# Question d9848

Aug 2, 2017

$\frac{\text{mol" = "volume}}{22.41}$

#### Explanation:

The ideal gas law states

ul(PV = nRT

where

• $P$ is the pressure (in $\text{atm}$) of the gas

• $V$ is the volume (in $\text{L}$) the gas occupies

• $n$ is the quantity (in $\text{mol}$) of gas present

• $R$ is the universal gas constant, equal to $0.082057 \left(\text{L"·"atm")/("mol"·"K}\right)$

• $T$ is the absolute temperature (in $\text{K}$) of the gas (absolute temperature indicates units of Kelvin)

Standard temperature and pressure (STP) conditions are commonly used in chemistry as

• ul(273.15color(white)(l)"K"

• ul(1color(white)(l)"atm"

(Standard pressure, since the year 1982, has been defined as $1$ $\text{bar}$ ($0.9869$ $\text{atm}$), but a lot of instructors teach it as $1$ $\text{atm}$. The difference is small, but can cause differing calculations, so be sure to know which standard pressure you are to be using.)

Plugging these and the constant $R$ into the equation, we have

$\left(1 \textcolor{w h i t e}{l} \text{atm")(V) = n(0.082057("L"·"atm")/("mol"·"K"))(273.15color(white)(l)"K}\right)$

We're asked to use the gas law to find the moles ($n$) from a given volume ($V$), so let's eliminate the units in the above expression, and rearrange to solve for $n$:

$\left(1\right) \left(V\right) = \left(22.41\right) \left(n\right)$

color(red)(ulbar(|stackrel(" ")(" "n = V/22.41" ")|)#

Does the number $22.41$ (or $22.4$) ring a bell, perhaps? This is where it comes from!