325 mg of gas has a volume of `0.5dm^(3)` at `-10^(@)C` and 1 bar pressure. What will be the volume of the gas at `10^(@)C` at the same pressure?

Explanation

To solve the problem, we will use Charles's Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure is held constant.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Mass of gas = 325 mg (not needed for the calculation since pressure and volume are constant)
- Initial volume (V1) = 0.5 dm³
- Initial temperature (T1) = -10°C
- Final temperature (T2) = 10°C
- Pressure is constant.

2. **Convert Temperatures to Kelvin:**
- T1 = -10°C + 273 = 263 K
- T2 = 10°C + 273 = 283 K

3. **Use Charles's Law:**
- According to Charles's Law:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]
- Rearranging gives us:
\[ V2 = V1 \times \frac{T2}{T1} \]

4. **Substitute Known Values:**
- Substitute V1, T1, and T2 into the equation:
\[ V2 = 0.5 \, \text{dm}^3 \times \frac{283 \, \text{K}}{263 \, \text{K}} \]

5. **Calculate V2:**
- Perform the calculation:
\[ V2 = 0.5 \times \frac{283}{263} \approx 0.5 \times 1.0757 \approx 0.538 \, \text{dm}^3 \]

6. **Final Answer:**
- The volume of the gas at 10°C and 1 bar pressure is approximately **0.538 dm³**.