# 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?

Jul 28, 2016

${\text{3 m}}^{3}$

#### Explanation:

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

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} P V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

Here you have

$P$ - the pressure of the gas
$V$ - the volume it occupies
$n$ - the number of moles of gas
$R$ - the universal gas constant
$T$ - the absolute temperature of 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 $R$, if any, match the value of $R$ and the units for pressure and volume given to you.

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

As you can see, you have

$R = 8.314 \textcolor{w h i t e}{.} \left(\text{Pa m"^3)/("mol K}\right)$

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 $V$

$P V = n R T \implies V = \frac{n R T}{P}$

Plug in your values to find

$V = \left(300 \textcolor{red}{\cancel{\textcolor{b l a c k}{{\text{moles"))) * 8.314(color(red)(cancel(color(black)("Pa"))) * "m"^3)/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 100color(red)(cancel(color(black)("K"))))/(8.314 * 10^4 color(red)(cancel(color(black)("Pa")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("3 m}}^{3}} \textcolor{w h i t e}{\frac{a}{a}} |}}\right)$

The answer must be rounded to one sig fig.