The temperature at which hydrogen molecules have the same kinetic energy as oxygen molecules have at `40^(@)C` is :

Options

A. `40^(@)C`
B. `5^(@)C`
C. `320^(@)C`
D. `640^(@)C`

Answer

To solve the problem, we need to determine the temperature at which hydrogen molecules have the same kinetic energy as oxygen molecules at 40°C.

### Step-by-Step Solution:

1. **Understand the Kinetic Energy Formula**:
The kinetic energy (KE) of a gas is given by the formula:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin.

2. **Convert the Given Temperature to Kelvin**:
The temperature of oxygen is given as 40°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
Therefore,
\[ T(O_2) = 40 + 273.15 = 313.15 \, K \]

3. **Set the Kinetic Energies Equal**:
Since we want the kinetic energy of hydrogen (\( KE_{H_2} \)) to be equal to that of oxygen (\( KE_{O_2} \)), we can write:
\[ KE_{H_2} = KE_{O_2} \]
This means:
\[ \frac{3}{2} R T_{H_2} = \frac{3}{2} R T_{O_2} \]
Since \( R \) and \( \frac{3}{2} \) are constants and will cancel out, we have:
\[ T_{H_2} = T_{O_2} \]

4. **Conclusion**:
Therefore, the temperature at which hydrogen molecules have the same kinetic energy as oxygen molecules at 40°C is:
\[ T_{H_2} = 313.15 \, K \]
To express this in Celsius:
\[ T_{H_2} = 313.15 - 273.15 = 40°C \]

### Final Answer:
The temperature at which hydrogen molecules have the same kinetic energy as oxygen molecules at 40°C is **40°C**.