Question

A spherical balloon of $21cm$ diameter is to be filled up with $H_2$ at NTP from a cylinder containing the gas at $20atm$ at ${27}^{\circ }C$. The cylinder can hold $2.82$ litre of water. The number of balloons that can be filled up is :

• A. $11$
• B. $10$
• C. $8$
• D. $1$

Answer 1

Answer: (B)

$10$

The volume of balloon = 4.851 L (GIVEN)

NOW,

Let no. of the balloon to be filled n

Total volume occupied by n balloons $=4.851\times n$

Volume of $H_2$ present in cylinder = 2.82 L (GIVEN)

→Total volume of $H_2$ at NTP $=(4.851\times n+2.82)L$

SINCE,$P_1=1atm$

$P_2=20atm$

$V_1=(4.85\times n)+2.82L$

$V_2=2.82L$

$T_1=273K$

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

$1\times \frac{(4.85\times n+2.82)}{273}=\frac{(20\times 2.82)}{300}$

$\therefore n=\frac{48.504}{4.851}=10$ balloons.

Hence, the correct option is $\text{B}$