A gas is held at 3.8 atm and 500 K. If the pressure is then decreased to 1.2 atm, what will the new temperature be?

1 Answer
Mar 18, 2017

Answer:

The final temperature will be #~~200color(white)(.)"K"#.

Explanation:

This question involves Gay-Lussac's law to answer, which states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.

This means that as the pressure goes up, the temperature also goes up, and vice-versa.

The equation to use is:

#P_1/(T_1)=P_2/(T_2)#,

where #P# is pressure in atm, and #T# is temperature in Kelvins.

Given/Known Information
#P_1="3.8 atm"#
#T_2="500 K"#
#P_2="1.2 atm"#

Unknown: #T_2#

Solution
Rearrange the equation to isolate #T_2#.

#T_2=(P_2T_1)/(P_1)#

#T_2=(1.2color(red)cancel(color(black)("atm"))xx500 "K")/(3.8color(red)cancel(color(black)("atm")))~~"200 K"# rounded to 1 significant figure