States of Matter - Result Question 85
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 $27^{\circ} \mathrm{C}$. If the cylinder can hold 2.82 L of water, calculate the number of balloons that can be filled up.
(1987, 5M)
Show Answer
Answer:
Correct Answer: 85. (10)
Solution:
Volume of balloon $=\dfrac{4}{3} \pi r^3=\dfrac{4}{3} \times 3.14 \times\left(\dfrac{21}{2}\right)^3 \mathrm{~cm}^3$ $$ =4847 \mathrm{~cm}^3 \approx 4.85 \mathrm{~L} $$
Now, when volume of $\mathrm{H}_2(\mathrm{~g})$ in cylinder is converted into NTP volume, then $$ \begin{aligned} & \dfrac{p_1 V_1}{T_1}=\dfrac{p_2 V_2}{T_2} \\ & \Rightarrow \quad \dfrac{20 \times 2.82}{300}=\dfrac{1 \times V_2}{273}, V_2=\mathrm{NTP} \text { volume } \\ & \Rightarrow \quad V_2=51.324 \mathrm{~L} \\ & \end{aligned} $$
Also, the cylinder will not empty completely, it will hold 2.82 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
$$ 51.324-2.82=48.504 \mathrm{~L} $$
$\Rightarrow$ Number of balloons that can be filled $=\dfrac{48.504}{4.85}=10$
BETA
