A spherical balloon of $$21$$ cm diameter is to be filled up with hydrogen at N.T.P. from a cylinder containing the gas at $$20$$ atmospheres at $$27$$ ºC. If the cylinder can hold $$2.82$$ liters of water, calculate the number of balloons that can be filled up.

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Infinity Learn · Accepted Answer

No. of balloons that can be $$filled=V$$ of $$H2$$ available V of one balloon Calculation of total volume of hydrogen in the cylinder at N.T.P.$$P1$$ $$V1$$ $$T1=P2$$ $$V2$$ $$T2P1$$ $$=$$ $$1$$ atm                      $$P2$$ $$=$$ $$20$$ atm  $$V1$$ $$=$$ ?                              $$V2$$ $$=$$ $$2.82$$ l  $$T1$$ $$=$$ $$273$$ K                      $$T2$$ $$=$$ $$273$$ $$+$$ $$27$$ $$=$$ $$300$$ ∴$$V1=20$$×$$2.82$$×$$273300$$×$$1=51.3241=51324$$ mLActual volume to be transferred into balloons $$=$$ $$51324$$ – $$2820$$ mL $$=$$ $$48504$$ mL [∵ $$2820$$ mL of $$H2$$ will remain in cylinder] Volume of one balloon $$=43$$$$π$$$$r3=43$$×$$227$$×$$2123$$∵$$r=$$ diameter $$2=$$ $$4851$$ mL $$=$$ $$4.851LNo$$. of balloons that can be filled $$up=485044851=9.999$$≈$$10$$

A spherical balloon of 21 cm diameter is to be filled up with hydrogen at N.T.P. from a cylinder containing the gas at 20 atmospheres at 27 ºC. If the cylinder can hold 2.82 liters of water, calculate the number of balloons that can be filled up.

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