States of Matter - Result Question 84
85. A spherical balloon of $21 cm$ diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at $20 atm$ at $27^{\circ} C$. If the cylinder can hold $2.82 L$ of water, calculate the number of balloons that can be filled up.
(1987, 5M)
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Answer:
Correct Answer: 85. (10)
Solution:
Volume of balloon $=\dfrac{4}{3} \pi r^{3}=\dfrac{4}{3} \times 3.14 \times\left(\dfrac{21}{2}\right)^{3} cm^{3}$
$ =4847 cm^{3} \approx 4.85 L $
Now, when volume of $H _2(g)$ in cylinder is converted into NTP volume, then
$\dfrac{p _1 V _1}{T _1} =\dfrac{p _2 V _2}{T _2}$
$\Rightarrow \quad \dfrac{20 \times 2.82}{300} =\dfrac{1 \times V _2}{273}, V _2=NTP \text { volume } $
$\Rightarrow \quad V _2 =51.324 L$
Also, the cylinder will not empty completely, it will hold $2.82 L$ of $H _2(g)$ when equilibrium with balloon will be established. Hence, available volume of $H _2(g)$ for filling into balloon is
$\begin{gathered}51.324-2.82=48.504 \mathrm{~L} \\ \Rightarrow \text { Number of balloons that can be filled }=\frac{48.504}{4.85}=10\end{gathered}$
BETA
