# A sample of oxygen gas occupies a volume of 365.2 L. When the volume is increased to 478.2 L, the new pressure is 24.13 atm. What was the original pressure?

##### 1 Answer

#### Explanation:

Before doing any calculation, try to predict what the original pressure of the gas must have been *relative* to its new value of

So, no mention is made about temperature or number of moles of gas, which means that you can consider them **constant**.

When temperature and pressure are kept constant, *volume* and *pressure* have an **inverse relationship** - this is known as Boyle's Law.

Simply put, when volume **Increases**, pressure **decreases**, and when volume **decreases**, pressure **increases**.

This happens because, as you know, gas pressure is caused by the collisions between the gas molecules and the walls of the container. The *more powerful* and *more frequent* these collisions, the **higher** the gas pressure.

*Temperature* is actually a measure of the gas molecules' **average kinetic energy**. When volume is **increased** at **constant temperature**, the force with which the molecules are hitting the wall is **kept constant**.

However, the larger volume means *more room* for these molecules to move around in, which in turn means **less frequent** collisions with the walls of the container **decreases**.

Since volume was increased for this gas, you can expect the *final pressure* to be **lower** than the *initial pressure*.

With this in mind, use the equation described by Boyle's Law to find the actual value of the initial pressure.

#color(blue)(P_1 * V_1 = P_2 * V_2)" "# , where

Plug in your values and solve for

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

#P_1 = (478.2color(red)(cancel(color(black)("L"))))/(365.2 color(red)(cancel(color(black)("L")))) * "24.13 atm"#

#P_1 = color(green)("31.60 atm")#

As predicted, the pressure **decreased** as a result of the *increase* in volume.