One moles each of four ideal gases are kept as follows.
I. 5 L of gas (A) at 2 atm pressure
II . 2.5 L of gas (B) at 2 atm pressure
III . 1.25 L of gas (C) at 2 atm pressure
IV . 2.5 L of gas (D) at 2.5 atm pressure
Which of the above gases is kept at highest temperature.

Options

A. Gas (A)
B. Gas (B)
C. Gas (C )
D. Gas (D)

Explanation

To determine which of the four ideal gases is kept at the highest temperature, we can use the ideal gas law equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature

Since we have one mole of each gas (\( n = 1 \)), we can rearrange the equation to find temperature:

\[ T = \frac{PV}{nR} \]

Given that \( n = 1 \) for all gases, we can simplify this to:

\[ T = \frac{PV}{R} \]

Since \( R \) is a constant for all gases, we can conclude that the temperature is directly proportional to the product \( PV \). Therefore, we need to calculate \( PV \) for each gas and compare the results.

### Step-by-Step Calculation:

1. **Gas A:**
- Volume \( V_A = 5 \, \text{L} \)
- Pressure \( P_A = 2 \, \text{atm} \)
- Calculate \( PV \):
\[ PV_A = P_A \times V_A = 2 \, \text{atm} \times 5 \, \text{L} = 10 \, \text{atm L} \]

2. **Gas B:**
- Volume \( V_B = 2.5 \, \text{L} \)
- Pressure \( P_B = 2 \, \text{atm} \)
- Calculate \( PV \):
\[ PV_B = P_B \times V_B = 2 \, \text{atm} \times 2.5 \, \text{L} = 5 \, \text{atm L} \]

3. **Gas C:**
- Volume \( V_C = 1.25 \, \text{L} \)
- Pressure \( P_C = 2 \, \text{atm} \)
- Calculate \( PV \):
\[ PV_C = P_C \times V_C = 2 \, \text{atm} \times 1.25 \, \text{L} = 2.5 \, \text{atm L} \]

4. **Gas D:**
- Volume \( V_D = 2.5 \, \text{L} \)
- Pressure \( P_D = 2.5 \, \text{atm} \)
- Calculate \( PV \):
\[ PV_D = P_D \times V_D = 2.5 \, \text{atm} \times 2.5 \, \text{L} = 6.25 \, \text{atm L} \]

### Summary of Results:
- \( PV_A = 10 \, \text{atm L} \)
- \( PV_B = 5 \, \text{atm L} \)
- \( PV_C = 2.5 \, \text{atm L} \)
- \( PV_D = 6.25 \, \text{atm L} \)

### Conclusion:
The gas with the highest \( PV \) product is Gas A, with \( PV = 10 \, \text{atm L} \). Therefore, Gas A is kept at the highest temperature.

### Final Answer:
**Gas A is kept at the highest temperature.**