Mole Fraction Formula

Concentration is defined as the amount of substance present in the given space. There are various methods to calculate concentration in chemistry, known as concentration units such as molarity, molality, mass percentage, normality, etc. One of the concentration terms is a mole fraction. In this article, we will study the mole fraction definition and formula in detail.

Mole Fraction Definition and Formula

The mole fraction is the number of molecules in a mixture of a specific component, divided by the total number of moles in that mixture. Mole fraction is a unitless quantity. Symbol  ‘X’ represents the mole fraction.

Mole Fraction Equation:

Let’s say the components ‘A’ and ‘B’ are a part of the solution. Then the mole fraction ‘X’ can be written as-

⇒ Mole fraction of component A = \[\frac{\text{no of moles of component A}}{\text{no of moles of component A + no of moles of component B}}\]

Mole fraction formula in chemistry can be written as-

⇒ X\[_{A}\] = \[\frac{nA}{nA+nB}\]

Here, ‘A’ represents the solvent so this equation represents the mole fraction of the solvent formula.

⇒ Mole fraction of component B = \[\frac{\text{no of moles of component B}}{\text{no of moles of component A + no of moles of component B}}\]

mole fraction formula in chemistry can be written as-

⇒ X\[_{B}\] = \[\frac{nB}{nA+nB}\]

Here, ‘B’ represents the solute so this equation represents the mole fraction of the solute formula.

Therefore, the sum of all the components of the mole fraction is always equal to one.

⇒ XA+XB=1

If one component of the mole fraction is known then another mole fraction can be calculated.

Lets XA is known then XB can be calculated as-

⇒ XB=1-XA

Partial Pressure:

It is defined as the pressure exerted by the individual gas in a mixture of gases. Using the mole fraction, the partial pressure of a gas in a mixture can be calculated.

Partial pressure formula with mole fraction:

PA=XAPtotal

Where,

PA= partial pressure of A

XA= mole fraction of A

Ptotal=total partial pressure of a mixture

Solved Examples-

Example 1: 23g of Ethyl Alcohol is Dissolved in 54g of Water. Calculate the Mole Fraction of Both Ethyl Alcohol and Water in Solution.

Solution: Mass of solute wB=23g

Mass of solvent wA=54g

The molecular formula of ethyl alcohol(C2H5OH)

So, the molar mass of C2H5OH= 12 x 2 + 5 x 1 + 16 + 1  

= 46 g/mol 

The molecular formula of water(H2O)

So, the molar mass of H2O = 2 x 1 + 16 

= 18 g/mol

Now, using the formula to find mole fraction-

⇒ No. of moles of solute(C2H5OH) = nB = 23/46 = 0.5 mol

⇒ No. of moles of water(H2O) =nA= 54/18 = 3mol

⇒ Total no. of moles = 0.5 + 3 = 3.5 mol

⇒ Mole fraction of B component(solute)= XB= 0.5/3.5 = 0.1429

⇒ Mole fraction of A component(solvent)=XA=3/3.5 = 0.8571

Hence, the mole fraction of component B= 0.1429 and the mole fraction of component A=0.8571

Example 2: The Gas Mixture Comprises 4.76 Moles of Ne, 0.74 Moles of Ar, and 2.5 Moles of Xe. If the Overall Pressure is 2 atm, Measure the Partial Pressure of the Gases. At a Fixed Temperature.

Solution: The total mole fraction of a mixture =4.76+0.74+2.5=8

Using the formula to find mole fraction-

⇒ XNe= 4.76/8=0.595

⇒ XAr=0.74/8=0.093

⇒ XXe=2.5 /8=0.312

Partial pressure-

⇒ PNe= XNePtotal (total pressure given is 2)

⇒ PNe= 0.595 x 2= 1.19atm

⇒ PAr= XArePtotal 

⇒ PAr= 0.093 x 2 = 0.186atm

⇒ PXe= XXePtotal 

⇒ PXe= 0.312 x 2= 0.624atm