A gas takes up a volume of 19.5 liters, has a pressure of 2.9 atm, and a temperature of 5.5°C. If I raise the temperature to 65°C and lower the pressure to 1.5 atm, what is the new volume of the gas?

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Answer 1 · 2016-02-01T19:33:37

#V_2=45.8L#

From the ideal gas law #PV=nRT# we can conclude that #n=(PV)/(RT)#.

If the pressure #P#, the volume #V# and the temperature #T# of the gas change between two points, this change can be illustrated by:

#n=(P_1V_1)/(RT_1)=(P_2V_2)/(RT_2)#

Therefore, this expression can be modified as:

#(P_1V_1)/(cancel(R)T_1)=(P_2V_2)/(cancel(R)T_2)=>(P_1V_1)/(T_1)=(P_2V_2)/(T_2)#

Thus, #V_2=(P_1V_1)/(T_1)xx(T_2)/(P_2)#

#V_2=(2.9cancel(atm)xx19.5L)/(278.5cancel(K))xx(338cancel(K))/(1.5cancel(atm))=45.8L#