Relation Between Molarity and Molality: Molarity, Molality, Relationship, Differences, Practice problems, FAQs: 

There is a group of 40 boys and 60 girls. You are asked to quantify their weight. One way is to measure their weight straight, average out for boys and girls and say as a ratio.

Instead, allow them to eat freely and find the average weight of boys and girls as before and compare them as a ratio. Do you think that the two ratios will be the same? It will not. Because eating capacity changes with the individual and hence the weight of an individual will vary greatly and cannot be considered standard. This time the ratio changes with the eating capacity also.

In the same way, there are two ways of quantifying substances in a mixture. One method is independent of the temperature at which it will be measured while the other is dependent on the temperature of measurement. Both are useful for specific circumstances.

Come let us see the two methods of expressing concentrations of components of a mixture.

Table of Content

• Molarity
• Molality
• Molarity and Molality - Relationship
• Molarity and Molality- Differences
• Practice Problems
• Frequently Asked Questions

Molarity

The amount of a substance in a specific volume of solution is known as its . in other words it is defined as, the number of moles of a solute per litre of a solution is known as molarity. The molar concentration of a solution is another name for molarity. Molarity is temperature-dependent. 

It varies inversely with temperature. 

Molarity ()

Mathematically this term is expressed as 

For instance, if one mole of salt was dissolved in one litre of water, the resulting solution would not be. (read as "one molar"). The volume would be measured after the solution has been thoroughly mixed. Number of moles present in a solution divided by the total volume of the solution in litres, to determine the molarity.

The quantity of a substance dissolved in a given mass of solvent is known as its molality (m), also known as molal concentration. In other words, it can also be defined as the moles of a solute dissolved in one kilogramme of a solvent. Molality is temperature independent. 

Mathematically this term is expressed as

For instance, if one mole of sugar was added to one litre of water, the resulting solution would not be . The mass would be measured after the solution has been thoroughly mixed. The number of moles of the solute dissolved is divided by the total mass of the solvent used for dissolving the solute to determine the molality.

Molarity and Molality - Relationship

Both molarity and molality are very useful concentration expressions. They can also be related to the density of the solution for converting one to the other. The derivation of the relationship is given below.

Assume the given solute has a mass of W1 g = .

The solute has a molar mass of .

The solvent is assumed to weigh .

Then, allow the volume of the prepared solution to be .

We know that 

According to the above formula molarity can be expressed as

Similarly,

From equation (2) we get

……………(4)

From equation (3) we get

Density,

Now,

Let’s multiply and divide by 1000 x on both numerator and denominator of

Substituting the value of and of V from equation (4) in the density formula we get,

Density of solution ()

The above equation gives the relationship between molarity and molality

Molarity and Molality - Differences

Parameters	Molarity	Molality
Definition	The number of moles of a solute per litre of a solution is known as molarity. The molar concentration of a solution is another name for molarity.	Molal concentration is another name for molality. It is a measurement of a solution's solute concentration. The number of moles of a solute dissolved per Kg of solvent is known as molarity
Measure	Concentration of solution	Concentration of solution
Representation
Formula
Temperature dependency	Molarity is temperature-dependent.  It varies inversely with temperature. Molarity ()	Molality is temperature-independent.
Unit

Practice Problems

 Q1. Calculate the molality of the solution if the density of the solution is .

1. m
2. 
3. m
4. m

Answer: (B)

Solution: We know, density of solution () =

Molar mass of =

=

= 0.12 +

= 1.21 - 0.12

=

Hence, correct option is (B).

Q2. Find molality of an aqueous solution of glucose having mole fraction and density of solution is 1.1  

Answer: (A)

Solution:

Molar mass of solute () = 180

Molar mass of solute () = 18

Solution: We know, Mole fraction ( ) =  

=  

Molality

Q3. Which of the following will change with an increase in temperature?

1. Molality
2. Molarity
3. Both of these
4. None of these

Answer: (B)

Solution: 

Molarity is temperature-dependent. it varies inversely with temperature. 

mathematically: Molarity ()

Q4. What is the unit of molarity?

Answer: (A)

Solution: The amount of a substance in a specific volume of solution is known as its . in other words it can also be defined as, The number of moles of a solute per litre of a solution is known as molarity. The molar concentration of a solution is another name for molarity.

Mathematically this term is expressed as 

Hence, the unit of molarity =

Frequently Asked Questions

Q1. Is it possible to convert any solution's molality into molarity without first knowing its density?

Answer: No, density is necessary for the conversion of molality into molarity or molarity into molality. While molality is only mass-dependent, molarity depends on volume as well.

The density of solution () =

Q2. Can we consider an infinitely diluted solution's molarity to be equal to its molality?

Answer: Yes. We can take into account molarity = molality for an extremely diluted aqueous solution to maintain numerical simplicity. 

Water has a known density of . Thus, the weight of the solute becomes very small for very dilute solutions (negligible). The volume of the solution now equals . You can consider the weight of the solution to be the solvent's weight.

Q3. What distinguishes density from specific density?

Answer: Material-specific densities are calculated in relation to water. It is therefore absolute and unitless. density measured in grammes per litre or other units.

Q4. Does temperature have an impact on mole fraction?

Answer: No, the mole fraction is unaffected by temperature. We can determine the mole fraction of any component by measuring the masses of the solute and solvent.

Q5. How can the concentration of a solution be altered?

Answer: A worker might occasionally need to change the concentration of a solution by changing the amount of solvent. When a solvent is added to a solution, the concentration of solutes in the solution is diluted. Concentration involves the removal of solvent, which raises the concentration of solutes in the solution.

Q6. How do you make a solution with a known concentration?

Answer: It is possible to prepare solutions with known concentrations by either dissolving a known mass of the solvent solution and diluting it to the desired final volume or by diluting the acceptable volume of the more concentrated solution to the desired final volume (the stock solution).

Related Topics:

Volume strength of	Mole
Strength of oleum	Normality
Strength of solution	Density