Chemistry · Physical Chemistry

Solutions formulas for JEE

Every Solutions formula you need for JEE, grouped by concept.

FormulasRevision notes
32 formulas4 concepts
01Solution Concentration02Liquid-Liquid Solutions03Colligative Properties04Abnormal Molar Mass and van't Hoff Factor
01

Solution Concentration

8 formulas

Henry's Law

p=KHxp = K_H x

Partial pressure of a gas is proportional to its mole fraction in solution.

applies whenConstant temperature. Gas must not highly react with or dissociate in the solvent.
solubilitygas_liquidhenry

Molality (m)

m=nsolutewsolvent(kg)m = \frac{n_{solute}}{w_{solvent}(\text{kg})}

Moles of solute per kilogram of solvent.

applies whenTemperature independent.
concentrationmolality

Molarity (M)

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

Moles of solute per litre of solution.

applies whenTemperature dependent.
concentrationmolarity

Mole Fraction

xA=nAnA+nBx_A = \frac{n_A}{n_A + n_B}

Ratio of moles of one component to total moles of all components.

applies whenTemperature independent. Sum of all mole fractions is 1.
concentrationmole_fraction

Mass Percentage (w/w)

Mass %=wiwtotal×100\text{Mass } \% = \frac{w_i}{w_{total}} \times 100

Mass of the component per 100 parts by mass of the solution.

applies whenTemperature independent.
concentrationmass_percentage

Mass by Volume Percentage (w/V)

w/V%=wsolute(g)Vsolution(mL)×100w/V \% = \frac{w_{solute} (\text{g})}{V_{solution} (\text{mL})} \times 100

Mass of solute dissolved in 100 mL of the solution.

applies whenTemperature dependent.
concentrationmass_by_volume

Parts Per Million (ppm)

ppm=Number of parts of componentTotal parts of all components×106\text{ppm} = \frac{\text{Number of parts of component}}{\text{Total parts of all components}} \times 10^6

Concentration of a component in trace quantities.

applies whenUsed for very dilute solutions/trace quantities.
concentrationppm

Volume Percentage (V/V)

Volume %=ViVtotal×100\text{Volume } \% = \frac{V_i}{V_{total}} \times 100

Volume of the component per 100 parts by volume of the solution.

applies whenTemperature dependent.
concentrationvolume_percentage
02

Liquid-Liquid Solutions

4 formulas

Raoult's Law

pi=pi0xip_i = p_i^0 x_i

Partial vapour pressure of a volatile component is proportional to its mole fraction.

applies whenVolatile liquids forming an ideal or nearly ideal solution.
vapour_pressureraoult

Clausius-Clapeyron Equation

ln⁡(P2P1)=ΔvapHR(1T1−1T2)\ln\left(\frac{P_2}{P_1}\right) = \frac{\Delta_{vap}H}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Temperature dependence of vapour pressure.

applies whenEnthalpy of vaporization is assumed constant over the temperature range.
vapour_pressuretemperaturejee-advanced

Total Vapour Pressure (Binary Liquid)

ptotal=p10+(p20−p10)x2p_{total} = p_1^0 + (p_2^0 - p_1^0)x_2

Total pressure over a solution of two volatile liquids.

applies whenIdeal behavior (obeys Raoult's and Dalton's laws).
vapour_pressuremixture

Vapour Phase Composition

yi=piptotaly_i = \frac{p_i}{p_{total}}

Mole fraction of a component in the vapour phase.

applies whenEquilibrium between liquid and vapour phases.
vapour_pressuredalton
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03

Colligative Properties

12 formulas

Elevation of Boiling Point

ΔTb=Kbm\Delta T_b = K_b m

Boiling point elevation is proportional to molality.

applies whenDilute solution; non-volatile solute.
colligativeboiling_point

Depression of Freezing Point

ΔTf=Kfm\Delta T_f = K_f m

Freezing point depression is proportional to molality.

applies whenDilute solution; solute does not form solid solution with solvent.
colligativefreezing_point

Relative Lowering of Vapour Pressure (RLVP)

p10−p1p10=x2\frac{p_1^0 - p_1}{p_1^0} = x_2

RLVP is equal to the mole fraction of the non-volatile solute.

applies whenNon-volatile solute in a volatile solvent.
colligativerlvp

Osmotic Pressure

Π=CRT=n2VRT\Pi = C R T = \frac{n_2}{V} R T

Osmotic pressure of a solution.

applies whenDilute solutions (obeys van't Hoff equation for solutions).
colligativeosmosis

Raoult's Law

pi=pi0xip_i = p_i^0 x_i

Partial vapour pressure of a volatile component is proportional to its mole fraction.

applies whenVolatile liquids forming an ideal or nearly ideal solution.
vapour_pressureraoult

Thermodynamic Ebullioscopic Constant

Kb=RM1Tb21000ΔvapHK_b = \frac{R M_1 T_b^2}{1000 \Delta_{vap}H}

Calculation of Kb from thermodynamic properties of the pure solvent.

applies whenDepends only on the nature of the solvent.
thermodynamicsebullioscopic

Thermodynamic Cryoscopic Constant

Kf=RM1Tf21000ΔfusHK_f = \frac{R M_1 T_f^2}{1000 \Delta_{fus}H}

Calculation of Kf from thermodynamic properties of the pure solvent.

applies whenDepends only on the nature of the solvent.
thermodynamicscryoscopic

Osmotic Pressure of a Mixture

Πmix=Π1V1+Π2V2V1+V2\Pi_{mix} = \frac{\Pi_1 V_1 + \Pi_2 V_2}{V_1 + V_2}

Osmotic pressure when two non-reacting solutions are mixed.

applies whenSolutions must be non-reacting and temperature constant.
colligativeosmosismixturejee-advanced

RLVP Molar Mass Approximation

p10−p1p10≈n2n1=w2M1M2w1\frac{p_1^0 - p_1}{p_1^0} \approx \frac{n_2}{n_1} = \frac{w_2 M_1}{M_2 w_1}

Calculation of molar mass from RLVP for dilute solutions.

applies whenDilute solutions where n2 << n1.
colligativerlvpmolar_mass

Exact RLVP Form (Ostwald-Walker)

p10−p1p1=n2n1\frac{p_1^0 - p_1}{p_1} = \frac{n_2}{n_1}

Precise formulation of RLVP without assuming dilute solution.

applies whenValid for all concentrations.
colligativerlvpexactjee-advanced

Molar Mass from Boiling Point Elevation

M2=1000⋅w2⋅KbΔTb⋅w1M_2 = \frac{1000 \cdot w_2 \cdot K_b}{\Delta T_b \cdot w_1}

Determining solute molar mass using boiling point elevation.

applies whenDilute solution.
colligativeboiling_pointmolar_mass

Molar Mass from Freezing Point Depression

M2=1000⋅w2⋅KfΔTf⋅w1M_2 = \frac{1000 \cdot w_2 \cdot K_f}{\Delta T_f \cdot w_1}

Determining solute molar mass using freezing point depression.

applies whenDilute solution.
colligativefreezing_pointmolar_mass
04

Abnormal Molar Mass and van't Hoff Factor

8 formulas

Van't Hoff Factor Definition

i=MnormalMabnormal=Observed PropertyCalculated Propertyi = \frac{M_{normal}}{M_{abnormal}} = \frac{\text{Observed Property}}{\text{Calculated Property}}

Ratio of normal to abnormal molar mass or observed to calculated colligative property.

applies whenApplies when solutes associate or dissociate.
abnormal_massvant_hoff

Van't Hoff Factor (Association)

i=1+(1n−1)αi = 1 + \left(\frac{1}{n} - 1\right)\alpha

Relationship between van't Hoff factor and degree of association.

applies whenn is the number of molecules associating to form a multimer.
associationvant_hoffjee-advanced

Van't Hoff Factor (Dissociation)

i=1+(n−1)αi = 1 + (n - 1)\alpha

Relationship between van't Hoff factor and degree of dissociation.

applies whenn is the number of ions produced per formula unit.
dissociationvant_hoffjee-advanced

Ostwald's Dilution Law (Ka)

Ka=Cα21−αK_a = \frac{C \alpha^2}{1 - \alpha}

Dissociation constant of a weak electrolyte related to concentration and degree of dissociation.

applies whenWeak electrolytes; hidden in chapter examples.
equilibriumdissociationjee-advanced

Modified Osmotic Pressure

Π=iCRT\Pi = i C R T

Osmotic pressure incorporating the van't Hoff factor.

applies whenSolute dissociates or associates.
colligativeosmosisvant_hoff

Modified RLVP (van't Hoff)

p10−p1p10=in2n1+n2≈in2n1\frac{p_1^0 - p_1}{p_1^0} = i \frac{n_2}{n_1 + n_2} \approx i \frac{n_2}{n_1}

RLVP incorporating the van't Hoff factor for dissociation/association.

applies whenSolute dissociates or associates.
colligativerlvpvant_hoff

Modified Boiling Point Elevation

ΔTb=iKbm\Delta T_b = i K_b m

Boiling point elevation incorporating the van't Hoff factor.

applies whenSolute dissociates or associates.
colligativeboiling_pointvant_hoff

Modified Freezing Point Depression

ΔTf=iKfm\Delta T_f = i K_f m

Freezing point depression incorporating the van't Hoff factor.

applies whenSolute dissociates or associates.
colligativefreezing_pointvant_hoff
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