## Pressure of Butane in a Gas Bottle

When butane gas is pumped into a metal bottle, it is compressed greatly, normally so that 1.67 litres contains 1kg of gas. We can use this to work out the pressure at which the butane is stored.The empirical formula for butane is

\[C_4H_{10}\]

, so that 1 mol of butane has a mass of \[12 \times 4 +1 \times 10=58 \; g = 0.058 \; kg\]

In 15 kg butane there are

\[\frac{15}{0.058} = 258.6 \: mol\]

A 15 kg butane bottle contains 15 kg butane, so \[15 \times 1.67 \: litres = 25 \times 10^{-3} m^3\]

Take the temperature as

\[25^{\circ} C \equiv 298^{\circ} K\]

Now use the ideal gas equation

\[pV=nRT\]

\[p= \frac{nRT}{V} = \frac{258.6 \times 8.314 \times 298}{25 \times 10^{-3}} = 2.563 \times 10^7 Pa\]

Atmospheric pressure is about

\[10^5 \; Pa\]

so this is equivalent to about \[\frac{2.568 \times 10^7}{10^5} = 256.8 \]

times atmospheric pressure.