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
Aug 2, 2017

Answer:

#T_2 = 317# #"K"#

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#:

#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 #color(red)(317# #sfcolor(red)("kelvin"#.