The molecules of which of the following gases have the largest mean average K.E. at `250^(@)C` ?

Options

A. Ar
B. CO
C. He
D. All have same K.E.

Explanation

To determine which gas has the largest mean average kinetic energy (K.E.) at a temperature of \(250^\circ C\), we can follow these steps:

### Step 1: Understand the Relationship Between Kinetic Energy and Temperature
The average kinetic energy of gas molecules is given by the formula:
\[ KE = \frac{3}{2} k T \]
where:
- \(KE\) is the average kinetic energy,
- \(k\) is the Boltzmann constant,
- \(T\) is the absolute temperature in Kelvin.

### Step 2: Convert the Temperature to Kelvin
To use the formula, we need to convert the temperature from Celsius to Kelvin. The conversion is done using the formula:
\[ T(K) = T(°C) + 273.15 \]
For \(250^\circ C\):
\[ T = 250 + 273.15 = 523.15 K \]

### Step 3: Analyze the Kinetic Energy Formula
From the formula, we can see that the average kinetic energy is directly proportional to the absolute temperature \(T\). This means that at a constant temperature, the average kinetic energy will be the same for all gases, regardless of their molecular mass.

### Step 4: Conclusion
Since the average kinetic energy of gas molecules at a given temperature is independent of the mass of the gas, all gases at \(250^\circ C\) will have the same mean average kinetic energy. Therefore, the answer to the question is that all the gases listed (Argon, CO, He) will have the same average kinetic energy at \(250^\circ C\).

### Final Answer
All gases listed will have the same mean average kinetic energy at \(250^\circ C\).

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