# What is the mole fraction?

## Molar fraction

The **mole fraction** is a unit of concentration that is defined as the **equality** in the number of moles of a component divided by the total number of moles of a **solution** . Because it is a ratio, it is an expression **unitless** . The mole fraction of all the components of a solution, when added together, will equal 1 and is considered a **dimensionless** unit of concentration .

It is a unit of the area of **chemistry** that is used to express the **concentration** that exists in a **solute** or in a **solution** . It is the quotient between the **moles** of solute and the total number of moles in the **solution** .

- For what do you use it
- Formula
- Molar fraction of a gas
- Molar fraction of a solute
- Molar fraction of a solvent
- Examples

## For what do you use it

Molar fractions are used to be able to express through them the **concentration** that a **solute** has in a **solvent** . They help us to express the **proportion** in which the moles that a solute has with respect to the total moles that are inside the solution are found and that are calculated by adding the moles of the **solutes** and the **solvents** .

It is also used to express the **concentration** is in the ratio of the **vapor pressure** in the **solutions** diluted and ideals of **solids** in liquids, in the study of the **equilibrium** that exists between the liquid and vapors solutions liquid .

## Formula

The formula to find the mole fraction of a gas is as follows:

**Molar fraction (X _{i} ) = n _{i } (moles of substance) / n _{t } (total moles of the solution )**

Where **x** is the **solute** and **n** is the number of **moles** that the solute has, measured in moles.

## Molar fraction of a gas

The ideal gas law tells us that all gases behave identically and that their behavior is independent of **attractive** and **repulsive** forces . If the **volume** and **temperature** are held constant, the ideal gas equation can be rearranged to show that the pressure of a gas sample is directly proportional to the number of moles of gas present.

**P = n (RT / V) **** = nx const**

## Molar fraction of a solute

The mole fraction of the solute (F1) is the **relationship** between the **number of moles** of the **solute** (n1) and the number of moles of the **solution** (n1 + n2).

## Molar fraction of a solvent

The mole fraction of a solvent (F _{2} ) is the ratio between the number of moles of the solvent (n _{2} ) and the number of moles of the solution (n _{1} + n _{2} ).

Where: F _{1} = **mole fraction of the solute** and F _{2} = **mole fraction of the solvent**

n _{1} = number of moles of the **solute** .

n _{2} = number of moles of **solvent** .

n = number of moles of the **solution** (n _{1} + n _{2} ).

The sum of the mole fraction of the solute (n _{1} ) and the mole fraction of the solvent (n _{2} ) all the time must be equal to **one.**

**F _{1 } + F _{2} = 1**

The number of moles is obtained through the application of the ratio of mass per mole.

## Examples

Some examples of mole fractions already solved are the following:

#### Example 1

**Calculate the molar fraction of each of the substances in the solution of: 10 moles of methanol, 1 mole of ethanol and 8 moles of water.**

n _{t } = total moles of the solution = n _{methanol} + n _{ethanol } + n _{ethanol } = 10 + 1+ 8 = 19

**x **_{methanol } = ** **n _{methanol } / n _{t} = **10/19** = **0.53**

**x _{ethanol }** =

**n**

_{ethanol }/ n

_{t}= 1/19 =

**0.05**

**x **_{water } = ** **n _{ethanol } / n _{t} = **8/19** = **0.42**

We can check that the solution is correct since the sum of the three is equal to 1: **x _{methanol } + x _{ethanol } + x **

_{water }= 0.53 + 0.05 + 0.42 =

**1**

#### Example 2

**Calculate the mole fraction of each component of a solution of 40 grams of ethyl alcohol (CH _{3} CH _{2} OH) and 100 grams of water.**

molecular weight of ethyl alcohol = 46 g / mol

molecular weight of water = 18 g / mol

moles of ethyl alcohol = n _{alcohol et }_{. } = 40 g / 46 g mol ^{-1} = 0.87 mol

moles of water = n _{water} = 100 g / 18 gmol ^{-1} = 5.56 moles

total moles solution = n _{t} = 0.87 + 5.56 = 6.43 moles

**mole fraction of ethyl alcohol**** ** = x _{alcohol et }_{. }_{ }= ** **n _{alcohol et. }/ n _{t} = 0.87 / 6.43 = **0.14**

**mole fraction of water**** ** = x _{water}_{ } = ** **n _{water } / n _{t} = 5.56 / 6.43 = **0.86**

we verify that the solution is correct: **x _{alcohol et. }**

_{ }+

**x**

_{water}_{ }= 0.14 + 0.86 =

**1**