Question

A balloon is filled at 27$^\circ$C and 1 atmospheric pressure by volume 500 m$^3$ helium gas. At -3$^\circ$C and 0.5 atmospheric pressure, the volume of helium gas will be ______.

• A. 500 m$^3$
• B. 700 m$^3$
• C. 900 m$^3$
• D. 1000 m$^3$

Hint:

The most common mistake in gas law problems is forgetting to convert Celsius to Kelvin. Remember, $0^\circ\text{C}$ would cause division by zero if left unconverted! Always use absolute temperature.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We use the Combined Gas Law: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$. Temperature must always be in Kelvin ($K = ^\circ C + 273$).

Step 2: Formula Application:
$P_1 = 1$ atm, $V_1 = 500$ m³, $T_1 = 27 + 273 = 300$ K.
$P_2 = 0.5$ atm, $T_2 = -3 + 273 = 270$ K.

Step 3: Explanation:
$\frac{1 \times 500}{300} = \frac{0.5 \times V_2}{270}$
$\frac{5}{3} = \frac{V_2}{540}$
$V_2 = \frac{5 \times 540}{3} = 5 \times 180 = 900$ m³.

Step 4: Final Answer:
The volume of helium gas will be 900 m³.