# A flask containing 155 #cm^3# of hydrogen was collected under a pressure of 22.5 #kPa#. What pressure would have been required for the volume of the gas to have been 90.0 #cm^3#, assuming the same temperature?

##### 1 Answer

#### Explanation:

Before doing any calculations, try to predict what you expect the required pressure to be *relative* to the given pressure of

As you know, *pressure* and *volume* have an **inverse relationship** when temperature and number of moles are **kept constant** - this is known as Boyle's Law.

Simply put, when volume **increases**, the pressure exerted by the gas molecules **decreases**. Likewise, when volume **decreases**, the pressure exerted by the gas molecules **increases**.

In your case, you want to know what pressure would have resulted in a **smaller** volume of hydrogen gas. Well, in order for the volume to be smaller, you'd need to have a **higher** pressure.

You can thus expect the required pressure to be **lower** than the given

Mathematically, Boyle's Law is expressed like this

#color(blue)(P_1V_1 = P_2V_2)" "# , where

Rearrange the equation to solve for

#P_2 = V_1/V_2 * P_1#

Plug in your values to get

#P_2 = (155 color(red)(cancel(color(black)("cm"^3))))/(90.0color(red)(cancel(color(black)("cm"^3)))) * "22.5 kPa" = color(green)("38.8 kPa")#

The answer is rounded to three sig figs.

So, **the same** number of moles of hydrogen gas kept **at the same temperature** will occupy a volume of