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 (NH₃) gas, we can follow these steps:

### Step 1: Understand the formula for molar kinetic energy
The average molar kinetic energy (KE) of an ideal gas is given by the formula:
\[ KE = \frac{3}{2}RT \]
where:
- \( R \) is the universal gas constant (8.314 J/(mol·K)),
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Identify the properties of the gas
The kinetic energy of an ideal gas is dependent only on the temperature and is independent of the type of gas or its molecular weight. This means that the average kinetic energy for any ideal gas at a given temperature is the same.

### Step 3: Apply the formula to NH₃
Since ammonia (NH₃) is an ideal gas, we can directly apply the formula for molar kinetic energy:
\[ KE_{NH_3} = \frac{3}{2}RT \]

### Step 4: Identify the correct option
From the options provided:
1. RT
2. \(\frac{1}{2}RT\)
3. \(\frac{3}{2}RT\)
4. 2RT

The correct answer is the one that matches our derived formula, which is:
\[ \frac{3}{2}RT \]
Thus, the correct option is option 3.

### Final Answer:
The average molar kinetic energy of NH₃ (g) is \(\frac{3}{2}RT\).

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