What is the resulting temperature if a sample of gas began with a temperature of 20 C, 1 liter, and 760 mmHg and now occupies 800 mL and has a pressure of 1000 mmHg?
1 Answer
Explanation:
We're asked to find the new temperature of a gas after it is subjected to changes in pressure and volume.
To do this, we can use the combined gas law:
#ulbar(stackrel(" ")(" "(P_1V_1)/(T_1) = (P_2V_2)/(T_2)" "))#
where

#P_1# is the original pressure (given as#760# #"mm Hg"# ) 
#V_1# is the original volume (given as#1# #"L"# ) 
#T_1# is the original absolute temperature, which is
#20# #""^"o""C"# #+ 273 = ul(298color(white)(l)"K"#

#P_2# is the final pressure (given as#1000# #"mm Hg"# ) 
#V_2# is the final volume (given as#800# #"mL"# #= ul(0.800color(white)(l)"L"# ) (units must be consistent, so convert this to liters) 
#T_2# is the final absolute temperature (what we're trying to find)
Let's rearrange this equation to solve for the final temperature,
#T_2 = (P_2V_2T_1)/(P_1V_1)#
Plugging in the above values:
#T_2 = ((1000cancel("mm Hg"))(0.800cancel("L"))(298color(white)(l)"K"))/((760cancel("mm Hg"))(1cancel("L"))) = color(red)(ulbar(stackrel(" ")(" "317color(white)(l)"K"" "))#
The final temperature of the gas is thus