500 mL of nitrogen at `27^(@)C` is cooled to `-5^(@)C` at the same pressure. The new volume becomes

Options

A. 326.32 mL
B. 446.66 mL
C. 546.32 mL
D. 771.56 mL

Explanation

To find the new volume of nitrogen gas when it is cooled from `27°C` to `-5°C` at constant pressure, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure is constant.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial volume, \( V_1 = 500 \, \text{mL} \)
- Initial temperature, \( T_1 = 27°C \)
- Final temperature, \( T_2 = -5°C \)

2. **Convert Temperatures from Celsius to Kelvin:**
- To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273 \]
- For \( T_1 \):
\[ T_1 = 27 + 273 = 300 \, K \]
- For \( T_2 \):
\[ T_2 = -5 + 273 = 268 \, K \]

3. **Apply Charles's Law:**
- According to Charles's Law:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
- Rearranging for \( V_2 \):
\[ V_2 = V_1 \times \frac{T_2}{T_1} \]

4. **Substitute the Known Values:**
- Plugging in the values:
\[ V_2 = 500 \, \text{mL} \times \frac{268 \, K}{300 \, K} \]

5. **Calculate \( V_2 \):**
- Performing the calculation:
\[ V_2 = 500 \times \frac{268}{300} = 500 \times 0.8933 \approx 446.66 \, \text{mL} \]

6. **Final Answer:**
- The new volume of nitrogen gas when cooled to `-5°C` is approximately \( 446.66 \, \text{mL} \).

### Summary of the Steps:
- Convert temperatures from Celsius to Kelvin.
- Use Charles's Law to relate the initial and final volumes and temperatures.
- Substitute the values and calculate the new volume.