What will be the new volume when 128ml of gas at `20.0^@c` is heated to `40^@c` while presuure remains unchanged?

Options

A. 64.0mL
B. 120mL
C. 128mL
D. 137mL

Answer

To find the new volume of the gas when heated from 20.0°C to 40.0°C while keeping the pressure constant, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin, provided the pressure remains constant.

### Step-by-Step Solution:

1. **Identify the Initial Conditions:**
- Initial volume (V1) = 128 ml
- Initial temperature (T1) = 20.0°C

2. **Convert Temperature to Kelvin:**
- To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273.15 \]
- For T1:
\[ T1 = 20.0 + 273.15 = 293.15 \text{ K} \]

3. **Identify the Final Conditions:**
- Final temperature (T2) = 40.0°C

4. **Convert Final Temperature to Kelvin:**
- For T2:
\[ T2 = 40.0 + 273.15 = 313.15 \text{ K} \]

5. **Apply Charles's Law:**
- According to Charles's Law:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]
- Rearranging to find V2:
\[ V2 = V1 \times \frac{T2}{T1} \]

6. **Substitute the Known Values:**
- Substitute V1, T1, and T2 into the equation:
\[ V2 = 128 \text{ ml} \times \frac{313.15 \text{ K}}{293.15 \text{ K}} \]

7. **Calculate V2:**
- Perform the calculation:
\[ V2 = 128 \times \frac{313.15}{293.15} \approx 137.0 \text{ ml} \]

8. **Conclusion:**
- The new volume (V2) when the gas is heated to 40.0°C is approximately **137 ml**.