# Question #fe72d

##### 1 Answer

#### Explanation:

*Pressure* and *volume* have an **inverse relationship** when temperature and number of moles of gas are **kept constant** - this is known as **Boyle's Law**.

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

When you **increase** the volume of gas while keeping the *average kinetic speed* of its molecules, i.e. the temperature, **constant**, you essentially reduce the **frequency** with which the gas particles collide with the walls of the container.

Since the molecules are not hitting the walls of the container *as often* as they did before you increased the volume, you can say that the pressure will **decrease**.

So, when volume **increases**, pressure **decreases**, and when volume **decreases**, pressure **increases**.

Mathematically, this is written as

#color(blue)(|bar(ul(color(white)(a/a)P_1V_1 = P_2V_2color(white)(a/a)|)))" "# , where

Rearrange the equation to solve for

#P_1V_1 = P_2V_2 implies P_2 = V_1/V_2 * P_1#

Plug in your values to get

#P_2 = (2.00color(red)(cancel(color(black)("L"))))/(3.00color(red)(cancel(color(black)("L")))) * "761 mmHg" = "507.33 mmHg"#

Rounded to two **sig figs**, the number of sig figs you have for the final volume of the gas, the answer will be

#P_2 = color(green)(|bar(ul(color(white)(a/a)"510 mmHg"color(white)(a/a)|)))#

As predicted by Boyle's Law, an **increase** in volume resulted in a **decrease** in pressure.