# A sample of a gas has a volume of 2.0 liters at a pressure of 1.0 atmosphere. What will the pressure be when the volume increases to 4.0 liters at constant temperature?

##### 1 Answer

#### Explanation:

The idea here is that the pressure of a gas and the volume it occupies have an **inverse relationship** when the temperature and the number of moles of gas, i.e. the amount of gas present in the sample, remain **constant** **Boyle's Law**.

Simply put, when the temperature and the number of moles of gas are constant, a *decrease* in the volume of the gas will cause an **increase** in its pressure and an *increase* in the volume of the gas will cause a **decrease** in its pressure.

In your case, you know that the volume is increasing

#"2.0 L " -> " 4.0 L"#

so you should expect the volume to **decrease**

#"1.0 atm " > " P"_2#

Your tool of choice here will be this equation

#color(blue)(ul(color(black)(P_1V_1 = P_2V_2)))#

Here

#P_1# and#V_1# represent the pressure and volume of the gas at an initial state#P_2# and#V_2# represent the pressure and volume of the gas at a final state

Rearrange to solve for

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

and plug in your values to find

#V_2 = (2.0 color(red)(cancel(color(black)("L"))))/(4.0color(red)(cancel(color(black)("L")))) * "1.0 atm" = color(darkgreen)(ul(color(black)("0.50 atm")))#

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