Question

A certain sample of gas has a volume of \(0.2\ \text{L}\) at one atmosphere pressure and \(273.15\ \text{K}\). What is the volume of gas at \(273.15^\circ\text{C}\) at the same pressure?

• A. 2.703 L
• B. 0.2 L
• C. 0.4 L
• D. 5.406 L

Hint:

At constant pressure, gas volume is directly proportional to absolute temperature (Charles’ law).

Answer 1

The Correct Option is C

Step 1: Convert temperature into Kelvin.
\[ 273.15^\circ\text{C} = 273.15 + 273.15 = 546.3\ \text{K} \]

Step 2: Apply Charles’ law.
At constant pressure: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

Step 3: Substitute given values.
\[ \frac{0.2}{273.15} = \frac{V_2}{546.3} \]

Step 4: Solve for \(V_2\).
\[ V_2 = 0.2 \times \frac{546.3}{273.15} = 0.4\ \text{L} \]

Step 5: Conclusion.
The volume of the gas at \(273.15^\circ\text{C}\) is \(0.4\ \text{L}\).