Mole fraction is a way of expressing the concentration of a chemical substance. It refers to determining the relative amount of one component in a mixture of components.
The mole fraction (X) of component A in a mixture containing three components (A, B, and C) is:
Where,
nA = Number of moles of component A
nB = Number of moles of component B
nC = Number of moles of component C
In this article, we will teach you how to calculate mole fractions under different situations. So, what are you waiting for?
Dive into the article and learn all you need to know about the concept of mole fractions.
The mole (mol) is a standard scientific unit. 1 mole is defined as the amount of a substance containing Avogadro number of particles, i.e., 6.022 x 1023.
The number of moles of a substance can be calculated by the formula:
∴ Moles (n) = Mass/Molar mass
If we know the number of moles of a substance, we can find its mole fraction by dividing the answer obtained by the total number of moles of all the substances in the mixture.
In this way, the mole fraction helps in determining the proportion of a specific substance in a mixture of substances. It is a ratio and, thus, a unitless entity.
In a homogenous solution containing a solute and a solvent;
How to calculate the mole fraction? – Examples
The mole fraction is calculated as per the data provided in the question statement. However, the most important part is to have the number of moles of each component in the given mixture.
For example, A gaseous mixture contains 2.2 moles He, 1.1 moles H2, and 4.2 moles N2. Calculate the mole fraction of N2 in this mixture.
Solution:
Result: The mole fraction of nitrogen in the gaseous mixture is 0.56.
Let’s see another example- A solution is prepared by dissolving 50 grams of ethanol (C2H5OH) in 100 grams of water. Calculate the mole fraction of each component.
Solution:
The two components in the solution are ethanol (solute) and water (solvent).
Also, mole fraction of water = 1 – mole fraction of ethanol = 1 – 0.16 = 0.84 and vice versa.
Result: The mole fraction of ethanol is 0.16, while that of water is 0.84 in the aqueous solution.
More Examples of calculating mole fraction
An aqueous solution of sodium chloride contains 7.5 moles of water. If 65 grams of NaCl is dissolved in water. Calculate its mole fraction.
Solution:
⇒ Moles of NaCl = Mass/Molar mass = 65/58.44 = 1.11
∴ Total number of moles of solution = 7.5 + 1.11 = 8.61
Result: The mole fraction of NaCl in the solution is 0.129.
Assuming that a gaseous mixture contains 7.8 grams N2, 2.1 grams O2, 0.90 grams Ar and 0.03 grams CO2, how do you calculate the mole fraction of each gas?
Solution:
As the mass of each gas present in the mixture is given in the question statement, thus we can find the number of moles of each gas as follows:
What is the mole fraction of cinnamic acid in a mixture that is 50% by weight urea in cinnamic acid?
Solution:
As per the question statement,
Urea present in cinnamic acid = 50% by weight or mass, which means 50 grams of urea dissolved in 100 grams of the mixture. Thus, we can first calculate the moles of urea as follows:
∴ Moles = Mass/Molar mass
Moles = 50/60.06 = 0.83
If the mixture contains 50 grams of urea (solute) in a total of 100 grams, thus there are 50 grams of cinnamic acid (solvent) present in it. Hence, the number of moles of cinnamic acid is:
Moles = 50/148.16 = 0.34
∴ Total number of moles of solution = Moles of solute + Moles of solvent = 0.83 + 0.34 = 1.17
Result: The mole fraction of cinnamic acid is 0.290.
A solution is prepared by mixing 100 mL of toluene with 300 mL of benzene. The densities of toluene and benzene are 0.867 g/mL and 0.877 g/mL, respectively. Assuming that the volume of the solution is equal to the sum of the volumes of two components. Calculate the mole fraction for toluene.
Solution:
The density of a substance is related to its mass by the formula given below:
Density = Mass/Volume
We can use this formula to find the mass of each component in the given mixture, from where we can determine the number of moles of each. Let us do that;
Mass of toluene = density x volume = 0.867 x 100 = 86.7 g
Mass of benzene = density x volume = 0.877 x 300 = 263.1 g
∴ Moles = Mass/Molar mass
Moles of toluene = 86.7/92.14 = 0.941
Moles of benzene = 263.1/78.11= 3.368
Total number of moles of the solution = 0.941 + 3.368 = 4.309
Result: Mole fraction of toluene = 0.941/4.309 = 0.218
FAQ
What is the mole fraction formula?
Mole fraction helps in determining the proportion of one component in a mixture of multiple components.
The general mole fraction formula is:
What is the effect of temperature on the mole fraction of a solution?
Mole fraction is temperature independent. There is no effect of temperature change on the mole fraction of a solution.
Why is the mole fraction unitless?
A mole fraction is a ratio where the number of moles of one substance is divided by the total number of moles in a mixture; hence, the mole fraction is a unitless entity.
How do you convert molality into mole fraction?
Molality = Moles of solute dissolved per kg (1000 g) of the solvent.Thus,
How do you calculate the mole fraction of a gas using partial pressures?
In a mixture of four gases, if the sum of the mole fractions of A, B, and C is 0.325, what is the mole fraction of gas D?
Ammara Waheed is a highly qualified and experienced chemist, whose passion for Chemistry is evident in her writing. With a Bachelor of Science (Hons.) and Master of Philosophy (M. Phil) in Physical and Analytical Chemistry from Government College University (GCU) Lahore, Pakistan, with a hands-on laboratory experience in the Pakistan Council of Scientific and Industrial Research (PCSIR), Ammara has a solid educational foundation in her field. She comes from a distinguished research background and she documents her research endeavors for reputable journals such as Wiley and Elsevier. Her deep knowledge and expertise in the field of Chemistry make her a trusted and reliable authority in her profession. Let's connect - https://www.researchgate.net/profile/Ammara-Waheed
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