A 1 mol gas occupies 2.4L volume at `27^(@)` C and 10 atm pressure
then it show :-

Options

A. `+"ve deviation"`
B. `"-ve deviation"`
C. Ideal behaviour
D. None of these

Answer

To solve the problem, we need to determine the compressibility factor (Z) of the gas using the formula:

\[ Z = \frac{PV}{nRT} \]

Where:
- \( P \) = pressure of the gas (in atm)
- \( V \) = volume of the gas (in liters)
- \( n \) = number of moles of the gas
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol) or 8.314 J/(K·mol))
- \( T \) = temperature of the gas (in Kelvin)

### Step-by-Step Solution:

1. **Identify Given Values:**
- Number of moles \( n = 1 \) mol
- Volume \( V = 2.4 \) L
- Pressure \( P = 10 \) atm
- Temperature \( T = 27^\circ C \)

2. **Convert Temperature to Kelvin:**
\[ T(K) = 27 + 273 = 300 \, K \]

3. **Use the Ideal Gas Constant:**
- We will use \( R = 0.0821 \, L \cdot atm/(K \cdot mol) \).

4. **Substitute Values into the Z Formula:**
\[ Z = \frac{PV}{nRT} = \frac{(10 \, atm)(2.4 \, L)}{(1 \, mol)(0.0821 \, L \cdot atm/(K \cdot mol))(300 \, K)} \]

5. **Calculate the Denominator:**
\[ nRT = (1)(0.0821)(300) = 24.63 \, L \cdot atm \]

6. **Calculate Z:**
\[ Z = \frac{24}{24.63} \approx 0.974 \]

7. **Determine the Deviation:**
- Since \( Z < 1 \), the gas shows a **negative deviation** from ideal behavior.

### Final Answer:
The gas shows a **negative deviation** from ideal behavior.