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Mole Fraction

A solution is a homogenous mixture of two or more substances on molecular level. The ingredients of the mixture present in lesser quantity is called the solute and the one present in a larger quantity is called a solvent.

For example, if a small quantity of sugar or the solute is mixed with water or the solvent, a homogenous solution in water could be produced. In this solution, the sugar solutes are uniformly dispersed in the water solvent.
The concentration of a solution is defined as the amount of solute present in a given amount of solution. There are several ways of stating the concentration of a solution. It is far more common to state the concentration of a solution by giving the number of moles of solute dissolved.
A solution with relatively lower concentration is called a dilute solution and a solution of higher concentration is called a concentrated solution.

Substances of any three states of matter, solid liquid or gas can act as a solute or solvent. 

There are several ways of expressing concentration of a solution
  1. Percent by weight
  2. Mole fraction
  3. Molarity
  4. Molality
  5. Normality

Related Calculators
Mole Fraction Calculator conversion of grams to moles calculator
convert moles to grams calculator
 

Mole fraction Definition

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A simple solution is produced out of two substances: solute and solvent.
Solute, a solid , liquid or gas, can be dissolved in a solvent to make a solution. 
Mole fraction, X, of solute is defined as
" The ratio of the number of moles of solute and the total number of moles of solute and solvent".
Thus,

Xsolute = $\frac{moles\ of\ solute}{moles\ of\ solute + moles\ of\ solvent}$

If n represents moles of the solute and N represents moles of the solvent,

Mole fraction formula/equation:
Xsolute = $\frac{n}{n+N}$The mole fraction of the solvent, then would be:
Xsolvent = $\frac{N}{n+N}$ Mole fraction does not have any unit.
Sum of the mole fractions of solute and solvent would be unity.
Xsolute + Xsolvent = 1

Calculate Mole Fraction

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Solved Examples

Question 1: Calculate the mole fraction of HCl in a solution of hydrochloric acid in water, containing 36% HCl by weight.
Solution:
 
The solution contains 36 grams of Hydrochloric acid and 64 grams of water. Also,
Molecular mass of HCl is 36.5 grams/mole.
Molar mass of water is 18 grams/mole.

Moles of HCl = 36grams of HCl x $\frac{1\ mole\ of\ HCl}{36.5\ grams\ of\ HCl}$

                   = 0.99 m      ole of HCl.

Moles of water = 64grams of H2O x $\frac{1\ mole\ of\ H_{2} O}{18\ grams\ of\ H_{2}O}$

                   = 3.6 moles of H2O.

Mole fraction of HCl = $\frac{Moles\ of\ HCl}{Moles\ of\ HCl + Moles\ of\ water}$

= $\frac{0.99}{36 + 0.99}$ = 0.22


Mole fraction of Hydrochloric acid in the given solution is 0.22.


 

Question 2: The dead sea contains approximately 332 grams of salt per kg of sea water. Assume that this salt is all sodium chloride(NaCl). Given that the density of the dead sea is approximately 1.20 kg/l, calculate the mass percent of NaCl.
Solution:
 
We need to determine the number of moles of both NaCl and water present in a given sample of seawater. Assume that we have 1 kg of seawater. This means we must have 332 g of NaCl and 668 grams of water in the sample (by conservation of mass). Therefore:


Number of moles of NaCl = 332 grams x $\frac{1\ mole\ of\ NaCl}{58.44\ grams\ of\ NaCl}$= 5.68 moles of NaCl.


Number of moles of water = 668 grams x $\frac{1\ mole\ of\ water}{18\ grams\ of\ water}$= 37.1 moles of water.


The mole fraction of NaCl in the seawater is = 5.68 / 5.68 + 37.1 = 0.133.
 


Convert Mass Fraction to Mole Fraction

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Mass fraction, denoted by 'w' is defined as "the ratio of mass of the solute and the total mass of solute and solvent present."It is denoted as:
wsolute = $\frac{Mass\ of\ solute}{mass\ of\ solute + mass\ of\ solvent}$To convert mole fraction to mass fraction, we multiply mole fraction with the ratio of molar mass of that particular component and average molar mass of the solution.
wsolute = xsolute x $\frac{M_{solute}}{M_{solvent} + M_{solute}}$

Solved Example

Question: The mole fraction of NaCl in water is 0.22. What is its mass percent?
Solution:
 
Using the moles fraction to mass fraction relationship,

wsolute = xsolute x $\frac{M_{solute}}{M_{solvent} + M_{solute}}$
                         

Molar mass of NaCl = 58.44 g/mol
Molar mass of H2O = 18 grams/mole.

So,  

wsolute = 0.22 x $\frac{58.44}{58.44 + 18}$ = 0.17

 

Mole Fraction to Mass Fraction

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Since we know that the relationship between mass fraction and mole fraction is:

wsolute = xsolute x $\frac{M_{solute}}{M_{solvent} + M_{solute}}$

We can use this with a slightly altered formula:

xsolute = wsolute x $\frac{M_{solute} + M_{solute}}{M_{solute}}$


Sometimes, if the moles of each component is given, we can determine the mass of the substance and then calculate the mass fraction.

Solved Example

Question: The mass fraction of KCl in its aqueous solution is 0.051. What is the mole fraction of sodium chloride in the solution?
Solution:
 

wsolute = 0.051
Molar mass of Potassium chloride = 74.55 g/mole.
Molar mass of water = 18 g/mole.

xsolute = 0.051 x $\frac{74.55 + 18}{74.55}$ = 3.81
 

Mole fraction to Molality

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Molality can be defined as:
"Number of moles of solute per kilogram of solvent."This is expressed as 'm' and has a unit of moles/kilograms.

Mole fraction can be converted into molality by converting the moles of the solvent to kilograms.

Solved Example

Question: Molality of toluene (Molar mass- 92.14g/mole) in benzene (Molar mass: 78.11) is 0.24 m. What is the mole fraction of toluene in benzene?
Solution:
 
Molality = moles of toluene / mass of benzene in kilograms
We have 0.24 moles of toluene in 1000 grams of solvent.
Moles of Benzene = mass of benzene / molar mass of Benzene = 1000grams/ 78.11 g/mole = 12.80 moles
                                           
Mole fraction of toluene = $\frac{moles\ of\ toluene}{moles\ of\ toluene + moles\ of\ benzene}$
                                                                            
Mole fraction of toluene = $\frac{0.24\ moles}{0.24 + 12.80\ moles}$ = 0.018
 

Mole fraction to molarity

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Molarity, another concentration term is defined as:
" The number of moles per liter of solution."

Molarity = $\frac{moles\ of\ solute}{volume\ in\ liters}$

We can calculate mole fraction using molarity values.

Solved Example

Question: The molarity of HCl in water is 0.18. what is its mole fraction?
Solution:
 
Moles of HCl in 1000 ml of water is 0.18.

Moles of water = $\frac{1000g}{18g/mole}$ = 55.55 moles.

Mole fraction = $\frac{0.18}{0.18+ 55.55}$ = 0.0032


 

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