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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. Any mixture of one or more solutes that have been dissolved in a solvent is referred to as a solution.
- A mole fraction is used to measure the concentration of the solution.
- The amount of solute that has been dissolved in a specific volume of solvent or solution is measured by the solution's concentration.
- A solution that contains a significant amount of dissolved solute is said to be concentrated.
- A solution is said to be dilute if it only contains a little amount of dissolved solute.
| Table of Content |
Key Terms: Mole Fraction, Solutions, Atoms, Molecules, Molality, Molarity, Solute, Mass Fraction
What is Mole Fraction?
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Mole fraction can be generated through various concentrations of molecules, including molarity, morality, and mass percent compositions. Mole is used in chemistry as a standard unit for measuring larger quantities of very small particles such as atoms and molecules, and other particles. The mole is designated for the number of units valued at 6.02214076 × 1023.
When two reactive components are combined, the ratio of the two components can be calculated if the mole fraction of each solvent is known. 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.
Solutions Video Lecture
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| Relevant Concepts | ||
|---|---|---|
| Elementary Reactions | Rate Determining Step | Surface Chemistry |
| Gay-Lussac’s Law | Dalton’s atomic theory | Critical temperature |
Mole Fraction Formula
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The mole fraction is denoted by the lowercase letter χ (chi), instead of the traditional Roman x.
Formula Related to Mole Fraction
Mole fraction is the division of molecules present in one mixture and the molecules present in all mixtures.
In mathematical terms,
| Mole fraction of a component = Number of Moles of the Component / Total Number of Moles of all Components. |
Formula of Mole Fraction Solute
Solute is a substance that, when dissolved in a solvent, creates a homogenous mixture.
| Mole fraction of solute = Moles of Solute / Moles of Solute + Moles of Solvent |
or
| \(\frac{n_A}{n_A + n_B}\) |
where,
Xa = Mole fraction of a substance
na = Number of moles of a substance
na + nb = Total moles in a solution
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.
- 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 the partial pressure of the mixture to the total pressure of the mixture.
- The mole fraction 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:
- The mole fraction is independent of 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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Some of the important quantities related to mole fraction are as follows:
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
\(\bar{M}\) = Average molar mass of the mixture.
2. Molar mixing ratio: The mixing of two or more ratios is called the 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.
Calculating Mole Fraction from Molality
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Mole fraction can be determined from the molality of a substance. By converting molality into the equivalent mole fraction, can yield the desired results.
Molality is the total moles of a solute contained in a kilogram of a solvent. It is also known as molal concentration.
Given:
| Molality = Moles Solute/kg Solvent |
therefore mole fraction can be determined through molality.
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Things to Remember
- Mole Fraction is used to determine the concentration of the solution.
- As opposed to molar concentration, mole fraction does not require information on the densities across the phases involved.
- When all components are considered, the sum of the mole fraction will always be equal to 1.
- Different molecules can have different masses, the individual fraction can also be different from the mass fraction.
- Mole Fraction is also known as amount fraction.
- The total number of moles of a solute present in one kilogram of a solvent is known as molality.
Previous Year Questions
- The vapour pressure of due to….[KCET 2012]
- Number of moles of ions which 1 mole of ionic compound produces...[NEET 2009]
- the boiling point of this solution will be….[NEET 2016]
- A 0.1 molal aqueous solution of a weak acid is...[NEET 2011]
- For an ideal solution, the correct option is….[NEET 2019]
- an aqueous solution of a protein contains its….[NEET 2011]
- Which solutions are mixed to form a buffer solution ?...[BHU UET 2000]
- The molecular weight of unknown organic substance will be:...[UPSEE 2017]
- At same temperature, which pair of the following solutions are isotonic solutions ?...[GUJCET 2006]
- The mass of oxalic acid present in 500 cc of the solution is….[COMEDK UGET 2009]
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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. (3 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. What are the properties of mole fraction? (5 Marks)
Ans. These are the mole fraction's primary characteristics:
- The temperature has no impact on a mole fraction.
- By considering the weight of the elements, a valid mixture of mole fractions can be created, unlike with other measuring techniques.
- In a mole fraction, the roles of "solute" and "solvent" are interchangeable because the measure is symmetric (x=0.1 and x=0.9).
- The mole fraction in ideal gases is the ratio of the mixture's partial pressure to its total pressure.
- In a ternary mixture, the mole fraction can be expressed as a component of functions.
Ques. Define Molality. (2 Marks)
Ans. The total number of moles of a solute present in one kilogram of a solvent is known as molality. It is sometimes also referred to as molal concentration.
Molality = Moles Solute/kg Solvent
Ques. What is the importance of the mole fraction? (2 Marks)
Ans. The ratio of the number of single component molecules (or moles) in the mixture to the overall number of molecules is known as the mole fraction (or moles). The mole fraction is helpful when two reactive components are combined because, if the mole fraction of each component is known, the ratio of the two components can be computed.
Ques. State the advantages of mole fraction. (3 Marks)
Ans. The advantages of mole fraction include:
- Temperature has no effect on the mole fraction.
- Calculating the mole fraction does not necessitate learning about the phase's density.
- The mole fraction of an ideal gas mixture is represented by the mixture's partial pressure to total pressure ratio.
Ques. Define mole percentage. (1 Mark)
Ans. Mole percentage is the result of multiplying the derived mole fraction by 100 to get a relative figure.
Ques: Find the mole fraction of sugar in 214. 2g sugar syrup. The sugar in the syrup is 34.2 g. (5 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. (5 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. (5 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. (5 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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