Question

A balloon blown with 1 mol of a gas, has a volume of 480 ml at $5^{\circ }C$. If the balloon is filled to $\frac{7}{8}$ 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 ${47.71}^{\circ }C$
• D. The pressure of gas when balloon burst at 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 ${47.71}^{\circ }C$

Max capacity of balloon $=\frac{8}{7}\times 480=548.57ml$

Also, $V_1=480ml,T_1=278K,n=1mol$

$\because \frac{V_1}{T_1}=\frac{V_2}{T_2}$

$\Rightarrow \frac{480}{278}=\frac{548.57}{T_2}$

$\Rightarrow T_2=317.71K={44.71}^{\circ }C$

From $PV=nRT$

$P\times \frac{480}{1000}=1\times 0.0821\times 278$

$\Rightarrow P=47.5atm$