When a sample of gas is compressed at contant temperature from 15 atm to 60 atm, its volume changes from `76 cm^(3) " to " 20.5 cm^(3)`. Which of the following statements are possible explanation of this behaviour ?
(1) The gas behaves non-ideally
(2) The gas dimerises
(3) The gas is adsorbed into the vessel walls

Options

A. 1, 2 and 3
B. 1 and 2 only
C. 2 and 3 only
D. 1 only

Explanation

To solve the problem, we need to analyze the behavior of the gas when it is compressed from 15 atm to 60 atm, and its volume changes from 76 cm³ to 20.5 cm³. We will use the ideal gas law and the principles of gas behavior to evaluate the given statements.

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Law**:
The ideal gas law states that for a given amount of gas at constant temperature, the product of pressure (P) and volume (V) is constant. This can be expressed mathematically as:
\[ P_1 V_1 = P_2 V_2 \]
where \(P_1\) and \(V_1\) are the initial pressure and volume, and \(P_2\) and \(V_2\) are the final pressure and volume.

2. **Substituting the Known Values**:
We know:
- \(P_1 = 15 \, \text{atm}\)
- \(V_1 = 76 \, \text{cm}^3\)
- \(P_2 = 60 \, \text{atm}\)
- \(V_2\) is what we need to find.

Plugging these values into the equation:
\[ 15 \times 76 = 60 \times V_2 \]

3. **Calculating the Ideal Volume \(V_2\)**:
Rearranging the equation to solve for \(V_2\):
\[ V_2 = \frac{15 \times 76}{60} \]
\[ V_2 = \frac{1140}{60} = 19 \, \text{cm}^3 \]

4. **Comparing the Ideal Volume to the Observed Volume**:
The calculated ideal volume \(V_2\) is 19 cm³, while the observed volume is 20.5 cm³. This indicates that the observed volume is greater than the ideal volume.

5. **Analyzing the Statements**:
- **Statement (1)**: The gas behaves non-ideally. This is true because the observed volume (20.5 cm³) is greater than the ideal volume (19 cm³). This suggests that the gas does not follow the ideal gas law perfectly.
- **Statement (2)**: The gas dimerizes. This is false because dimerization would typically lead to a decrease in volume, not an increase.
- **Statement (3)**: The gas is adsorbed into the vessel walls. This is also false because adsorption would lead to a decrease in the volume of gas in the container.

6. **Conclusion**:
The only correct explanation for the observed behavior of the gas is that it behaves non-ideally.

### Final Answer:
The correct statement is (1) The gas behaves non-ideally.