
\[ KE = \frac{3}{2} \times 2494.2 = 3741.3 \, \text{J/mol} \]

### Final Answer
Thus, the average kinetic energy of 1 mole of \( SO_2 \) at \( 300 \, K \) is:

\[ \boxed{3741.3 \, \text{J/mol}} \]