Molarity and Molality - Important Concepts for JEE

The vast majority of laboratory reactions take place in solutions. In most cases, two components are present in solutions. The one in lower concentrations is known as the solute, while the one in higher concentrations is known as the solvent. The concentration of a solute in a given amount of solvent is expressed in terms of volume. For example, salt water is a solution made up of water (the solvent) and salt (the solute). A solution's concentration is the amount of dissolved substance. In other words, it refers to the amount of stuff mixed into your liquid. There are various ways to describe the concentration which include molarity, molality, normality, mole fraction, and so on. In this article, we mainly focus on molarity and molality.

Molarity

What is molarity? The number of moles of solute per liter of solution is defined as a solution's molarity. A capital M denotes molarity. The molarity of a solution is unaffected by the type of reaction the solute undergoes. Molarity is measured in mol/L.

By increasing the volume of a solution, the temperature can alter its molarity.

We can say that the molarity of a solution is affected by temperature, volume, the addition of more solutes, and the stability of a solute.

Molarity formula

$\text { Molarity }(M)=\dfrac{\text { no. of moles of solute }}{\text { volume of solution in } L}$

As we know, 

$\begin{align} &\text { Moles }=\dfrac{\text { mass }}{\text { molar mass }} \\ &\text { Molarity }(M)=\dfrac{\text { mass of solute }(W)}{\text { molar mass of solute }(M)} \times \text { volume of solution }(V) \\ &\quad\quad\quad\quad\quad\quad=\dfrac{\text { mass of solute } \times 1000}{\text { molar mass of solute } \times V(m L)} \end{align}$

The units of molarity are $\dfrac{mol}{L}$ or $\dfrac{mol}{dm^3}$

If we have % by mass and specific gravity or density, the molarity is calculated by the expression,

$M=\dfrac{\% \text { by weight } \times \text { specif ic gravity } \times 10}{\text { molar mass }}$

In case of dilution,

M₁V₁=M₂V₂

where M₁V₁ are respectively the molarity and volume before dilution and M₂V₂ are molarity and volume after dilution. The molarity of a solution is temperature-dependent because the volume of a solution is temperature-dependent.

Molality

The molality of the solution is a another way to express its concentration. The molality (m) of a solution is the number of moles of solute upon the mass of the solvent. A 1.0 mol sodium chloride solution contains 1.0mol of NaCl dissolved in 1.0kg of water. Molality is represented by a lower-case m in italics. Unit of molality $=\dfrac{mol}{Kg}$

Molality equation:

$\begin{align} &\text { Molality }(m)=\dfrac{\text { no. of moles of solute }}{\text { mass of solvent in } \mathrm{kg}} \\ &m=\dfrac{\text { mass of solute } \times 1000}{\text { molar mass of solute } \times \text { mass of solvent in } g} \end{align}$

The only difference between molality and molarity is in the denominator. Molality is measured in kilograms of solvent, whereas molarity is measured in liters of solution. When studying the properties of solutions related to vapour pressure and temperature changes, concentrations expressed in molality are used. Molality is used because its value does not vary with temperature.

Molality and molarity have a close relationship in value for dilute aqueous solutions because their density is close to $1.0~\dfrac{g}{ml}$. This means that 1.0L of solution weighs nearly 1.0kg. As the solution becomes more concentrated, its density will not be as close $1.0~\dfrac{g}{ml}$ and the molality value will differ from the molarity. For solutions containing solvents other than water, the molality will be very different from the molarity.

Because it is unaffected by temperature and pressure changes, molality is a more precise and accurate method of determining concentration. 

Difference Between Molarity and Molality

There is a basic difference in molarity and molality are given below:.

1. Molarity is a substance's concentration calculated as the number of moles of solute dissolved in 1 liter of solution, whereas molality is a substance's concentration calculated as the number of moles of solute found in one kg of the solvent of the solution.

2. M is the symbol for molarity, while m is the symbol for molality (sometimes written as –m to distinguish it from mass).

3. The molarity formula is moles per liter, whereas the molality formula is moles per kilogram.

4. Molarity is affected by temperature changes, whereas molality is unaffected by temperature changes.

5. Changes in pressure affect molarity, but not molality.

6. Molarity can lead to imprecise and inaccurate concentration measurements, whereas molality leads to accurate and precise concentration measurements.

Some Important Points

• Because 1 litre of water weighs 1 kg, the molarity and molality of water may be the same, but this may not be the case with all liquids. This means that when it comes to colligative properties, molality must be used.

• Molality is more accurate and provides greater concentration precision, but it takes longer to prepare because the solute must be added to the weight of a solvent. If the solvent is liquid, it must be weighed.

• Because molarity involves a liquid, the concentration can change. This is since the volume of a liquid can change with changes in temperature and pressure.

• Because it is unaffected by temperature and pressure changes, molality is a more precise and accurate method of producing a specific concentration.

• This can be accomplished using a gravimetric system and an analytical balance to weigh the solvent.

Relationship Between Molarity (M) and Molality (m)

Molarity of solution (M ) means M moles of the solute are present in 1000 ml. of the solution. If the density of the solution is d =ML^-1, the mass of the solution = 1000 d gram

$\text { Mass of solute }=M M_{2}\left(M_{2} \text { is the molar mass of the solute }\right)$

$\text { Mass of solvent }=1000 d-M M_{2} \text { gram }$

$\therefore \operatorname{Molality}(m)=\dfrac{M}{1000 d-M M_{2}} \times 1000$

$\begin{aligned} &m=\dfrac{M}{d-\dfrac{M M_{2}}{1000}} \\ &m\left(d-\dfrac{M M_{2}}{1000}\right)=M \\ &M\left(1+\dfrac{m M_{2}}{1000}\right)=m d \\ &M=\dfrac{m d}{1+\dfrac{m M_{2}}{1000}} \end{aligned}$

Conclusion

Concentration can be measured using both molarity and molality. The number of moles of a solute dissolved in one litre of solution is defined as molarity. Molality is the number of moles of a solute dissolved in one kilogram of a solvent. molarity is temperature-dependent whereas molality is independent of temperature.