Mole fraction is one of the ways to represent the concentration of the solution. It is defined as the number of molecules of component A divided by the total number of molecules of all the components in the solution. Let's learn about the mole fraction its formula and examples in this article.
What is Mole Fraction?
Mole fraction is defined as,
Number of moles of component A in a mixture divided by the total number of moles of all the components in that mixture.
Mole fraction is one of the measurements of the concentration of the solution. The image given below tells the formula used to calculate the mole fraction.
The mole fraction is represented by the letter 'X'. For example for a solution that has 'a' moles of solute and 'b' moles of the solvent the total moles in the solution is 'a+b'. Now, the mole fraction of solute is Xsolute = a / (a+b), similarly the mole fraction of solvent Xsolvent = b / (a+b).
A Mole is a unit of measurement for measuring a larger number of substances such as molecules, atoms, and other particles in chemistry. One mole is equal to 6.02214076 × 1023 values.
Mole Fraction Formula
The formula to calculate the mole fraction of any substance is discussed below in the article. Let's take a solution in which two compounds compound A and compound B are mixed and the moles of compound A is nA and the moles of compound B are nB then,
Mole Fraction of A = Number of moles of A / (Number of moles of A + Number of moles of B)
XA = nA / (nA+nB)
Mole Fraction of B = Number of moles of B / (Number of moles of A + Number of moles of B)
XB = nB / (nA+nB)
Also, one of the most used properties of mole fraction is,
Xsolute + Xsolvent = 1
Proof:
Using Mole Fraction Formula
Xsolute + Xsolvent = a /(a+b) + b/(a+b)
= (a+b) / (a+b)
Xsolute + Xsolvent = 1
Now, by using the above formula
- Xsolute = 1 - Xsolvent
- Xsolvent = 1 - Xsolute
Unit of Mole Fraction
Mole fraction is a way of representing the concentration of the solution. It is the ratio of the moles of the solute or the mole of the solvent to the total moles of the solution. As we see it is a ratio of two similar quantities thus, it is a dimensionless quantity.
So, Mole Fraction has no Unit.
Properties of Mole Fraction
Mole fraction is one the most important way for finding the concentration of the solution and it helps in studying the various properties of the solution. Some of the basic properties of Mole Fractions are,
- Mole fraction is independent of the temperature. Unlike other molar concentrations, mole fraction does not require knowledge of phase densities.
- The roles of 'solvate' and 'solvent' are reversible in a mole fraction as it is symmetric.
- For any Ideal gas mole fraction is defined as the ratio of the partial pressure of individual gas to the total pressure of the mixture.
- Finding the mole faction of the liquid solutions is difficult.
Advantages of Mole Fraction
The following are some of the advantages of using a mole fraction:
- Change in temperature has no effect on the mole fraction of the solution.
- Mole fraction in an ideal gas mixture is equal to the ratio of partial pressure to total pressure.
- Density of various phases is not required for finding the mole fraction of any solution.
Disadvantages of Mole Fraction
There are not many disadvantages of using mole fraction as the measure of the concentration of the solution. The only disadvantage of using mole fraction is that it cannot be used properly with liquid solutions.
Note:
- Sum of all the mole fractions in a solution is always one.
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Solved Examples on Mole Fraction
Example 1: If the molecular mass of CH3OH is 39 and the molecular mass of H2O is 27, what is the mole fraction of CH3OH and H2O in a solution made by dissolving 4.1 g of alcohol in 36 g of H2O?
Answer:
Using the formula for moles,
Moles = wt(in gm) / molecular mass
Moles of H2O = 36 / 27
= 1.3 moles
Moles of CH3OH = 4.1 / 39
= 0.10 mole
Mole fraction of CH3OH = 0.10 / (1.3 + 0.10)
= 0.10 / 1.4
Mole fraction of CH3OH = 0.0714
Now,
Mole fraction of H2O = 1.3/(1.3+0.1)
= 1.3/1.4
Mole fraction of H2O = 0.9286
Example 2: Calculate the mole fraction of each gas in a tank containing 2.5 × 104 mol oxygen and 4.8 × 104 mol helium.
Answer:
Number of moles of Helium = 4.8 × 104
Number of moles of Oxygen = 2.5 × 104
Since,
Mole Fraction of Helium = Number of moles of Helium / (Number of moles of Helium + Number of moles of Oxygen)
XHelium = 4.8 × 104 / (4.8 × 104 + 2.5 × 104)
= 4.8 × 104 / 7.3 × 104
XHelium = 0.6575
Mole Fraction of Oxygen = Number of moles of Oxygen / (Number of moles of Helium + Number of moles of Oxygen)
XOxygen = 2.5 × 104 / (4.8 × 104 + 2.5 × 104)
= 2.5 × 104 / 7.3 × 104
Xoxygen = 0.3424
Example 3: Calculate the acetone mole fraction in a solution of 6-mole benzene, 13 moles carbon tetrachloride, and 21 moles acetone.
Answer:
Moles of Benzene = 6
Moles of Carbon Tetrachloride = 13
Moles of Acetone = 21
Now,
Mole Fraction of Acetone = Moles of Acetone / (Moles of Benzene + Moles of Carbon Tetrachloride + Moles of Acetone)
Xacetone = 21 / (6+13+21)
Xacetone = 21 / 40
Xacetone = 0.525
Mole Fraction of Benzene = Moles of Benzene / (Moles of Benzene + Moles of Carbon Tetrachloride + Moles of Acetone)
Xbenzene = 6 / (6+13+21)
Xbenzene = 0.15
Mole Fraction of Carbon Tetrachloride = Moles of Carbon Tetrachloride / (Moles of Benzene + Moles of Carbon Tetrachloride + Moles of Acetone)
Xcarbon tetrachloride = 6 / (6+13+21)
Xcarbon tetrachloride = 0.15
Example 4: Calculate the mole fraction of solute, when the mole fraction of solvent is 0.23
Answer:
Since,
Xsolute = 1 - Xsolvent
Xsolute = 1 - 0.23
Xsolute = 0.77
Example 5: If the mole fraction of the solute is 0.64, determine the mole fraction of the solvent.
Answer:
Since,
Xsolvent = 1 - Xsolute
Xsolvent = 1 - 0.64
Xsolvent = 0.36
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