The most probable speed of 8 g of `H_(2)` is `200 ms^(-1)`. Average kinetic energy (neglect rotational and vibrational energy ) of `H_(2)` gas is :

Options

A. 480 J
B. 240 J
C. 120 J
D. none of these

Explanation

To find the average kinetic energy of hydrogen gas (H₂) given the most probable speed, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass of H₂ = 8 g
- Most probable speed (u_mp) = 200 m/s

2. **Convert Mass to Kilograms:**
- Since we need the mass in kilograms for the calculations, convert 8 g to kg:
\[ \text{Mass in kg} = \frac{8 \text{ g}}{1000} = 0.008 \text{ kg} \]

3. **Use the Formula for Most Probable Speed:**
- The formula for the most probable speed (u_mp) is given by:
\[ u_{mp} = \sqrt{\frac{2RT}{M}} \]
- Where:
- R = universal gas constant = 8.314 J/(mol·K)
- T = temperature in Kelvin
- M = molar mass in kg/mol (for H₂, M = 0.002 kg/mol)

4. **Rearranging the Formula to Find RT:**
- Squaring both sides:
\[ u_{mp}^2 = \frac{2RT}{M} \]
- Rearranging to find RT:
\[ RT = \frac{M \cdot u_{mp}^2}{2} \]

5. **Substituting Values:**
- Substitute M = 0.002 kg/mol and u_mp = 200 m/s:
\[ RT = \frac{0.002 \cdot (200)^2}{2} \]
- Calculate \( (200)^2 = 40000 \):
\[ RT = \frac{0.002 \cdot 40000}{2} = \frac{80}{2} = 40 \text{ J/mol} \]

6. **Calculate Number of Moles (n):**
- Using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{8 \text{ g}}{2 \text{ g/mol}} = 4 \text{ mol} \]

7. **Calculate Average Kinetic Energy (KE_avg):**
- The average kinetic energy of the gas is given by:
\[ KE_{avg} = \frac{3}{2} nRT \]
- Substitute n = 4 mol and RT = 40 J/mol:
\[ KE_{avg} = \frac{3}{2} \cdot 4 \cdot 40 \]
- Calculate:
\[ KE_{avg} = \frac{3 \cdot 4 \cdot 40}{2} = \frac{480}{2} = 240 \text{ J} \]

### Final Answer:
The average kinetic energy of H₂ gas is **240 J**.

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