How to convert molality to mole fraction? –(Molality to mole fraction)
Molality and mole fraction are two different ways of expressing the concentration of a chemical solution.
But do you know how we can use the molality of a solution to find the mole fractions of the respective solute and the solvent? Probably this is why you are here.
So, continue reading to learn everything about converting molality into mole fractions.
A solution consists of two parts, i.e., a solute and a solvent.
The solute is the minor component. It may be a solid, liquid or gas that dissolves in a major component, i.e., the solvent.
The solute particles get evenly distributed in the solvent to yield a homogenous solution.
Molality is defined as the moles of solute dissolved per kilogram of the solvent.
A 1 molal solution of substance X is prepared by dissolving 1 mole of X in a kilogram of the solvent.
1 kg = 1000 g
∴ Molality formula = Moles of solute/100 g solvent
Units of molality are mol/kg or m.
What is mole fraction?
The mole fraction helps in determining the proportion of a specific substance in a mixture of substances.
It is calculated by dividing the moles of one substance by the total number of moles of all the substances in the mixture.
In a homogenous solution containing a solute and a solvent;
How to convert molality to mole fractions? –Example
If we know the molality of a solution, we can easily find the mole fractions of the solute and the solvent by following thesimple steps given below.
Example- Calculate the mole fraction of H2SO4 in a 10 m aqueous solution of sulfuric acid.
Solution:
In this example, H2SO4 is the solute, while water is the solvent.
A 10 molal aqueous solution of sulfuric acid means that 10 moles of H2SO4 are dissolved completely in 1 kg (1000 g) of water.
Step I: Find the number of moles of 1 kg solvent
The solvent in this example is water, and the molar mass of water is 18.01 g/mol, so,
∴ Moles = mass/molar mass = 1000/18.01 = 55.52
Step II: Find the total number of moles of the solution
∴ Total moles = moles of solute + moles of solvent = 10 + 55.52 = 65.52
Step III: Find the mole fraction of the solute, dividing the moles of the solute by the total number of moles of the solution
∴ Mole fraction of H2SO4 = 10/65.52 = 0.153
Result: The mole fraction of H2SO4 in its 10 molal aqueous solution is 0.153.
In short, combining all the above steps into a single formula for converting molality into a mole fraction of solute is:
More Examples of converting molality to mole fractions
You have a homogenous solution of sodium chloride (NaCl) dissolved in water. Find the mole fractions of NaCl and H2O if the molality of the solution is 2.5 mol/kg.
Solution:
As per the question statement,
Solute = NaCl
Solvent = H2O
2.5 molal solution means 2.5 moles of NaCl are dissolved in 1 kg of water. Therefore, the mass of water is 1 kg (1000 g).
Finding the moles of water
∴ Moles = Mass/Molar mass
Assuming complete dissolution, find the mole fraction of naphthalene if it is a 0.5 molal solution of naphthalene prepared in benzene.
Solution:
As per the question statement,
Solute = Naphthalene (C10H8)
Solvent = Benzene (C6H6)
0.5 molal solution means 0.5 moles of naphthalene are completely dissolved in 1 kg of benzene. Therefore, the mass of benzene is 1 kg (1000 g).
What is the mole fraction of solute in a 2 molal solution prepared in acetic acid as the solvent?
Solution:
Let’s apply the short-cut formula to find the mole fraction of solute:
Result: The mole fraction of the given solute in 2 molal solutions is 0.107.
FAQ
How do you convert molality to mole fraction?
The molality of a solution can be converted into the mole fraction of the solute by using the formula given below:
Which of the following options provides the correct relationship between the molality (m) and mole fraction of the solvent? Here XA = mole fraction of solvent, XB = mole fraction of solute, and MA = molar mass of the solvent.
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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