# Relation Between Molarity And Molality

## What Is Molarity?

Molarity is the concentration of a solution. It is also known as molar concentration. Molarity is the number of moles of solute per litre of solution. It is denoted by the symbol M. The formula is given below:

$$\begin{array}{l}Molarity = \frac{moles\, of\,solute}{liters\,of\,solution}\end{array}$$

## What Is Molality?

Molality can be defined as the number of moles of solute in one kilogram of solvent. It is denoted by the symbol m. The formula is given below:

$$\begin{array}{l}Molality = \frac{moles\, of\,solute}{kilograms\,of\,solvent}\end{array}$$

## Relation Between Molarity And Molality:

Let the mass of given solute be W.

Let the volume of the solution be V.

Let the molality be m.

Let the molar mass of solute be M’.

Let the Molarity be M.

Let the weight of the solvent be W’.

Therefore the Molarity,

$$\begin{array}{l}M = \frac{W}{M’}*\frac{1000}{V}………(1)\end{array}$$

Therefore the molality,

$$\begin{array}{l}m = \frac{W}{M’}*\frac{1000}{W’}…….(2)\end{array}$$

Density,

$$\begin{array}{l}d = \frac{M}{V}\end{array}$$
$$\begin{array}{l}= \frac{W+W’}{V}\end{array}$$

From (1)

$$\begin{array}{l}V = \frac{W*1000}{MM’} …………. (3)\end{array}$$

From (2)

$$\begin{array}{l}W^{1} = \frac{W*1000}{mM’}\end{array}$$

Therefore,

$$\begin{array}{l}W+W^{1} = W+\frac{W*1000}{mM’}\end{array}$$

$$\begin{array}{l}\left ( \frac{W * 1000 *M^{1}}{m^{1}*1000} \right ) + \left ( \frac{W * 1000}{mM^{1}} \right )\end{array}$$

$$\begin{array}{l}\frac{W * 1000}{M^{1}}\left ( \frac{M^{1}}{1000}+\frac{1}{m} \right ) …………(4)\end{array}$$

By dividing equation (4) by (3) we get,

$$\begin{array}{l}d = \left ( \frac{M^{1}}{1000}+\frac{1}{m} \right )M\end{array}$$

$$\begin{array}{l}\frac{d}{M} = \frac{M^{1}}{1000}+\frac{1}{m}\end{array}$$

$$\begin{array}{l}\frac{1}{m}=\frac{d}{M}-\frac{M^{1}}{1000}\end{array}$$

Hence the relation between molality and Molarity proved.

### Practice questions on molarity and molality:

1. 15.0 g of NaOH is dissolved in enough water to make a total of 224 mL of solution. Calculate the molarity.
2. Given, 123.2 gm of NaOH is dissolved in 1 kg of water.

Calculate the molality.