JEE Advance - Chemistry (1987 - No. 11)
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 27oC. If the cylinder can hold 2.82 litres of water, calculate the number of balloons that can be filled up.
คำตอบ
10
คำอธิบาย
Let V1 be the volume of H2 in the cylinder at NTP. According to gas equation,
$${{{P_1}{V_1}} \over {{T_1}}} = {{{P_2}{V_2}} \over {{T_2}}}$$
$$\therefore$$ $${{1 \times {V_1}} \over {273}} = {{20 \times 2.82} \over {300}}$$
or $${V_1} = {{20 \times 2.82 \times 273} \over {300}}$$
= 51.324 L = 51324 mL
Volume of H2 left in the cylinder = Volume of cylinder = 2820 mL
Actual volume transferred to balloons
= 51324 $$-$$ 2820 = 48504 mL
Radius of balloon (r) = 21/2 = 10.5 cm
Volume of each balloon = $${4 \over 3}\pi {r^3}$$
$$ = {4 \over 3} \times 3.142 \times {(10.5)^3}$$
$$ = 4849.67 = 4850$$ mL
Number of balloons which can be filled up
$$ = {{48504} \over {4850}} = 10$$