Solutions formulas for JEE Main & Advanced

15 formula entries for Solutions, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Concentration Terms

Mass % =

\frac{mass of solute}{mass of solution} \times 100

; Mole fraction

x_{A} = \frac{n_{A}}{n_{A} + n_{B}}

; Molarity

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

; Molality

m = \frac{n_{solute}}{mass of solvent (kg)}

; ppm =

\frac{mass of solute}{mass of solution} \times 10^{6}

When to use. Use to calculate or convert between concentration units in problems.

Trap. Molarity depends on temperature (volume changes), molality does not.

Molarity & Molality Conversion

m = \frac{1000 M}{1000 ρ - M \cdot M_{solute}}

where

ρ

is density in g/mL,

M_{solute}

is molar mass of solute.

When to use. When a problem gives molarity and density and asks for molality or vice versa.

Trap. Density must be in g/mL; if given in kg/L, convert to g/mL.

Henry's Law

p = K_{H} \cdot x

where

p

is partial pressure,

x

is mole fraction of gas in solution,

K_{H}

is Henry's constant.

When to use. Use to calculate gas solubility at different pressures or to find Henry's constant.

Trap. Henry's constant $K_{H}$ is temperature-dependent; higher $K_{H}$ means lower solubility.

Raoult's Law for Volatile Liquids

p_{A} = x_{A} p_{A}^{0}

p_{B} = x_{B} p_{B}^{0}

; Total pressure

P = p_{A} + p_{B} = x_{A} p_{A}^{0} + x_{B} p_{B}^{0}

When to use. Use to calculate vapor pressure of a mixture of volatile liquids or to find composition of vapor.

Trap. Raoult's law applies only to ideal solutions; deviations occur for non-ideal solutions.

Ideal & Non-Ideal Solutions

For ideal:

Δ H_{mix} = 0

Δ V_{mix} = 0

; Positive deviation:

P > x_{A} p_{A}^{0} + x_{B} p_{B}^{0}

; Negative deviation:

P < x_{A} p_{A}^{0} + x_{B} p_{B}^{0}

When to use. Use to classify solutions and predict deviations based on intermolecular forces.

Trap. Positive deviation occurs when A-B interactions are weaker than A-A and B-B (e.g., ethanol + water, acetone + CS2); negative deviation when A-B interactions are stronger (e.g., acetone + chloroform, HNO3 + water).

Relative Lowering of Vapor Pressure

\frac{p^{0} - p}{p^{0}} = x_{solute} = \frac{n_{solute}}{n_{solute} + n_{solvent}}

When to use. Use to calculate molar mass of non-volatile solute from vapor pressure data.

Trap. For dilute solutions, $x_{solute} \approx \frac{n_{solute}}{n_{solvent}}$ .

Boiling Point Elevation

Δ T_{b} = K_{b} \cdot m

where

K_{b}

is ebullioscopic constant,

m

is molality.

When to use. Use to find molar mass of solute or to calculate boiling point of a solution.

Trap. $K_{b}$ is solvent-specific (e.g., water $K_{b} = 0.512 K kg/mol$ ).

Freezing Point Depression

Δ T_{f} = K_{f} \cdot m

where

K_{f}

is cryoscopic constant.

When to use. Use to find molar mass of solute or to calculate freezing point of a solution.

Trap. $K_{f}$ is solvent-specific (e.g., water $K_{f} = 1.86 K kg/mol$ ).

Osmotic Pressure

Π = i M R T

where

Π

is osmotic pressure,

M

is molarity,

R

is gas constant,

T

is temperature in Kelvin.

When to use. Use to determine molar mass of macromolecules or to compare osmotic pressures.

Trap. Use molarity, not molality, in osmotic pressure formula.

Van't Hoff Factor (i)

i = \frac{observed colligative property}{expected for non-electrolyte}

; For dissociation:

i = 1 + α (n - 1)

where

α

is degree of dissociation,

n

is number of ions.

When to use. Use when dealing with electrolytes or solutes that associate/dissociate.

Trap. For association (e.g., dimerization), $i < 1$ .

Abnormal Molar Mass & van't Hoff Factor

i = \frac{normal molar mass}{observed molar mass}

When to use. Use to determine if a solute dissociates or associates from experimental molar mass data.

Trap. For dissociation, observed molar mass < normal molar mass, so $i > 1$ .

Determination of Molar Mass Using Colligative Properties

From freezing point depression:

M = \frac{i K_{f} \cdot w_{solute} \times 1000}{Δ T_{f} \cdot w_{solvent}}

; From osmotic pressure:

M = \frac{i w_{solute} R T}{Π V}

When to use. Use when experimental data for colligative property is given to find molar mass.

Trap. Ensure units: solute and solvent masses in grams (with the ×1000 factor), volume in L for osmotic pressure.

Common Exam Problems: Mixing Solutions

M_{f} = \frac{M_{1} V_{1} + M_{2} V_{2}}{V_{1} + V_{2}}

When to use. Use when diluting or mixing solutions of same solute.

Trap. This formula assumes volumes are additive, which is not always true (non-ideal solutions).

Raoult's Law for Non-Volatile Solute

p = x_{solvent} p^{0}

;

\frac{p^{0} - p}{p^{0}} = x_{solute}

When to use. Use to calculate vapor pressure of solution or molar mass of non-volatile solute.

Trap. The solute must be non-volatile; if volatile, use Raoult's law for both components.

Colligative Properties of Electrolytes

Δ T_{f} = i K_{f} m

;

Π = i M R T

When to use. Use when solute is an electrolyte or when degree of dissociation is given.

Trap. For strong electrolytes, $i$ equals number of ions (e.g., NaCl $i = 2$ , CaCl2 $i = 3$ ).

Values to remember

$K_{b} (water) = 0.512 K kg/mol$ Boiling Point Elevation
$K_{b} (benzene) = 2.53 K kg/mol$ Boiling Point Elevation
$K_{f} (water) = 1.86 K kg/mol$ Freezing Point Depression
$K_{f} (benzene) = 5.12 K kg/mol$ Freezing Point Depression
$R = 0.0821 {L atm mol}^{- 1} K^{- 1}$ Osmotic Pressure
$R = 8.314 {J mol}^{- 1} K^{- 1}$ Osmotic Pressure
$K_{f} (water) = 1.86$ Key Constants for Solvents
$K_{b} (water) = 0.512$ Key Constants for Solvents
$K_{f} (benzene) = 5.12$ Key Constants for Solvents
$K_{b} (benzene) = 2.53$ Key Constants for Solvents
$K_{f} (camphor) = 39.7$ Key Constants for Solvents

Read the full chapter: Solutions for JEE, with what JEE asks and the common traps.