Question

Question #d9848

Answer 1

`"mol" = "volume"/22.41`

Explanation:

The ideal gas law states

`ul(PV = nRT`

where

• `P` is the pressure (in `"atm"`) of the gas

• `V` is the volume (in `"L"`) the gas occupies

• `n` is the quantity (in `"mol"`) of gas present

• `R` is the universal gas constant, equal to `0.082057("L"·"atm")/("mol"·"K")`

• `T` is the absolute temperature (in `"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` `"bar"` (`0.9869` `"atm"`), but a lot of instructors teach it as `1` `"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

`(1color(white)(l)"atm")(V) = n(0.082057("L"·"atm")/("mol"·"K"))(273.15color(white)(l)"K")`

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`:

`(1)(V) = (22.41)(n)`

`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!