# What is mole percent?

Jan 8, 2014

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

#### Explanation:

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

The mole fraction of component a is

${\chi}_{a} = {n}_{a} / {n}_{t}$

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

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?

(a) Identify the components making up the solution.

$\text{NaCl}$ is the solute and $\text{H"_2"O}$ is the solvent.

(b) Calculate the moles of each component.

${n}_{\text{NaCl" = 5.0 color(red)(cancel(color(black)("g NaCl"))) × "1 mol NaCl"/(58.44 color(red)(cancel(color(black)("g NaCl")))) = "0.086 mol NaCl}}$

${n}_{\text{H₂O" = 25.0 color(red)(cancel(color(black)("g H"_2"O"))) × ("1 mol H"_2"O")/(18.02 color(red)(cancel(color(black)("g H"_2"O")))) = "1.38 mol H"_2"O}}$

(c) 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]

(d) 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

${\chi}_{\text{NaCl" = "0.058; mole % NaCl" = color(white)(ll)"5.8 mole %}}$

${\chi}_{\text{H₂O" = 0.942; color(white)(l)"mole % H"_2"O"color(white)(l) = "94.2 mole %}}$