JEE Mains Chemistry · Some Basic Concepts of Chemistry

Molarity, Dilution and Mixing

Molarity from a mass and a volume, dilution and mixing of solutions, and which concentration terms change with temperature.

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Why this matters

Eighteen PYQs, fourteen of them numerical, which makes this the chapter's most numerical page; none yet from 2026. Ten find a molarity, or the mass needed for one, often from a hydrate. Four dilute or mix solutions, and four ask which concentration terms change with temperature. The arithmetic is short, so the marks go to whoever keeps the units straight.

Concept 1 of 3: Molarity from mass and volume

Molarity counts the moles of solute in each litre of solution. Weigh the solute, divide by its molar mass, then divide by the volume in litres. For a hydrate, the water of crystallisation is part of the molar mass.

Definition

$M=\frac{n}{V(\mathrm{L})}=\frac{m\times1000}{M_B\times V(\mathrm{mL})}$ .
Hydrates: $\mathrm{CuSO_4\cdot5H_2O}$ is 249.5 g mol $^{-1}$ ; $\mathrm{H_2C_2O_4\cdot2H_2O}$ is 126 g mol $^{-1}$ .
An ion's concentration: multiply by its count per formula unit. $\mathrm{Na_3PO_4}$ gives 3 $\mathrm{Na^+}$ .
A solute that reacts with water: count the product. $\mathrm{Na_2O}$ gives 2 NaOH.
'Dissolved in 500 mL of water' is taken as 500 mL of solution unless a density is given.

Molarity

M=\frac{n_{\text{solute}}}{V_{\text{solution}}(\mathrm{L})}

Worked example

Find the molarity when

24.95

g of

\mathrm{CuSO_4\cdot5H_2O}

is dissolved to make 500 mL of solution.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2021 · Paper 22 · Q52Moderate

Example 1 · Some Basic Concepts of Chemistry · Molarity, Dilution and Mixing

The molarity of the solution prepared by dissolving

6.3\text{ }g

of oxalic acid

\left( H_{2}C_{2}O_{4}\cdot 2H_{2}O \right)

250\text{ }mL

of water in

molL^{- 1}

x \times10^{- 2}

. The value of

x

is (Nearest integer) [Atomic mass:

H:1.0,C:12.0,O:16.0

]

Forgetting the water of crystallisation

Copper sulphate crystals are 249.5 g mol

^{-1}

, not 159.5. Using the anhydrous value overstates the moles by more than half.

Drill 9 more on molarity from mass and volume

Concept 2 of 3: Dilution and mixing

Adding water changes the volume, not the moles. Mixing two solutions of one solute adds their moles and their volumes. If acid and water both boil off, recount both.

Definition

Dilution: $M_1V_1=M_2V_2$ .
Mixing the same solute: $M=\frac{M_1V_1+M_2V_2}{V_1+V_2}$ .
Evaporation: moles left $=$ moles at the start $-$ moles lost; divide by the new volume.
Millimoles $=M\times V(\mathrm{mL})$ .

Mixing rule

M_{\text{mix}}=\frac{M_1V_1+M_2V_2}{V_1+V_2}

Worked example

50 mL of

1.0

M HCl is mixed with 150 mL of

0.2

M HCl. Find the molarity of the mixture.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2025 · 22 Jan 2025 · Q125Moderate

Example 2 · Some Basic Concepts of Chemistry · Molarity, Dilution and Mixing

20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is

\_\_\_\_\_\_\_

\times10^{- 2}M

. (Nearest integer).

Water added is not the final volume

Water added

=

final volume

-

starting volume. Taking 200 mL of

0.6

M to

0.2

M needs a final 600 mL, so you add 400 mL.

Drill 3 more on dilution and mixing

Concept 3 of 3: Which concentration terms depend on temperature

A liquid expands when it is warmed. Any concentration term with a volume in it changes with temperature. Any term built only from masses and moles does not.

Definition

Changes with temperature: molarity and normality, because both are per litre of solution.
Does not change: molality, mole fraction, mass percent and ppm by mass.
Water is densest at 4 °C, so a fixed amount of an aqueous solution has its smallest volume, and its highest molarity, near 4 °C.
The usual concentration terms are mass percent, mole fraction, molarity, molality and ppm. A mole is an amount, not a concentration.

Term	Defined with	Changes with temperature?
Molarity	Volume of solution (L)	Yes
Normality	Volume of solution (L)	Yes
Molality	Mass of solvent (kg)	No
Mole fraction	Moles only	No
Mass percent	Masses only	No
ppm (by mass)	Masses only	No
Mole	An amount of substance	Not a concentration term at all In a list of 'units of concentration', the mole is the one to leave out.

Water is densest at 4 °C, so the molarity of an aqueous solution peaks near 4 °C.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2024 · 27 Jan 2024 · Q136Moderate

Example 3 · Some Basic Concepts of Chemistry · Molarity, Dilution and Mixing

The quantity which changes with temperature is:

Heating does not always lower molarity

Warming an aqueous solution from 1 °C to 4 °C shrinks it slightly, so molarity first rises, then falls above 4 °C. A graph with a single maximum near 4 °C is the right shape.

Drill 3 more on which concentration terms depend on temperature

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Molarity from mass and volume
Molarity
$M=\frac{n_{\text{solute}}}{V_{\text{solution}}(\mathrm{L})}$
Dilution and mixing
Mixing rule
$M_{\text{mix}}=\frac{M_1V_1+M_2V_2}{V_1+V_2}$

Reference tables (1)

Which concentration terms depend on temperature7 rows

Term	Defined with	Changes with temperature?
Molarity	Volume of solution (L)	Yes
Normality	Volume of solution (L)	Yes
Molality	Mass of solvent (kg)	No
Mole fraction	Moles only	No
Mass percent	Masses only	No
ppm (by mass)	Masses only	No
Mole	An amount of substance	Not a concentration term at all In a list of 'units of concentration', the mole is the one to leave out.

Water is densest at 4 °C, so the molarity of an aqueous solution peaks near 4 °C.

Watch out for (3)

Forgetting the water of crystallisation
→ Molarity from mass and volume
Water added is not the final volume
→ Dilution and mixing
Heating does not always lower molarity
→ Which concentration terms depend on temperature

Test yourself on Some Basic Concepts of Chemistry

20 past JEE Mains questions from this chapter, timed at 48 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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