Question

A spherical balloon of $21 \,cm$ diameter is to be filled up with hydrogen at STP from a cylinder containing the gas at $20\, atm$ at $28^{\circ} C$. If the cylinder can hold $2.82 \,L$ of water, the number of balloons that can be filled up are

• A. 5
• B. 7
• C. 9
• D. 10

Answer 1

Answer: (D)

We have,
Volume of balloon $=\frac{4}{3} \pi r^3$
$=\left(\frac{4}{3}\right)\left(\frac{22}{7}\right)\left(\frac{21 cm }{2}\right)^3=4851 \,cm ^3$
Total volume of the gas available at STP conditions is
$V=\frac{p_1 V_1}{T_1} \times \frac{T_0}{P_0}=\frac{(20 \,atm )(2.82\, L )}{(300\, K )} \times\left(\frac{273 K }{1 atm }\right)$
$=51.324 \,L =51324 c\,m ^3$
When the balloons are being filled, the pressure in the cylinder will decrease. We can continue filling from the cylinder till the pressure within the cylinder is also $1 \,atm$. At this stage, the volume of $2820\,cm ^3$ of the gas will remain within the cylinder.
Hence, Volume of the gas which can be transferred to balloons will be
$=51324\, cm ^3-2820 \,cm ^3=48504\, cm ^3$
Number of balloons that can be filled up
$\frac{48504 \,cm ^3}{4851 \,cm ^3 / \text { balloon }}=10$ balloons