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Mole fraction Formula

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  • Last Updated : 23 Jun, 2022

The mole fraction is defined as the number of molecules of a single component divided by the total number of molecules in a combination. A mole fraction is defined as the amount of one constituent divided by the total amount of all constituents in chemistry. Let’s have a look at the formula for mole fractions.

Mole Fraction

The number of moles of a specific component in a mixture divided by the total number of moles in the mixture is referred to as the mole fraction. 

It’s a measurement of a solution’s concentration. The mole fraction is symbolized by the letter ‘X’.

Mole is a unit of measurement for larger amounts of very small particles such as molecules, atoms, and other particles in chemistry. The mole is named for the 6.02214076 × 1023 unit value.

If the mole fraction of each solvent is known, the ratio of the two reactive components can be computed. Mole fractions can be made using a variety of molecular concentrations, such as molarity, morality, and mass percent compositions. The quantity fraction, or mole fraction, is a prominent term. The mole fraction is a wonderful way to show how a mixture’s composition can change due to lack of competition, volume fraction, or mass fraction.

Mole Fraction Formula

Assume that the solution includes the components ‘A’ and ‘B.’ Then you may write the mole fraction ‘X’ as

Here A is Solvent and B is solute,

Mole Fraction of Compound A = Number of moles of Compound A / (Number of moles of Compound A + Number of moles of Compound B)

XA = nA / (nA+nB)

Mole Fraction of Compound B = Number of moles of Compound B / (Number of moles of Compound A + Number of moles of Compound B)

XB = nB / (nA+nB)

Therefore, Xsolute + Xsolvent = 1

A mole fraction can be computed if one of its components is known (Xsolvent is known).

∴ Xsolute = 1 – Xsolvent

In mathematical terms, 

The mole fraction of a component = number of moles of the component / Total number of moles of all components

Mole Fraction Properties

In the study of diagrams, mole fraction is essential. In the production of phase figures, this derivation is commonly utilized. The following are the most important mole fraction properties:

  1. The temperature has no impact on a mole fraction. Mole fraction, unlike molar concentration, does not require knowledge of phase densities.
  2. In contrast to other methods of measurement, the weight of the elements can be used to generate a valid mixture of mole fractions.
  3. Because the measure is symmetric (x=0.1 and x=0.9), the roles of ‘solvate’ and ‘solvent’ are reversible in a mole fraction.
  4. The mole fraction in ideal gases is defined as the ratio of the mixture’s partial pressure to its total pressure.

Advantages of mole fraction

The following are some of the advantages of using a mole fraction:

  1. The temperature has no bearing on the mole fraction.
  2. The mole fraction in an ideal gas mixture is equal to the ratio of partial pressure to total pressure.

Disadvantages of mole fraction

The only disadvantage of mole fraction is that it cannot be used with liquids.

Remember the following points:

  • The sum of the mole fraction will always be 1 when all components are factored in.
  • Only a portion of molecules is represented by the mole fraction. Individual fractions can differ from mass fractions due to the various masses of distinct molecules.

Sample Questions

Question 1: If the M of CH3OH is 39 and the M of H2O is 27, what is the mole fraction of CH3OH and H2O in a mixed solution made by dissolving 4.1 g of alcohol in 36 g of H2O?

Answer:

Moles of H2O = 36 / 27 = 1.3 moles

Moles of CH3OH = 4.1 / 39 = 0.10 mole

Since, Mole fraction of

CH3OH = 0.10 / (1.3 + 0.10)

CH3OH = 0.10 / 1.4

CH3OH = 0.0714

Now, Mole fraction of H2O

H2O = 1.3/(1.3+0.1)

H2O = 1.3/1.4

H2O = 0.9286

Question 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)

XHe = 4.8 × 104 / (4.8 × 104 + 2.5 × 104)

∴ XHe = 4.8 × 104 / 7.3 × 104

∴ XHe = 0.6575

Mole Fraction of Oxygen = Number of moles of Oxygen / (Number of moles of Helium + Number of moles of Oxygen)

XO2 = 2.5 × 104 / (4.8 × 104 + 2.5 × 104)

∴ XO2 = 2.5 × 104 / 7.3 × 104

∴ XO2 = 0.3424

Question 3: Calculate the acetone mole fraction in a solution of 6 mole benzene, 13 moles carbon tetrachloride, and 21 moles acetone.

Answer:

Number of moles of benzene = 6 mole

Number of moles of carbon tetrachloride = 13 mole

Number of moles of acetone = 21 mole

Since,

Mole Fraction of acetone = Number of moles of acetone / (Number of moles of benzene + Number of moles of carbon tetrachloride + Number of moles of acetone)

Xacetone = 21 / (6+13+21)

∴ Xacetone = 21 / 40

∴ Xacetone = 0.525

Mole Fraction of benzene = Number of moles of benzene / (Number of moles of benzene + Number of moles of carbon tetrachloride + Number of moles of acetone)

Xbenzene = 6 / (6+13+21)

∴ Xbenzene = 0.15

Mole Fraction of carbon tetrachloride = Number of moles of carbon tetrachloride / (Number of moles of benzene + Number of moles of carbon tetrachloride + Number of moles of acetone)

Xcarbon tetrachloride = 6 / (6+13+21)

∴ Xcarbon tetrachloride = 0.15

Question 4: Calculate the mole fraction of solute, when the mole of solvent is 0.23

Answer:

Since,

Xsolute = 1 – Xsolvent

∴ Xsolute = 1 – 0.23

∴ Xsolute = 0.77

Question 5: If the mole of solute is 0.64, determine the mole fraction of solvent.

Answer:

Since,

Xsolvent = 1 – Xsolute

∴ Xsolvent = 1 – 0.64

∴ Xsolvent = 0.36

Question 6: Write two properties of the Mole fraction.

Answer:

In the study of diagrams, mole fraction is essential. In the production of phase figures, this derivation is commonly utilized. The following are the most important mole fraction Properties:

  1. A mole fraction is unaffected by temperature. Unlike molar concentration, mole fraction does not require knowledge of phase densities.
  2. The weight of the components, unlike other methods of measurement, can be utilized to construct a valid combination of mole fractions.

Question 7: What is Mole Fraction’s Purpose?

Answer:

The mole fraction is the ratio of the number of single component molecules (or moles) in the mixture to the total number of molecules (or moles). When two reactive components are combined, the mole fraction is useful because the ratio of the two components can be calculated if the mole fraction of each component is known.

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