Question

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

Answer 1

2.78 litres

Explanation:

If you treat it as an ideal gas, then `PV=nRT` 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 = (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 = (3 . 253)/(273) = 2.78` litres.