Question

A spherical balloon of $21cm$ diameter is to be filled up with hydrogen at STP from a cylinder containing the gas at $20atm$ at $28^{\circ }C$. If the cylinder can hold $2.82L$ 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 $=\frac{4}{3}\pi r^3$
$=\left(\frac{4}{3}\right)\left(\frac{22}{7}\right){\left(\frac{21cm}{2}\right)}^3=4851c{m}^3$
Total volume of the gas available at STP conditions is
$V=\frac{p_1{V}_1}{T_1}\times \frac{T_0}{P_0}=\frac{(20atm)(2.82L)}{(300K)}\times \left(\frac{273K}{1atm}\right)$
$=51.324L=51324c{m}^3$
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 $1atm$. At this stage, the volume of $2820c{m}^3$ of the gas will remain within the cylinder.
Hence, Volume of the gas which can be transferred to balloons will be
$=51324c{m}^3-2820c{m}^3=48504c{m}^3$
Number of balloons that can be filled up
$\frac{48504c{m}^3}{4851c{m}^3/\text{ balloon }}=10$ balloons