A container with a volume of #42 L# contains a gas with a temperature of #150^o K#. If the temperature of the gas changes to #75 ^o K# without any change in pressure, what must the container's new volume be?

1 Answer
Aug 14, 2017

Answer:

#V_2 = 21# #"L"#

Explanation:

We're asked to find the final volume of a gas, given information about the temperature and volume.

To do this, we can use the temperature-volume relationship of gases, illustrated by Charles's law:

#ulbar(|stackrel(" ")(" "(T_1)/(V_1) = (T_2)/(V_2)" ")|)#

where

  • #T_1# and #T_2# are the initial and final absolute temperatures of the gas system (which must be in units of Kelvin)

  • #V_1# and #V_2# are the initial and final volumes of the gas

We know:

  • #V_1 = 42# #"L"#

  • #T_1 = 150# #"K"#

  • #V_2 = ?#

  • #T_2 = 75# #"K"#

Let's rearrange the equation to solve for the final volume*, #V_2#:

#V_2 = (T_2V_1)/(T_1)#

Plugging in known values:

#V_2 = ((75cancel("K"))(42color(white)(l)"L"))/(150cancel("K")) = color(red)(ulbar(|stackrel(" ")(" "21color(white)(l)"L"" ")|)#

The final volume of the gas container is thus #color(red)(21color(white)(l)"liters"#.