# Question #644b9

##### 1 Answer

#### Explanation:

The thing to remember about pressure and volume is that they have an **inverse relationship** when temperature and number of moles of gas are kept constant, as described by **Boyle's Law**.

In other words, when you keep the temperature of the gas and the amount of gas, i.e. the number of moles of gas, constant, **increasing** its pressure by a factor *decrease* by the **same factor**

Similarly, **decreasing** its pressure by a factor *increase* by the **same factor**

Mathematically, you can say that

#color(blue)(ul(color(black)(P_1 * V_1 = P_2 * V_2)))#

Here

#P_1# and#P_2# represent the initial and the final pressure of the gas#V_1# and#V_2# represent the initial and final volume of the gas

In your case, you know that a sample of gas starts at a pressure

#P_2 = 2 xx P_1 -># the pressure isdoubled

This means that you can expect the volume of the gas to **decrease** by a factor of

Rearrange the equation for Boyle's Law and plug in your values to confirm that this is the case

#V_2 = P_1/P_2 * V_1#

#V_2 = color(red)(cancel(color(black)(P_1)))/(2color(red)(cancel(color(black)(P_1)))) xx "540 mL" = color(darkgreen)(ul(color(black)("270 mL")))#

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

As predicted, **increasing** the pressure by a factor of **decrease** by a factor of