A container has a volume of #21 L# and holds #24 mol# of gas. If the container is compressed such that its new volume is #12 L#, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

1 Answer
Oct 25, 2016

Answer:

The amount of gas that needs to be released to maintain constant pressure and temperature is #"10 mol"#.

Explanation:

This is an example of Avogadro's law, which states that the volume of a gas is directly proportional to the amount in moles (n), as long as the pressure and temperature are kept constant. The proportion #V/n=C# (a constant) means that #V_1/n_1=V_2/n_2=V_3/n_3#, etc... .

Since there are only two sets of data, the equation to use is #V_1/n_1=V_2/n_2#, where #V_1# is the initial volume, #n_1# is the original amount in moles, #V_2# is the final volume, and #n_2# is the final amount in moles.

Given
#V_1="21 L"#
#n_1="24 mol"#
#V_2="12 L"#

Unknown
#n_2#

Solution
Rearrange the equation to isolate #n_2#. Substitute the given values into the equation and solve.

#n_2=(V_2xxn_1)/(V_1)#

#n_2=(12"L"xx24"mol")/(21"L")="14 mol"#

The amount of gas that must be released to maintain constant pressure and temperature is #n_1-n_2#.

#"24 mol"-"14 mol"="10 mol"#