States of Matter 1 Question 84
85. A spherical balloon of $21 \mathrm{~cm}$ diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at $20 \mathrm{~atm}$ at $27^{\circ} \mathrm{C}$. If the cylinder can hold $2.82 \mathrm{~L}$ of water, calculate the number of balloons that can be filled up.
(1987, 5M)
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Answer:
Correct Answer: 85. $\left(3.42 \mathrm{gL}^{-1}\right)$
Solution:
- Volume of balloon $=\frac{4}{3} \pi r^{3}=\frac{4}{3} \times 3.14 \times\left(\frac{21}{2}\right)^{3} \mathrm{~cm}^{3}$
$$ =4847 \mathrm{~cm}^{3} \approx 4.85 \mathrm{~L} $$
Now, when volume of $\mathrm{H}_{2}(g)$ in cylinder is converted into NTP volume, then
$$ \begin{aligned} \frac{p_{1} V_{1}}{T_{1}} & =\frac{p_{2} V_{2}}{T_{2}} \ \Rightarrow \quad \frac{20 \times 2.82}{300} & =\frac{1 \times V_{2}}{273}, V_{2}=\mathrm{NTP} \text { volume } \ \Rightarrow \quad V_{2} & =51.324 \mathrm{~L} \end{aligned} $$
Also, the cylinder will not empty completely, it will hold $2.82 \mathrm{~L}$ of $\mathrm{H}{2}(\mathrm{~g})$ when equilibrium with balloon will be established. Hence, available volume of $\mathrm{H}{2}(\mathrm{~g})$ for filling into balloon is
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