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. $\left(3.42 gL^{-1}\right)$
Topic 2
Solution:
- Volume of balloon $=\frac{4}{3} \pi r^{3}=\frac{4}{3} \times 3.14 \times\left(\frac{21}{2}\right)^{3} cm^{3}$
$$ =4847 cm^{3} \approx 4.85 L $$
Now, when volume of $H _2(g)$ in cylinder is converted into NTP volume, then
$$ \begin{aligned} \frac{p _1 V _1}{T _1} & =\frac{p _2 V _2}{T _2} \ \Rightarrow \quad \frac{20 \times 2.82}{300} & =\frac{1 \times V _2}{273}, V _2=NTP \text { volume } \ \Rightarrow \quad V _2 & =51.324 L \end{aligned} $$
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
$$
