How to convert molarity to molality? – (Molarity to Molality)
The concepts of molarity and molality, although distinct, are profoundly interrelated.
These are two different ways of expressing the concentration of a chemical solution. Together, these are helpful in finding a balance between the moles and masses of substances.
In this article, we will teach you all the tips and tricks to find the molality of a solution if its molarity is given.
However, before that, let us first revise some basics.
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 prepare a homogenous solution.
Molarity is defined as the moles of solute dissolved per liter of the solution.
A 1 molar solution of substance X is prepared by dissolving 1 mole of X in a litre of the solution.
1 L = 1000 mL
Units of molarity are mol/L or M.
What is molality?
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
Units of molality are mol/kg or m.
How to convert molarity to molality? –Example
As discussed above, the number of moles of solute is the common factor between the molarity and the molality formula. Therefore, here is how we can convert molarity into molality:
For example,find the molality of 10 M aqueous solution of H2SO4 given that the density of the solution is 1.84 g/mL.
Solution
Step I:Use the given density to find the mass of the solution. Take volume = 1 L = 1000 mL.
∴ Density = Mass/Volume
∴ Mass of the solution = density x volume = 1.84 x 1000 = 1840 g
Step II:10 M solution means 10 moles of solute dissolved per liter of the solution. Use this concept to find the mass of the solute.
∴ Moles = mass/molar mass
∴ Mass of H2SO4 = moles x molar mass = 10 x 98.079 = 980.79 g
Step III: Find the mass of the solvent (H2O in this case) by subtracting the mass of H2SO4 from that of the solution.
∴ Mass of H2O in the solution = 1840 – 980.79 = 859.21 g
The calculation so far shows that 10 moles of H2SO4 are dissolved per 859.21 g of water.
Step IV: Find the molality, i.e., the moles of solute dissolved per kg of water.
10 moles H2SO4 in 859.21 g water
Moles of H2SO4 per gram of water = 10/859.21
∴ Moles of H2SO4 per 1000 g water = (10/859.21) × 1000 = 11.6 molal
Result: The molality of 10 M aqueous solution of sulfuric acid is 11.6 mol/kg.
In short, the direct formula to convert molarity to molality is:
Nevertheless, you must take into account what sort of information is provided in the question statement and solve it accordingly.
Let’s see some other examples.
More Examples of converting molarity to molality
Calculate the molality of a 1.75 molar solution of glycerin (C3H8O3) with a density of 1.45 g/cm3.
Solution
1 cm3 = 1 mL therefore, the given density is 1.45 g/mL.
Finding the mass of 1 liter of solution:
∴ Density = mass/volume
Mass = 1.45 x 1000 = 1450 g
Find the mass of the solute:
∴ Moles = mass/molar mass
Mass of glycerin in the solution = 1.75 x 92.093 = 161.2 g
Calculating the difference between the mass of solution and that of solute:
Mass of solvent = 1450 – 161.2 = 1288.8 g
Applying the molality formula and substituting the known values:
Result: The molality of 1.75 molar solution of glycerin is 1.36 mol/kg.
Convert from molarity to molality a NaCl (MW = 58.44 g/mol) solution that has a concentration of 0.736 M and a density of 1.25 g/mL.
Solution
Finding the mass of 1 liter of solution:
∴ Density = mass/volume
Mass = 1.25 x 1000 = 1250 g
Finding the mass of the solute:
∴ Moles = mass/molar mass
Mass of NaCl in the solution = 0.736 x 58.44 = 43.0 g
Calculating the difference between the mass of solution and that of solute:
Mass of solvent = 1250 – 43 = 1207 g
Applying the molality formula and substituting the known values:
Result: The molality of 1.75 molar NaCl solution is 0.61 mol/kg.
FAQ
How can I convert molarity into molality?
The following formula is used to convert molarity into molality:
Why is the molality of a solution always larger than its molarity?
It is not necessary that molality is always greater than the molarity of a solution (as can be seen from the examples provided in this article).
Both are two separate ways of measuring the concentration of a solution.
Molarity is moles of solute per liter of solution. In contrast, molality is moles of solute per kg solvent.
Which of the two is temperature dependent? – Molarity or Molality?
Molarity is temperature dependent as it is determined in terms of volume, and volume is directly proportional to temperature.
Contrarily, molality is calculated using the mass of a solute thus, it is not affected by changes in temperature.
Under what conditions molarity and molality are identical?
If the density of a solvent is exactly equal to 1 g/mL, the difference in molarity and molality will be minimal.
However, it is only a rough approximation as other factors may also intervene.
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
Topblogtenz is a website dedicated to providing informative and engaging content related to the field of chemistry and science. We aim to make complex subjects, like chemistry, approachable and enjoyable for everyone.
