Question

A balloon blown with 1 mole of a gas, has a volume of 480 mL at $5^{\circ }$ C. If the balloon is filled to ${\frac{8}{7}}^{th}$ of its maximum capacity, then which of the following is/ are correct?

• A. The balloon will burst at ${30}^{\circ }C$
• B. The pressure of the gas inside the balloon at $5^{\circ }C$ is 47.5 atm
• C. The minimum temperature at which the balloon will burst is ${44.71}^{\circ }C$
• D. The pressure of the gas when the balloon bursts at the minimum temperature is 50 atm.

Answer 1

Answer: (B), (C)

The correct options are
B The pressure of the gas inside the balloon at $5^{\circ }C$ is 47.5 atm
C The minimum temperature at which the balloon will burst is ${44.71}^{\circ }C$

Max capacity of balloon $=\frac{8}{7}\times 480=548.57mL$
$Also,V_1=480mL,T_1=278K,n=1mol$
$\ast )\frac{V_1}{T_1}=\frac{V_2}{T_2}\Rightarrow \frac{480}{278}=\frac{548.57}{T_2}$
$T_2=317.71={44.71}^{\circ }C$
$\ast )FromPV=nRT$
$P\times \frac{480}{1000}=1\times 0.0821\times 278$
$=47.5atm$