Question

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

Answer 1

Pressure (P) = 20 atm

Temperature (T) = 300 K

Volume of the cylinder (Vc): 2.82 L of water = 2820 ${ cm }^{ 3 }$

Volume of the balloon (Vb): $4\pi { r }^{ 3 }$

Radius of balloon: $\frac { 21 }{ 2 } \quad =\quad 10.5$

Volume of balloon: $4\quad \times \quad 3.14\quad \times \quad { \left( 10.5 \right)  }^{ 3 }\quad =\quad 4851\quad { cm }^{ 3 }$

As per the STP, volume: $\frac { { P }_{ 1 }{ V }_{ 1 } }{ { T }_{ 1 } } \quad =\quad \frac { { P }_{ 2 }{ V }_{ 2 } }{ { T }_{ 2 } }$

Substituting the formula with the respective values, we have,

$\frac { 20\quad \times \quad 2820 }{ 300 } \quad =\quad \frac { 1\quad \times \quad { V }_{ 2 } }{ 273 }$

So, ${ V }_{ 2 }\quad =\quad 51324\quad { cm }^{ 3 }$

Amount of ${ H }_{ 2 }$  used to fill the balloon: ${ V }_{ 2 } - Vc = 51324 - 2820 = 48504 { cm }^{ 3 }$

So, $\frac { Volume\quad of\quad { H }_{ 2 }\quad used }{ Volume\quad of\quad the\quad balloon } \quad =\quad \frac { 4504 }{ 4851 } \quad =\quad 10$

The total number of balloons filled: 10