# Molality | Defintion, Units, Calculation, Origin, Examples

## Definition of Molality

The molality of a solution is the moles of solute divided by the kilograms of solvent. A solution that contains 1.0 mol of NaCl dissolved into 1.0 kg of water is a “one-molal” solution of sodium chloride. The symbol for molality is a lower-case m written in italics.

A final way to express the concentration of a solution is by its molality.

m=moles of solute /kilograms of solvent=mol/ kg

• In electrolyte solutions, it is common to distinguish between the solvent (usually water) and the dissolved substance, or solute, dissociating into ions. For these solutions, it is helpful to express composition in terms of molality, designated as m. Because a unit proportional to the number of undissociated solute molecules (or the number of ions) per 1,000 grams of solvent. The number of molecules or ions in 1,000 grams of solvent usually is huge. And the molality is defined as the number of moles per 1,000 grams of solvent.
• The molalitiy is also sometimes referred to as molal concentration. It is usually denoted by the letter “m.”
• The concept of molality was framed as a relation to molarity which is described as the molar concentration of a solution.
• The use of this property was first recorded in the publication authored by G. N. Lewis and M. Randall in 1923.
• You have to remember that molality is used to measure the moles in relation to the mass of the solvent and not the mass of the solution.
• Sometimes, there are also instances where the solutions contain more than one solvent. In such cases, we consider or define the molality of the mixed solvent. Alternatively, the units are expressed as mole solute per kilogram mixed solvent. Because, change in temperature will not affect this unit of concentration.

## How Molality Differs from Molarity

• Molality differs from molarity only in the denominator.
• Molality is based on the kilograms of solvent, while molarity is based on the liters of solution. Concentrations expressed in molality are used when studying the properties of solutions related to vapor pressure and temperature changes. The molality is used because its value does not change with temperature changes. And, on the other hand, it is slightly dependent upon temperature.
• Compared to molar concentration or mass concentration, to preparing a solution of a given molality is easy because, it requires only a good scale. And the both solvent and solute are massed rather than measured by volume. In many weak aqueous solutions, the molarity and molalitiy are similar because one kilogram of water (the solvent) occupies one litre of volume at room temperature. And the small amount of solute has little effect on the volume of the solvent.

## Relation Between Molality and Molarity

1/m = d/M − Ms /1000

Where

m=molality of Solution

M=Molarity of Solution

d=Density of solution in g/ml

Ms =Molar Mass of solute

## Units of Molality

The SI unit of molality is moles per kilogram (mol/kg).

For example; A solution whose molality is given as 6 mol/kg is stated as 6 molal or 6 m.

## Origin of Molality

• The term molality is formed in analogy to molarity which is the molar concentration of a solution.
• The earliest known use of the intensive property molalitiy and its adjectival unit, the now-deprecated molal, appears to have been published by G. N. Lewis and M. Randall in the 1923 publication of Thermodynamics and the Free Energies of Chemical Substances.
• Though the two terms are subject to being confused with one another, the molaliity and molarity of a dilute aqueous solution are nearly the same, as one kilogram of water (solvent) occupies the volume of 1 liter at room temperature and a small amount of solute has little effect on the volume.

• The primary advantage of using molality as a measure of concentration is that molaliity only depends on the masses of solute and solvent, unaffected by variations in temperature and pressure. In contrast, solutions prepared volumetrically (e.g., molar concentration or mass concentration) are likely to change as temperature and pressure change. This is a significant advantage in many applications because the mass, or the amount, of a substance is often more important than its volume (e.g., in a limiting reagent problem).
• Another advantage of molality is that the molaliity of one solute in a solution is independent of the presence or absence of another solute.
• Molality is one of the important properties of solutions. It is used to express the concentration of a solute in a solution and mainly depends on the mass of the solvent.

• It is not applicable in instances where there is no pure substance in a mixture.

For example, the mixtures such as water and alcohol or alloys are the examples. Here, anyone of the substance can be considered as the solvent.

## How to Calculate the Molality of a Solution

• It is easy to calculate molality if we know the mass of solute and solvent in a solution.
• Molality is an intensive property and is therefore independent of the amount being measured. This is true for all homogeneous solution concentrations, regardless of examining a 1.0 L or 10.0 L sample of the same solution. The concentration, or molality, remains constant.

## Examples

Here are some solved examples of molality

### Example-1

Determine the molality of a solution prepared by dissolving 28.60 g of glucose (C6H12O6) into 250. g of water.

Solution:

Step-1: List the known quantities and plan the problem.

Known: mass solute= 28.60 g C6H12O6

mass solvent = 250. g = 0.250 kg

molar mass C6 H12 O6 = 180.18 g/mol

Unknown: molality = ? m

Convert grams of glucose to moles and divide by the mass of the water in kilograms.

Step 2: Solve

28.60g C6H12O6 = 1mol C6H12O6 / 180.18g C6H12O6 = 0.1587 mol C6H12O6

0.1587 mol of C6H12O6 / 0.250kg H2O = 0.635m C6H12O6

The answer represents the moles of glucose per kilogram of water and has three significant figures.

Molality and molarity are closely related in value for dilute aqueous solutions because the density of those solutions is relatively close to 1.0 g/mL. This means that 1.0 L of the solution has nearly a mass of 1.0 kg.

As the solution becomes more concentrated, its density will not be as close to 1.0 g/ml, and the molality value will be different than the molarity. But solutions with solvents other than water, the molallity will be very different than the molarity.

### Example-2

Calculate the ‘m’ of a solution where 0.5 grams of toluene (C7H8 ) is dissolved in 225 grams of Benzene (C6H6).

Solution: Calculate the moles of the given solute.

Toluene – Molecular weight = C7H8 = 7 X 12 X + 1 X 8 = 92 moles / gram

Using the formula:

Moles of Toluene = Mass in grams / Molecular weight = 0.054 mole.

So, the mole of toluene is 0.054 mole.

Now calculate the kilogram of solvent.

225gramsofBenzene / 1000 = 0.225 kilogram

As the final step, calculate the molality using the formula.

m =Moles of Toluene / Mass of benzene in grams

m =0.054 moles / 0.225 kg

And, the Molality = 0.24 m

### Example-3

Find out the molality of a solution of glucose in water is labeled as 10% w/w,

Solution: 10% w/w solution of glucose in water means 10g of glucose is present in 100g of the solution i.e., 10g of glucose is present in (100 – 10)g = 90g of water.

The Molar mass of glucose (C6H12O6) = 6 × 12 + 12 × 1 + 6 × 16 = 180 g/mol

Then, number of moles of glucose = 10 / 180 mol = 0.056 mol

So, the Molality of solution = 0.056 mol / 0.09kg = 0.62 m