Average molar kinetic energy of `NH_3 (g)` is

Options

A. `RT`
B. `1`/`2RT`
C. `3`/`2 RT`
D. `2RT`

Answer

To find the average molar kinetic energy of ammonia gas (NH₃), we can use the formula for the molar kinetic energy of an ideal gas. The formula is:

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

Where:
- \( KE \) is the average molar kinetic energy,
- \( R \) is the universal gas constant (approximately 8.314 J/(mol·K)),
- \( T \) is the absolute temperature in Kelvin.

### Step-by-Step Solution:

1. **Identify the Formula**:
We start with the formula for the average molar kinetic energy of an ideal gas:
\[ KE = \frac{3}{2} RT \]

2. **Understand the Variables**:
- \( R \) is a constant, and its value is approximately 8.314 J/(mol·K).
- \( T \) is the temperature in Kelvin.

3. **Determine the Temperature**:
The problem does not specify a temperature, so we will keep \( T \) as a variable.

4. **Substitute the Values**:
Since we are not given a specific temperature, we can express the average molar kinetic energy in terms of \( T \):
\[ KE = \frac{3}{2} \times 8.314 \times T \]

5. **Simplify the Expression**:
We can simplify the expression, but since \( T \) is variable, we leave it in this form:
\[ KE = 12.471 T \]

### Final Expression:
Thus, the average molar kinetic energy of NH₃ gas at temperature \( T \) is:
\[ KE = 12.471 T \text{ J/mol} \]