Question

A cylindrical balloon of $21$ cm diameter is to be filled up with $H_2$ at $NTP$ from a cylinder containing the gas at $20$ atm at $27°C$. The cylinder can hold $2.82$ litres of water at $NTP$.

Calculate the number of balloons that can be filled up.

• A. $14$
• B. $40$
• C. $17$
• D. $10$

Answer 1

Answer: (D)

$10$

Given:
d= 21 cm $\Rightarrow$ r= 21/2 cm

Volume of 1 balloon which has to be filled

$=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (\frac{21}{2}{)}^3=4846.6mL=4.85L$

Let $n$ balloons be filled, then volume of $H_2$ occupied by balloons $=4.851\times n$

Also, cylinder will not be empty and it will occupy volume of $H_2=2.82$ litre.

∴ Total volume occupied by $H_2$ at NTP $=4.851\times n+2.82$ litre

∴ At STP $P_1=1$ atm Available $H_2$ $V_1=4.851\times n+2.82$

$P_2=20$ atm $T_1=293K;T_2=300K$

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

$V_2=2.82$ litre

Substituting, $1\times \left(\frac{4.851n+2.82}{293}\right)=20\times \frac{2.82}{300}$

$\therefore n=10$ so number of balloons that can be filled up = 10
Option D is correct answer.