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A spherical balloon of 21 CM diameter to be filled with hydrogen gas at NTP from a cylinder containing a gas containing a gas 20 atm at 300K. The cylinder can hold 2.82 litre of water at ntp .Calculate the number of balloons that can be filled up.

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2 years ago

```							Dear Avanish No. of balloons that can be filled = V of H2available/V of one balloonCalculation of total volume of hydrogen in the cylinder at N.T.PP1V1/T1 = PV2/T2P1 = 1 atm P2 = 20 atmV1 = ? V2 = 2.82 lT1 = 23 K T2 = 273 + 27 = 300 K∴ V1 = 20 * 2.82 * 273/300 * 1 = 51.324 l = 51324 mlActual volume to be transferred into balloons= 51324 – 2820 ml = 48504 ml[∵ 2820 ml of H2 will remain in cylinder]No. of balloons that can be filled up -= 48504/4851 = 9.999 = 10Volume of one balloon = 4/3 πr3 = 4/3 * 22/7 * (21/2)3[∵ r = diameter/2]= 4851 ml = 4.851LALTERNATESOLUTIONVolume of balloon = 4.851 L (as calculate above)Let no. of balloon to be filled n∴ Total volume occupied by n balloons = 4.851 * nVolume of H2 present in cylinder = 2.82 L (given)∴ Total volume of H2 at NTP = (4.851n + .82)LP1 = 1 atm P2 = 20 atmV1 = 4.85 * n + 2.82 L V2 = 2.82 LT1 = 273 KP1V1/T1 = P2V2/T2or 1 * (4.85 * n + 2.82)/273 = 20 * 2.82/300∴n = 48.504/4.851 = 10 RegardsArun, (askIITians Forum Expert) If you find the solution correct then please approve it & in case of any confusion further please do feel free to write me here. I would be more than happy to help further
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2 years ago
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