# If the pressure is #8.314 * 10^4# #Pa#, #R# is #8.314#, the temperature is #100# #K#, and the number of moles of gas (#n#) is #300#, what is the volume of a gas in #m^3#?

##### 1 Answer

#### Explanation:

Your tool of choice here will be the **ideal gas law** equation, which looks like this

#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#

Here you have

#P# - the pressure of the gas

#V# - the volume it occupies

#n# - the number of moles of gas

#R# - theuniversal gas constant

#T# - theabsolute temperatureof the gas

Now, it's important to notice that the problem doesn't provide you with the **units** used for the universal gas constant. This means that you're going to have to do some research and see what units of *value* of **pressure** and **volume** given to you.

http://www.cpp.edu/~lllee/gasconstant.pdf

As you can see, you have

#R = 8.314color(white)(.) ("Pa m"^3)/("mol K")#

In this case, the units and the value match those given to you, so this is what you'll use in your calculations.

Your goal here is to figure out the **volume** of the gas, so rearrange the ideal gas law equation to solve for

#PV = nRT implies V = (nRT)/P#

Plug in your values to find

#V = (300 color(red)(cancel(color(black)("moles"))) * 8.314(color(red)(cancel(color(black)("Pa"))) * "m"^3)/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 100color(red)(cancel(color(black)("K"))))/(8.314 * 10^4 color(red)(cancel(color(black)("Pa")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("3 m"^3)color(white)(a/a)|)))#

The answer must be rounded to one **sig fig**.