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

1 Answer
Simon Moore
Nov 22, 2017

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.

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