Question #d9848

1 Answer
Aug 2, 2017

"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!