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# Molarity, Molality, and Mole fraction-Relation Between Molarity-Molality, Interconversion of Mole Fraction-Molality

Sachin Tendulkar got bowled by an inswinger from Brett Lee or Virat Kohli got caught at slips by a doosra from Adil Rashid. I am sure you must have heard such talk by the commentator during a cricket match.

Or the fact that commentators usually are talking about “variations in bowling” such as yorker, outswinger, googly, slider, etc. Technically speaking, bowlers are releasing the cricket ball in distinct styles but each one of them has its own advantages.

Similarly, while dealing with chemical solutions, the relative proportions of two or more quantities in a mixture can be expressed in multiple ways. Each of these terms has its own advantages and it serves a different purpose according to one’s needs. So, naturally different concentration term is used in different chemical procedures.

• Molarity ()
• Molality ()
• Mole fraction ()
• Relation between molarity () & molality ()
• Relation between mole fraction () and molality ()
• Practice Problems

## Molarity

• Molarity is defined as the number of moles of a solute dissolved in 1000 or of the solution.
• The mathematical form of Molarity is =

=

• Molarity is temperature-dependent.
• It varies inversely with temperature.
• Mathematically: Molarity ()

Case 1: Calculation of molarity, when solution having molarity (), diluted from to

Initial molarity = , Final molarity =

Initial volume = , diluted to volume =

Case 2: Calculation of molarity when solution having molarity () & volume () mixed with a solution having the same solute with molarity () & volume ()

## Molality

• Molality is defined as the number of moles of a solute dissolved in 1000 or of the solvent.
• The mathematical form of Molality ) = =
• Molarity is temperature independent.

## Mole fraction )

The ratio of the number of moles of the solute or solvent present in the solution and the total number of moles present in the solution is known as the mole fraction of substances concerned.

Let, number of moles of solute in a solution = & number of moles of solvent in a solution =

Mole fraction () of solute =

Mole fraction () of solvent =

For Binary solution;

## Relation between molarity (M) & molality

is molality of solution

Weight of solute =

Weight of solvent =

Molar mass of solute =

Molar mass of solvent =

Molality () = —-------- (1)

Molarity () = —---------(2)

= —------- (3)

—------- (4)

Weight of solution = + = +

Density of solution () = = =

Density of solution () = = =

Relation between molality () & mole fraction ()

Let mole of solute present in 1000 of solvent

is molality of solution

weight of solute =

weight of solvent =

Molar mass of solute =

Molar mass of solute =

Mole of solute = =

Mole of solvent = =

Mole fraction of solute () = —-----(1)

Mole fraction of solute () = —-----(2)

Molality () = —------(3)

—---(4)

On dividing equation (1) and (2), we get

Mole fraction of solute () = = =

We know, +

= = —-----(5)

Put equation (4) in (5)

=

=

## Practice problems:

Q1. Calculate molality of solution if density of 1.5 M solution is 1.21.

1. 2.96 m
2. 1.85 m
3. 1.34 m
4. 1.73 m

Solution: We know, Density of solution () =

Molar mass of =

=

= 0.09 +

= 1.21 - 0.09

=

Q2. Find molality of aqueous solution of glucose having mole fraction 0.1 and density of solution is 1.1

1. 6.17 M
2. 3.85 m
3. 5.34 m
4. 4.73 m

Molar mass of solute () = 180

Molar mass of solute () = 18

Solution: We know, =

=

Molality

Q3. Which will change with an increase in temperature ?

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

Solution:

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

mathematically: Molarity ()

Q4. Find mole fraction of solute for 2 NaOH solution.

1. 0.887
2. 0.143
3. 0.012
4. 0.035

Solution: molar mass of NaOH =

2 NaOH solution means, 2 moles of NaOH present in 1000 g of water

Moles of water = mol

Mole fraction of solute ( =

Q1. Can the molality of any solution convert into molarity without knowing the density of the solution?

Answer: No, for conversion of molality into molarity or molarity into molality, density must be required. Molarity is volume dependent and molality is only mass-dependent.

The density of solution () =

Q2. Can we consider molarity equal to molality for an infinitely dilute solution?

Answer: Only for numerical simplicity for a very dilute aqueous solution, we can consider molarity = molality. (only for aqueous solution)

We know, the density of water = . So, for very dilute solutions weight of solute become very small (negligible). So, the Volume of solution = 1L becomes equal to 1 kg. The weight of the solution can be treated as the weight of the solvent.

Q3. What is the difference between density and specific density?

Answer: Specific density of material calculated with respect to the water. So, it is unitless and absolute. Density calculated in or other units.

Q4. Is mole fraction affected by temperature?

Answer: No, mole fraction is temperature independent. By measurement of solute & solvent masses, we can calculate the mole fraction of any components.

Q5. How do you change the concentration of a solution?

Answer: Sometimes, by modifying the quantity of solvent, a worker would need to modify the concentration of a solution. Dilution is the addition of a solvent that reduces the solute concentration of the solution. Concentration is solvent elimination, which increases the solute concentration in the solution.

Q6. How do you prepare a solution of known concentration?

Answer: Solutions of known concentration can be prepared either by dissolving the known mass of the solvent solution and diluting it to the desired final volume or by diluting it to the desired final volume by diluting the acceptable volume of the more concentrated solution (the stock solution).

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