# Question #cbc5e

##### 1 Answer

#### Explanation:

Right from the start, you should be able to look at the information provided by the problem and be able to say that the new volume will **definitely** be **smaller** than

That is the case because pressure and volume have an **inverse relationship** when temperature and number of moles are *kept constant, as given by **Boyle's Law**.

Simply put, when you keep the temperature and the number of moles of gas constant, you can **increase** its volume by **decreasing** its pressure and **decrease** its volume by **increasing** its pressure.

In your case, the pressure is **increasing**, which can only mean that the volume must **decrease**.

Now, the inverse relationship that exists between pressure and volume is given by the equation

#color(purple)(bar(ul(|color(white)(a/a)color(black)(P_1 * V_1 = P_2 * V_2)color(white)(a/a)|)))#

Here

Rearrange to solve for

#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 = (1.50 color(red)(cancel(color(black)("atm"))))/(4.50color(red)(cancel(color(black)("atm")))) * "75.0 mL" = color(green)(bar(ul(|color(white)(a/a)color(black)("25.0 mL")color(white)(a/a)|)))#

The answer is rounded to three **sig figs**.

As you can see, because the pressure increased by a factor of