# A gas occupies 246 mL at 567.3 Torr and 24.0 °C. When the pressure is changed to 771.0 Torr, what temperature is needed to maintain the same volume?

##### 1 Answer

#### Explanation:

It's always a good idea to start with what you know.

You know that the volume of the container, which is given to you as **remain constant**. Since no mention of the number of moles of gas was made, you can safely assume that it remains **constant** as well.

This means that only temperature and pressure will change.

When *volume* and *number of moles* are kept constant, pressure and temperature have **direct relationship** - this is known as Gay Lussac's Law.

In other words, if pressure **increases**, temperature increases as well. If pressure **decreases**, temperature decreases as well.

Mathematically, this is written as

#P_1/T_1 = P_2/T_2" "# , where

In your case, you know that the pressue is *increasing* from **higher** than the initial

Plug in your values and solve for

#T_2 = P_2/P_1 * T_1#

#T_2 = (771.0color(red)(cancel(color(black)("torr"))))/(567.3color(red)(cancel(color(black)("torr")))) * 24.0^@"C" = color(green)(32.6^@"C")#

As predict, the temperature must be higher than what it initially was.