Question

# A spherical balloon of 21cm diameter is to be filled up with H2 at NTP from a cylinder containing the gas at 20atm at 27oC. The cylinder can hold 2.82 liter of water. The number of balloons that can be filled up will be:

A
11
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B
10
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C
8
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D
1
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Solution

## The correct option is B 10The total volume of hydrogen in the cylinder at N.T.P can be calculated as:P1V1T1=P2V2T2Here,P1 = 1 atm P2 = 20 atmand V2= 2.82 lT1 = 23 K T2 = 273 + 27 = 300 K∴ V1 = 20 * 2.82 * 273/300 * 1 = 51.324 l = 51324 ml.Actual volume to be transferred into balloons = 51324 – 2820 ml = 48504 mlNumber of balloons that can be filled up,485044850 = 9.99 =10The Volume of one balloon can be calculated as 43πr343×227×(212)3 = 4851 ml = 4.851Lby using this volume value,The volume of balloon = 4.851 L taking a number of balloons to be filled = n∴ Total volume occupied by n balloons = 4.185×5Volume of H2 present in cylinder = 2.82 L (given)∴ Total volume ofH2 at NTP = (4.851n + .82)LP2= 20atm P1= 1atmV1 = 4.85× n + 2.82 LV2 = 2.82 LT1 = 273 KP1V1T1=P2V2T2∴ n = 48.504/4.851 =10Hence, 10 is the answer.

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