Question

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?

Answer 1

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