A-spherical-balloon-of-21-cm-diameter-is-to-be-filled-with-hydrogen-at-NTP-from-a-cylinder-containing-the-gas-at-20-atmosphere-at-27-C-If-the-cylinder-can-hold-2-82-litres-of-water-calculate-the-num

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Question Number 16081 by Tinkutara last updated on 17/Jun/17

$$\mathrm{A}\mathrm{spherical}\mathrm{balloon}\mathrm{of}21\mathrm{cm}\mathrm{diameter}$$$$\mathrm{is}\mathrm{to}\mathrm{be}\mathrm{filled}\mathrm{with}\mathrm{hydrogen}\mathrm{at}\mathrm{NTP}$$$$\mathrm{from}\mathrm{a}\mathrm{cylinder}\mathrm{containing}\mathrm{the}\mathrm{gas}\mathrm{at}$$$$20\mathrm{atmosphere}\mathrm{at}27°\mathrm{C}.\mathrm{If}\mathrm{the}\mathrm{cylinder}$$$$\mathrm{can}\mathrm{hold}2.82\mathrm{litres}\mathrm{of}\mathrm{water},\mathrm{calculate}$$$$\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{balloons}\mathrm{that}\mathrm{can}\mathrm{be}$$$$\mathrm{filled}\mathrm{up}.$$

Answered by mrW1 last updated on 18/Jun/17

$$\mathrm{volume}\mathrm{of}\mathrm{ballon}$$$${\mathrm{V}}_{\mathrm{b}}=\frac{\pi {\mathrm{d}}^3}{6}=\frac{\pi \times {21}^3}{6}=4849{\mathrm{cm}}^3$$$$$$$$\mathrm{volume}\mathrm{of}\mathrm{gas}\mathrm{at}1\mathrm{atomospere}\mathrm{and}\mathrm{NTP}$$$${\mathrm{V}}_{\mathrm{g}}=\frac{20+273}{27+273}\times \frac{20}{1}\times 2.82\times 1000=55084{\mathrm{cm}}^3$$$$$$$$\mathrm{number}\mathrm{of}\mathrm{ballons}$$$$\mathrm{n}=\lfloor \frac{{\mathrm{V}}_{\mathrm{g}}}{{\mathrm{V}}_{\mathrm{b}}}\rfloor =\lfloor \frac{55084}{4849}\rfloor =\lfloor 11.3\rfloor =11$$

Commented by mrW1 last updated on 18/Jun/17

$$\mathrm{I}\mathrm{corrected}\mathrm{my}\mathrm{answer},\mathrm{but}\mathrm{the}\mathrm{result}$$$$\mathrm{is}\mathrm{still}11.$$

Answered by Tinkutara last updated on 02/Sep/17

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