Question

A spherical balloon is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atm and ${27}^{\circ }C$. If the cylinder can hold 8.21 litres of water and one balloon can contain maximum of 0.3165 moles of hydrogen, then the number of balloons that can be filled up are : (Summed upto the nearest integer)

• A. $11$
• B. $6$
• C. $20$
• D. $31$

Answer 1

The correct option is C $20$

No. of moles of $H_2$, the balloon can contain is $0.3165mol$
Cylinder is at 300 K and 20 atm.
No. of moles of $H_2$ in the cylinder $=\frac{20atm\times 8.21L}{0.0821L.atm{K}^{-1}mo{l}^{-1}\times 300K}$
$=6.66mol$
While filling the last balloon, when the pressure of the cylinder will drop to 1 atm, gas cannot be withdrawn.
Now, no. of moles of $H_2$ remaining in the cylinder unused
$=\frac{1atm\times 8.21L}{0.0821L.atm{K}^{-1}mo{l}^{-1}\times 300K}=0.33mol$
$\therefore$ No. of balloons that can be filled
$=\frac{\text{no. of moles of}{H}_2\text{in the cylinder that can be used}}{\text{no. of moles of}{H}_2\text{one balloon can contain}}$
$=\frac{6.66-0.33}{0.3165}=20$