# Question #b100e

##### 1 Answer

#### Explanation:

For starters, I will assume that the problem meant

...note that the gashad double the volumewhen she started...

Now, Jessica's in luck because she can use **Boyle's Law** to find the initial pressure of the gas.

The idea here is that the *temperature* and *number of moles* of gas are being **kept constant** in the experiment, which means that you can use the **direct relationship** that exists between pressure and volume described by Boyle's Law.

Simply put, when temperature and number of moles of gas are being kept constant, **increasing** the pressure of the gas will result in a **decrease** in volume.

Likewise, **decreasing** the pressure of the gas swill result in an **increase** in volume.

Now, Jessica knows that the gas had **double** the volume *before the experiment started*, which means that the volume of the gas got **halved**.

If you take **initial volume of the gas**, you can say that the final volume of the gas,

#V_2 = 1/2 * V_1" " " "color(orange)("(*)") -># the volume of the gas gothalved

Mathematically, Boyle's Law can be expressed like this

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

Your job here is to solve for **initial pressure** of the gas. Rearrange the equation to isolate

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

Use equation

#P_1 = (1/2 * color(red)(cancel(color(black)(V_1))))/color(red)(cancel(color(black)(V_1))) * "300. kPa" = 1/2 * "300. kPa" = color(green)(|bar(ul(color(white)(a/a)"150. kPa"color(white)(a/a)|)))#

*Now, does this result make sense?*

According to Boyle's Law, a **decrease** in volume is the result of an **increase** in pressure. It thus follows that **doubling** the pressure of the gas would cause the volume to be **halved**.