# A gas occupies 3 litres at 0°C. what volume will it occupy at -20°C, assuming pressure remaining constant?

Nov 22, 2017

2.78 litres

#### Explanation:

If you treat it as an ideal gas, then $P V = n R T$ where P is pressure, V is volume, n is number of moles, R is the gas constant and T is temperature in K.

If you assume pressure is constant, and we know that the amount of substance will remain constant, and of course the gas constant is a constant, then $V$ varies directly with $T$. So for the two temperatures you can say:

${V}_{1.} {T}_{1} = {V}_{2.} {T}_{2}$
${V}_{2} = \frac{{V}_{1.} {T}_{1}}{{T}_{2}}$

${T}_{2}$, the higher of the two temperatures, will be 273 K and ${T}_{1}$ will be 20 degrees lower, so 253 K.

Now plug in the numbers:

${V}_{2} = \frac{3 . 253}{273} = 2.78$ litres.