# Question #d794a

##### 1 Answer

#### Answer:

#### Explanation:

The problem wants to test if you're familiar with the fact that the **pressure** and **volume** of a gas have an **inverse relationship** when temperature and number of moles are kept *constant*, as described by **Boyle's Law**.

Simply put, when temperature and number of moles of gas, which essentially means that *quantity* of gas, are kept constant, **increasing** the pressure will cause a **decrease** in volume.

Similarly, **decreasing** the pressure will cause an **increase** in volume.

Mathematically, you can express this relationship as

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

In your case, the pressure of the gas is **increasing** from **smaller** than

You will thus have

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

Plug in your values to find

#V_2 = (108 color(red)(cancel(color(black)("kPa"))))/(224color(red)(cancel(color(black)("kPa")))) * "8 L" = "3.857 L"#

I'll leave this rounded to two **sig figs**, but keep in mind that you only have one sig fig for the initial volume of the gas

#V_2 = color(green)(|bar(ul(color(white)(a/a)color(black)("3.9 L")color(white)(a/a)|)))#