Molality

Molality definition can be given as the concentration of the substance essential in our everyday lives. Household items, like mouthwash, rubbing alcohol, bleach and multiple different products can have different concentrations of their active ingredients. When we buy products, we at times take the concentration of an active ingredient into consideration, such as when buying a skin-treating astringent; it is either 1% or 2% of the salicylic acid, so we make our choice based on how sensitive our skin is.

Also, chemists have to be aware of the concentration of solutions they use during aboratory procedures. One of the ways concentration can be expressed through molality. Molality is symbolized by a small' m,' which is given as the number of moles of solute per kilogram of solvent. This is the simple molality definition.

What is Molality?

The number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent is known as molality. The definition of molarity, on the other hand, is based on a certain volume of solution.

Molality Formula

The ratio of the moles of solute to a kilogram of a solvent is given as molality. The SI unit of molality is given as moles per kilogram of solvent. The Systeme International d'Unites of units, the National Institute of Standards & Technology, US authority on the measurement, considers the term "molal" and thus the unit symbol "m" to be obsolete, and suggests moles/kg or a related unit of the SI. So,

$Molality \left ( M \right ) = \frac{Number \ of \ moles \ of \ solute}{Mass \ of \ solvent \ in \ kgs} \\ Molality \left ( M \right )= \frac{g\times 1000}{W\times m}$

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Molality of a Solution

When there are multiple solvents in a solution, the mixed solvent's molality is treated as a pure pseudo-solvent. Rather than the mole solute per one-kilogram solvent as within the binary case, units are determined as mole solute per one kilogram mixed solvent. Molality is not as common as its counterpart molarity, but it is utilized in very specific calculations, most notably involving the colligative properties.

The primary objective of this article is to develop skills to convert the measurement of concentration from one measurement type to the other.

Molarity vs. Molality

Let us look at how molarity and molality differentiate in detail. To define Molarity and molality, they both are measures of concentration of a chemical solution. Molarity is defined as the ratio of moles to solution volume (mol/L), whereas molality is defined as the ratio of moles to solvent mass (mol/kg). Most of the time, it does not matter which unit of concentration that you use. However, molality is preferred when the solution will undergo temperature changes because altering temperature affects volume (thus by changing the concentration if molarity is used).​

Molarity is also referred to as molar concentration. It is given as the number of moles of a substance per one litre of solution. Solutions that are labelled with the molar concentration are denoted with a capital 'M.,' Whereas a 1.0 M of solution contains 1 mole of solute per one litre of solution.​

The number of moles of solute per kilogram of solvent is known as molality. It is also important that the mass of solvent can be used and not the mass of the solution. Solutions that are labelled with molal concentration are denoted with a lowercase 'm.,' Whereas a 1.0 m solution contains 1 mole of solute per one kilogram of solvent.​

For aqueous solutions (solutions where water is present as the solvent) near room temperature, the difference between the molal and molar solutions is negligible. This is because water has a density of 1 kg/L at room temperature. It means the "per L" of molarity is equal to the "per kg" of molality.

For a solvent like ethanol, where the density is given as 0.789 kg/L, a 1 M solution would be given as 0.789 m.

The most important part of remembering the difference is:

• molality - m → moles per one kilogram solvent

• molarity - M → moles per one litre solution

Converting Molarity to Molality

• The number of moles of solute per litre of solution is known as molarity. ($\frac{n}{v}$)

• The amount of moles of solute per kilogramme of solvent is known as molality. (n/m)

• To convert molarity to moles of solute, multiply the molarity by the volume of the solution, then divide by the mass of the solution to get molality.

• Of fact, you can generally reduce this even more by remembering that (D = m/v), which means that molality equals the molarity divided by the density of the solution.

Molarity, Molality, Normality

Let us look at more about molarity, molality and normality.

Molarity is defined as the number of moles of the solute, which is dissolved per litres of the solution. It is represented by the symbol 'M' and is given as:

$M = \frac{Mass \ of \ the \ solute}{Volume \ of \ the \ solution \ in \ litres}$

The unit of Molarity is given as mol/L.

Molality is defined as the number of moles of solute, which is dissolved in 1 kg of the solvent. It is represented by the symbol 'm' and can be given as:

$M = \frac{Moles \ of \ solute}{Weight \ of \ the \ Solvent \ in \ Kilogram}$

The unit of molality is given as mol/kg.

Normality is defined as the number of grams equivalent to the solute, which is dissolved per litre of solution. It can be denoted by N and is given as:

$Normality\left ( N \right ) = \frac{Number \ of \ equivalents\ of \ solute}{Volume \ of \ the \ solution}$

The unit of Normality is gram equivalent per one litre.

Same as molarity, normality relates the amount of solute to the total volume of the solution; however, normality (N) is specifically used for both acids and bases.

Calculating Normality from Molarity

The mole equivalents of either an acid or base can be calculated by determining either the number of H+ or OH- ions per one molecule. It is determined as:

N = n x M (where n is given as an integer)

For an acid solution, n is given as the number of H+ ions, which are provided by a formula unit of acid.

Example

A 3 M of H2SO4 solution is similar to a 6 N H2SO4 solution.

For a basic solution, n is given as the number of OH- ions that are provided by a formula unit of base.

Example

A 1 M of Ca(OH)2 solution is similar to a 2 N Ca(OH)2 solution.

Note that a solution's normality is NEVER less than its molarity!

Solved Examples

Problem 1

A solution can be prepared by dissolving 10.2gms of glucose, C6H12O6, in 405 gms of water. The solution's final volume is stated as 414mL. Then, find the concentration of the solution in units of molality.

Solution

The Molality formula can be given as:

$Molality\left ( M \right ) = \frac{Moles \ of \ solute}{Kilograms \ of \ Solvent}$

First, let us start by finding the moles of glucose, which we have. The molar mass of glucose can be given as follows:

$10.2 \ gms \ of \ glucose\times \frac{1 \ mole \ of \ glucose}{180.16 \ gms \ of \ glucose}= 0.0566 \ moles \ of \ glucose$

Now, convert the grams of water into kilograms, which can be done as:

$405 \ gms \ \times \frac{1 \ kilogram}{1000 \ gms}= 0.405 \ kg$

After that, plug in the moles of glucose and kilograms of water into the molality equation. It can be shown as follows:

$Molality = \frac{0.0566}{0.45}= 0.14 \ m$

Problem 2

A solution of hydrogen peroxide is given as 15.2% by mass. Find the molarity of the solution if it is assumed that the solution contains a density of 1.01g/mL?

Solution

First, let us start by assuming that we contain 1.00L of this solution. And, recall that hydrogen peroxide contains a molecular formula of H2O2.

Now, use the given density to find the mass of the solution.

$1.00 l \times \frac{1000 \ ml}{1 \ l}\times \frac{1.01 \ g }{ml}= 1010 \ g$

Then, find the mass of hydrogen peroxide that is present in the solution.

1010 g (0.152) = 153.52 g.

Now, convert the mass of hydrogen peroxide into the moles of hydrogen peroxide.

153.52 g of H2O2 $\times\frac{1 \ mole \ of \ H_2O_2}{31.04 \ g \ H_2O_2} = 4.92 \ moles \ of \ H_2O_2$

Now, recall how to find the molarity of a solution as:

$Molarity = \frac{Moles \ of \ the \ solute}{Litres \ of \ Solution}$

Since we have 1.00L of the solution, the molarity is given as 4.95M.

Advantages of Molality

• Molality only depends on both the masses of solvent and solute as it is given as the measure of concentration. And it is unaffected by variations in both pressure and temperature. This is an advantage of molality. Volumetric solutions, on the other hand, are more likely to alter when pressure and temperature vary.

• Another advantage of the molality is given as the proven fact that the molality of one solute during the solution is completely independent of either the presence or absence of the other solutes.

Conclusion

Molality is given as a property of the solution. It is defined as the number of moles of solute per one kilogram of solvent. The SI unit of molality is mol/kg. A solution having a molality of 3 mol/kg is often defined as either “3 molal” or “3 m.” However, the SI system of units, mol/kg or a related SI unit is preferred now. Since the volume of the solution is completely dependent on pressure and ambient temperature, its mass can be more relevant for measuring solutions. In such cases, morality is the appropriate measurement.