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# 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 .

What is the mole fraction?

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  (moles of substance) / n  (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
1  = number of moles of the solute .
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 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.

= total moles of the solution = n methanol  + n ethanol  + n ethanol  = 10 + 1+ 8 = 19

methanol  =  methanol  / n t  = 10/19 = 0.53

ethanol  =  ethanol  / n t  = 1/19 = 0.05

water  =  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:  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   alcohol et. / n t  = 0.87 / 6.43 = 0.14

mole fraction of water  = x water  =  water  / n t  = 5.56 / 6.43 = 0.86

we verify that the solution is correct:  alcohol et.  +  water  = 0.14 + 0.86 =  1