Mole percent is the percentage that the moles of a particular component are of the total moles that are in a mixture.

MOLE FRACTION

Let’s start with the definition of mole fraction.

Mole fraction ##chi## (the Greek letter chi) is the number of moles of a given component of a mixture divided by the total number of moles in the mixture.

##n_t = n_a + n_b + n_c + … ## , where
##n_t## = total number of moles
##n_a## = moles of component a
##n_b## = moles of component b
##n_c## = moles of component c

fraction of component a is

##chi_a = n_a/n_t##

If a system consists of only two components, one component is the and the other is the .

The more abundant component, the solvent, is usually called component 1, and the solute is called component 2.

##chi_1 = n_1/n_t##

##chi_2 = n_2/n_t##, where

##n_t = n_1 + n_2##

The sum of the mole fractions for each component in a solution is equal to 1. For a solution containing two components, solute and solvent,

##chi_1 + chi_2 = 1##

MOLE PERCENT

Mole percent is equal to the mole fraction for the component multiplied by 100 %

mole % a = ##chi_a## × 100 %

The sum of the mole percentages for each component in a solution is equal to 100 %.

For a solution containing two components, solute and solvent,

mole % solute + mole % solvent = 100 %

EXAMPLE

What are the mole fraction and mole percent of sodium chloride and the mole fraction and mole percent of water in an aqueous solution containing 25.0 g water and 5.0 g sodium chloride?

Identify the components making up the solution.

##”NaCl”## is the solute and ##”H”_2″O”## is the solvent.

Calculate the moles of each component.

##n_”NaCl” = 5.0 color(red)(cancel(color(black)(“g NaCl”))) × “1 mol NaCl”/(58.44 color(red)(cancel(color(black)(“g NaCl”)))) = “0.086 mol NaCl”##

##n_”H₂O” = 25.0 color(red)(cancel(color(black)(“g H”_2″O”))) × (“1 mol H”_2″O”)/(18.02 color(red)(cancel(color(black)(“g H”_2″O”)))) = “1.38 mol H”_2″O”##

Calculate the mole fraction of each component.

##n_t = n_1 + n_2## = (1.38 + 0.086) mol = 1.46 mol

##chi_2 = n_2/n_t = (0.086 color(red)(cancel(color(black)(“mol”))))/(1.46 color(red)(cancel(color(black)(“mol”)))) = “0.058”##

##chi_1 = n_1/n_t = (1.38 color(red)(cancel(color(black)(“mol”))))/(1.46 color(red)(cancel(color(black)(“mol”)))) = “0.942”##

(Note: We could also have written ##chi_1 = 1 – chi_2 = 1 – 0.058 = 0.942##)

Calculate the mole percent of each component.

Mole % 2 = ##chi_2 × 100 % = 0.058 × 100 % = “5.8 mole %”##

Mole % 1 = ##chi_1 × 100 % = 0.942 × 100 % = “94.2 mole %”##

[Note: We could also have written mole % 1 = 100 – mole % 2 = (100 – 5.8) % = 94.2 mole %]

Summary

##chi_”NaCl” = “0.058; mole % NaCl = 5.8 mole %”##

##chi_”H₂O” = “0.242; mole % H”_2″O = 94.2 mole %”##

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