# A gas occupies a volume of 0.2 L at 25 kPa. What volume will the gas occupy at 2.5 kPa?

##### 1 Answer

#### Explanation:

Right from the start, assuming, of course, that the temperature and the number of moles of gas **remain unchanged**, you can say that the volume of the gas will **increase** as pressure changes from

That is the case because when the temperature and the number of moles of gas remain constant, the pressure of a gas varies **indirectly** with its volume, as described by **Boyle's Law**.

In other words, when pressure **decreases** by factor **increases** by the same factor

#P * V = k#

This implies that you can write

#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 V_2 = P_1/P_2 * V_1#

Plug in your values to find

#V_2 = (25 color(red)(cancel(color(black)("kPa"))))/(2.5color(red)(cancel(color(black)("kPa")))) * "0.2 L" = color(darkgreen)(ul(color(black)("2 L")))#

The answer is rounded to one **significant figure**, the number of significant figures you have for the initial volume of the gas.

As predicted, the volume of the gas **increased** as a result of the *decrease* in pressure. Moreover, it increased by *the same factor*!