# A gas at a constant volume has an initial temperature of 300.0 K and an initial pressure of 10.0 atm. What pressure does the gas exert at a temperature of 500.0 K?

##### 1 Answer

#### Explanation:

As you know, gas pressure is caused by the collisions between the gas molecules and the walls of the container.

The **more powerful and frequent** these collisions are, the **higher** the pressure exerted by the gas.

Now, temperature is actually a measure of the *average kinetic speed* of the gas molecules. This means that **increasing** the temperature of a gas is equivalent to **increasing** the average kinetic energy of its molecules.

When volume and number of moles of gas are **kept constant**, *increasing* the temperature of the gas will result in an **increase** in pressure - this is known as **Gay Lussac's Law**.

This happens because if the molecules are moving at a *higher* average kinetic energy, they will hit the walls of the container with **more force** and **more frequent** **increase**.

Mathematically, this is written as

#color(blue)(|bar(ul( color(white)(a/a)P_1/T_1 = P_2/T_2color(white)(a/a)|)))" "# , where

It's **very important** to remember that the temperature of the gas **must** be expressed in *Kelvin*!

So, rearrange the equation to solve for

#P_2 = T_2/T_1 * P_1#

Plug in your values to find

#P_2 = (500.0 color(red)(cancel(color(black)("K"))))/(300.0color(red)(cancel(color(black)("K")))) * "10.0 atm" = "16.667 atm"#

Rounded to three **sig figs**, the number of sig figs you have for the initial pressure of the gas, the answer will be

#P_2 = color(green)(|bar(ul(color(white)(a/a)"16.7 atm"color(white)(a/a)|)))#