# A given mass of oxygen at room temperature occupies a volume of 500.0 mL at 1.50 atm pressure. What pressure must be applied to compress the gas to a volume of only 150.0 mL?

##### 1 Answer

#### Explanation:

The idea here is that *pressure* and *volume* have an **inverse relationship** when temperature and number of moles are kept constant, as described by **Boyle's Law**.

This implies that **decreasing** the pressure by a given factor, let's say **increase** by the **same factor**

Similarly, **increasing** the pressure by a factor **decrease** by the same factor

In your case, the volume decreases by a factor of

#(500.0color(red)(cancel(color(black)("mL"))))/(150.0color(red)(cancel(color(black)("mL")))) = color(blue)(10/3)#

This means that the pressure of the gas **increased** by a factor of

#P_"final" = color(blue)(10/3) * "1.50 atm" = color(green)(|bar(ul(color(white)(a/a)color(black)("5.00 atm")color(white)(a/a)|)))#

The answer is rounded to three **sig figs**, the number of sig figs you have for the initial pressure of the gas.