# Relation Between Molarity and Molality: Definition, Formula

The composition of a solution is described by the term 'Concentration'. Now, it depends on us whether we define it quantitatively or qualitatively. Like if we define it qualitatively, we would say that the solution is either dilute (less quantity of solute is present) or concentrated (more quantity of solute is present).

But there's a problem in defining the concentration of a solution qualitatively, like what should be the minimum amount of solute for the solution to be called the concentrated or maximum amount of solute present in the solution for it to be called dilute.

So, in order to solve this problem, we have to define concentration quantitatively. For example, molarity and molality are two concentration terms.

MOLARITY – It is defined as the number of moles of solute per litre of the solution. MOLALITY – It is defined as the number of moles of solute per kilogram of the solvent. ## Relation between molarity and molality a = number of moles of solute

V = volume of solution in a litre m = molality

a = number of moles of solute

W1 = mass of solvent

Therefore, a = m(W1) -----(2)

Putting (2) in (1), we get

C=mW1V  ----(3)

W1 = (mass of solution) – (mass of solute)

W1=d ×V-a ×M1000 ----(4)

Where M = molar mass of solute

d = density of the solution

Putting (4) in (3), we get

C=mVd×V-a×M1000

m=C×Vd×V-a×M1000

m=C×VVd-a×M1000V

Now putting a/V = C in the above equation

m=C×1d-C×M1000

m=1000C1000d-C×M

Where C = molarity

d = density of solution

M = molar mass of solute

Some questions on molarity and molality

Q1) Why molality is preferred over molarity?

Molality is defined as the number of moles of solutes that are present in 1kg solvent. We know that mass is independent of temperature. Therefore, if there is any change in temperature, then molality remains the same.This is why molality has a preference over molarity.

Q2) What are the S.I. units of molarity and molality?

Molarity is the number of moles of solute per litre of solution. Therefore, its S.I. unit is mol/lt. Whereas molality is the number of moles of solute per kg of solvent, therefore, S.I. unit of molality is mol/kg.

Q3) Which has more concentration: 1M or 1m?

1M means 1 molar solution, which contains 1 mole of solute in a 1-litre solution and that 1-litre solution consists of both solute and solvent. On the other hand, 1m means 1 molal solution, which contains 1 mole of solute in 1 kg of solvent, which is around 1-litre solvent. Now, we can clearly see that 1m solution contains more quantity of solvent as compared to 1M solution, and both has 1-mole solute. Therefore, 1M has more concentration as compared to 1m.

Q4) How molarity is dependent on temperature?

We know that molarity is the number of moles of solute per litre of solution, and when we increase the temperature, we also have an increase in volume. Therefore, the molarity decreases, and this way, molarity is dependent on temperature.

Q5) Which of the following depends on pressure: molality or molarity?

Molality depends only on the mass of the solvent, but molarity is dependent on the volume of solution, and volume can be changed through a change in pressure and temperature. Also, therefore unlike molality, molarity is dependent on pressure.

Q6) If we are working with a range of temperatures, then which is more preferable: molality or molarity?

We know that molality does not change with a change in temperature. Therefore, molality will be more convenient to use when working with a range of temperatures.

Q7) Which is the S.I. unit of mole fraction?

This is unitless because it is the ratio of moles to moles which too are individually unitless.

Q8) What is normality?

Normality is also a way that is used to calculate the concentration of a solution. It is equal to the gm equivalent weight of solute per litre of the solution. Its S.I. unit is eq/lt. 'N' stands for normality.

Q9) What do you mean by 1 to 3 dilution?

1:3 dilution means that you have 1 unit volume of solute and 3 unit volume of solvent, and when both are combined, then a solution of 4 unit volume is produced.

Q10) What is meant by 2% w/w and 5% w/v solution?

2% w/w - It means that in 100 grams solution, 2 grams of solute is present.

5%w/v– It means that in 100 ml of solution, there is 5 grams of solute.

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