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The number of molecules of one component, divided by the number of total molecules present in one mixture is called mole fraction. In Chemistry, mole fraction is defined as the unit of the amount of a constituent, divided by the amount of all constituents. Here we will discuss the advantages, formula, properties of the topic along with some solved questions.
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Key Terms: Solutions, Mole function, Formula of mole function, molar mass, mass function, mole percentage, mass concentration.
Define Mole Fraction?
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The word Mole is used in chemistry as a standard unit for measuring larger quantities of very small particles such as molecules, atoms, and other particles. The mole is designated for the number of units valued at 6.02214076 × 10²³.
Figure: Mole Fraction
When two reactive components are combined, the ratio of two components can be calculated if the mole fraction of each solvent is known. Mole fraction can be generated through various concentrations of molecules, including molarity, morality, and mass percent compositions. The mole fraction is popularly known as the amount fraction. The mole fraction is a great way to express that the composition of a mixture can happen with the lack of competition, volume fraction, and mass fraction.
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Mole Fraction: Symbols and Denotation
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The mole fraction is denoted by the lowercase letter χ (chi), instead of the traditional Roman x.
The Formula Related to Mole Fraction
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In mathematical terms, the mole fraction of a component = number of moles of the component / the Total number of moles of all components.
Mole fraction is the division of molecules present in one mixture and the molecules present in all mixtures.
The Formula of Mole Fraction Solute
Mole fraction of solute = Moles of Solute / Moles of Solute + Moles of Solvent
nA ⁄ nA + nB
Properties of Mole Fraction
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Mole fraction is critical to the study of diagrams. The derivation is frequently used in the construction of phase figures. Here are the main properties of mole fraction:
- A mole fraction is not dependent on temperature. As opposed to molar concentration, mole fraction does not require the information of the densities across phases involved.
- Unlike other methods of measurement, a legitimate mixture of mole fractions can be constructed by taking into account the weight of the constituents.
- The roles of 'solute' and 'solvent' are reversible in a mole fraction, as the measure is symmetric (x=0.1 and x=0.9).
- In ideal gases, the mole fraction can be denoted as the ratio of partial pressure of the mixture to the total pressure of the mixture.
- The mole express can be expressed as a component of functions in a ternary mixture. Here's how the functions of other components and binary mole ratio look like:
Advantages of Mole Fraction
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The advantages of mole fraction are:
- Mole fraction is not dependent on the temperature.
- Finding out the information about the density of the phase is not required to calculate the mole fraction.
- In case of an ideal gas mixture, the mole fraction is represented by the ratio of partial pressure to the total pressure of the mixture.
Disadvantages of Mole Fraction
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There is only one drawback of mole fraction that is, mole fraction is not applicable for liquid solutions.
Mole Fraction: Related Quantities
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1. Mass fraction: Mass fraction is the molar mass of the component. It is denoted by wi.
The formula of mass fraction:
Mi = Molar mass of the component
M‾ = Average molar mass of the mixture.
2. Molar mixing ratio: The mixing of two or more ratios is called the molar mixing ratio.
Molar Mixing Ratio
3. Mole percentage: Multiplying the derived mole fraction by 100 to determine a relative number is called mole percentage.
(n/n)%
4. Mass concentration: The measure of the concentration of a chemical species present in a solution.
Mass Concentration
Calculating Mole Fraction from Molality
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Mole fraction can be determined from the molality of a substance. By converting morality into the equivalent mole fraction, we can come to the desired results.
Understanding with an example. Suppose we have a 1.62 m solution of table sugar in water. What will be the mole fraction of table sugar?
As we know that Molality = Moles Solute/kg solvent, therefore mole fraction can be determined through molality.
Things to Remember
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- When all components are considered, the sum of the mole fraction will always be equal to 1.
- The mole fraction represents only a portion of molecules. Since different molecules can have different masses, the individual fraction can also be different from the mass fraction.
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Sample Questions
Ques: What is the mole fraction of CH3OH and H2O is a combined solution prepared by dissolving 5.5 g of alcohol in 40 g of H2O; if the M of CH3OH is 32 AND M of H2O is 18. (2 marks)
Ans: Moles of H2O = 40 / 18 = 2.2 moles
Moles of CH3OH = 5.5 / 32 = 0.17 mole
Therefore, mole fraction will be:
CH3OH = 0.17 / 2.2 + 0.17
CH3OH = 0.073
Ques: Find the mole fraction of sugar in 214. 2g sugar syrup. The sugar in the syrup is 34.2 g. (3 marks)
Ans: To find out the mole fraction of sugar in the syrup, we need to calculate the number of modes in the given solvent.
Here, the mass of the water is (2x1) + (1x16) = 18u.
Therefore, the mass will be 18 grams.
When the mass of water is 180 grams, the number of moles can be determined as:
n = n / m = 180 / 18 = 10.
Now, the mole fraction of sugar is the division of the number of moles of sugar by the total number of moles.
The total number of moles = number of moles of water + Number of moles of sugar.
Total number of moles = 0.1 + 10 = 10.1
Therefore, mole fraction of sugar = 0.1 / 10.1 = 9.90 x 10³
Ques: Calculate the mole fraction of each gas of a tank charged with a mixture of 1.0 x 103 mol of oxygen and 4.5 x 103 mol of helium. (3 marks)
Ans:We know that,
NHe = 4.5 x 103
NO2 = 1.0 x 103 mo
Now, the mole fraction can be calculated through the simple formula of division:
XHe = 4.5 x 103 mol / (4.5 x 103 mol + 1.0 x 103 mol)
XHe = 4.5 mol / 5.5 mol
XHe = 0.82
XO2 = (2.0 x 103 mol / (4.5 x 103 mol + 1.0 x 103 mol)
XO2 = 1.0 x 103 / 5.5 x 103
XO2 = 0.18
Ques: Distinguish between molarity and molality of a solution. (3 marks)
Ans: Molarity is the number of moles of solute dissolved in 1 litre of solution. It is dependent on temperature.
M = ω×1000/mol.mass ×V
While molality is the number of moles of solute dissolved in 1 kg of the solvent.
m = ω×1000/M2×W
The relationship between the morality and molality is:
m = M/ (d−MM2/1000)
When molality = morality we get,
1 = M/ (d−MM2/1000) or, d - MM2/1000 = 1
Therefore, d = 1 + MM2/1000
Molarity is temperature dependent, while molality is not. For very dilute solutions, MM2/1000 can be neglected in comparison to 1. Thus, molality can be equal to molarity when density d = 1. Molality is independent of temperature, whereas molarity is function of temperature as volume depends on temperature and mass does not.
Ques: Calculate the mole fraction of acetone in the solution that contains 1 mole of benzene, , 2 moles of carbon tetrachloride, and 7 moles of acetone. (3 marks)
Ans: Mole fraction of acetone is 0.7
Therefore, number of moles of acetone = 7
Total number of moles in the solution = number of moles of benzene + number of moles of carbon tetrachloride + number of moles of acetone
1 mole + 2 moles + 7 moles = 10 moles
Mole fraction of acetone = (number of moles of acetone)/ (total number of moles in the solution)
= 7 moles/ 10 moles
Mole fraction of acetone = 0.7
Mole fraction of benzene = 1 mole/ 10 moles = 0.1
Mole fraction of carbon tetrachloride = 2 moles / 10 moles = 0.2
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