A given mass of gas occupies `4.5dm^(3)` at 1.2 bar pressure. Calculate the change in volume of the gas at the same temperature if pressure of the gas is changed to 1.8 bar.

Explanation

To solve the problem of calculating the change in volume of a gas when its pressure changes, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. This can be expressed mathematically as:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial volume, \( V_1 = 4.5 \, \text{dm}^3 \)
- Initial pressure, \( P_1 = 1.2 \, \text{bar} \)
- Final pressure, \( P_2 = 1.8 \, \text{bar} \)

2. **Use Boyle's Law to find the final volume \( V_2 \):**
\[ P_1 V_1 = P_2 V_2 \]
Rearranging the equation to solve for \( V_2 \):
\[ V_2 = \frac{P_1 V_1}{P_2} \]

3. **Substitute the known values into the equation:**
\[ V_2 = \frac{(1.2 \, \text{bar}) \times (4.5 \, \text{dm}^3)}{1.8 \, \text{bar}} \]

4. **Calculate \( V_2 \):**
\[ V_2 = \frac{5.4 \, \text{bar} \cdot \text{dm}^3}{1.8 \, \text{bar}} = 3.0 \, \text{dm}^3 \]

5. **Calculate the change in volume:**
\[ \text{Change in Volume} = V_1 - V_2 \]
\[ \text{Change in Volume} = 4.5 \, \text{dm}^3 - 3.0 \, \text{dm}^3 = 1.5 \, \text{dm}^3 \]

### Final Answer:
The change in volume of the gas is \( 1.5 \, \text{dm}^3 \).