k = A e^(-Ea/RT)

“Just like a car needs a spark to start, molecules need enough energy to cross the activation barrier.”

The Arrhenius equation k = A e^(–Ea/RT) shows rate rises exponentially with temperature because more molecules surpass Ea. Ea must be in J mol⁻¹ and T in Kelvin; A is temperature-independent only approximately. Forgetting unit conversion or assuming A constant at all T gives wrong k.

k = A e^(-Ea/RT)

Memory trick: ln k vs 1/T → slope = –Ea/R

t_1/2 = 0.693/k

“A radioactive isotope halves its count just like a candle burns half its wax in a fixed time.”

For a first-order reaction t½ = 0.693/k, so half-life is independent of the initial concentration. The formula fails for zero- or second-order kinetics and for reversible first-order steps where the effective k changes. Applying it blindly leads a wrong half-life.

t₁/2 = 0.693/k

Memory trick: t½ = 0.693/k → k = 0.693/t½

ln([A]0/[A]) = k t

“When a dye fades, the log of its remaining intensity drops linearly with time.”

Integrated first-order law ln([A]₀/[A]) = kt gives a straight line of ln([A]₀/[A]) vs t; slope equals k. Use natural log—not log₁₀—or k will be off by a factor of 2.303. Applying it to non-first-order reactions gives curved plots.

ln([A]0/[A]) = k t

Memory trick: Plot ln([A]₀/[A]) vs t; slope = k

k = 1/t * (1/[A] - 1/[A]0)

“When two identical molecules react, 1/[A] rises linearly with time, like a draining bathtub filling up.”

For a second-order reaction in one reactant, k = (1/t)(1/[A] – 1/[A]₀); thus 1/[A] vs t is a straight line with slope k. The relation holds only when the reaction is truly second order in that species; mixed-order or parallel pathways break linearity.

k = 1/t * (1/[A] - 1/[A]0)

Memory trick: 1/[A] vs t straight line; slope = k

ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)

“Heating a popcorn bag from room temp to microwave shows a sudden rate jump; comparing k at two temps reveals Ea.”

The two-temperature Arrhenius form ln(k₂/k₁) = (Ea/R)(1/T₁ – 1/T₂) lets you extract Ea from rate constants at two temperatures. Temperatures must be in Kelvin; swapping T₁ and T₂ flips the sign and gives a negative Ea, a common trap.

ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)

Memory trick: ln(k₂/k₁) = (Ea/R)(1/T₁ – 1/T₂)

order of reaction vs molecularity

“A billiard break shows three balls colliding (molecularity 3) but the table’s overall score (reaction order) may be 1.5.”

Molecularity counts the number of molecules in an elementary step and is always a positive integer. Reaction order is the sum of concentration exponents in the rate law; it can be zero, fractional or even negative. Assuming they are equal for complex mechanisms misidentifies the pathway.

Memory trick: Molecularity = # colliding molecules; order = sum of concentration exponents

rate vs rate constant

“A car’s speed changes with traffic, but its engine’s maximum power stays the same at a fixed temperature.”

Rate = k·[A]^m·[B]ⁿ, so it varies as reactant concentrations fall. The rate constant k depends only on temperature (and catalyst) and is unchanged as the reaction proceeds. A common trap is treating k as varying with concentration or assuming it equals the overall order.

Memory trick: Rate ∝ k·[conc]; k fixed at given T.

activation energy vs enthalpy of reaction

“Climbing a hill shows the activation energy, while the height difference between start and finish is the reaction enthalpy.”

Ea is the energy barrier reactants must overcome; it appears in the Arrhenius factor e^(−Ea/RT). ΔH is the net heat released or absorbed, a state function independent of the path. Catalysts lower Ea but leave ΔH unchanged – a frequent misconception.

Memory trick: Ea = hill top; ΔH = start-finish height.

Memory trick: Order ≠ recipe; experiment decides.

Raoult's law

“Adding salt to water is like diluting perfume; the vapor pressure drops proportionally to the fraction of water left.”

Raoult’s law: P_solution = X_solvent·P°_solvent, so the solvent’s vapor pressure falls linearly with its mole fraction in an ideal dilute solution. Trap: applying it to strong electrolytes or highly non-ideal solutions leads to large errors.

Memory trick: P ∝ X_solvent (ideal)

Raoult's law — common mistake

“Diluting a fizzy drink, the drop in CO₂ pressure follows the solute’s mole fraction, not its weight.”

Raoult’s law states that the vapor-pressure lowering of a solvent equals the mole fraction of the non-volatile solute times the pure solvent pressure (ΔP = X_solute·P°_solvent). The law uses mole fraction because vapor pressure depends on particle number, not mass. A common trap is inserting mass fraction; the error grows when solute and solvent have very different molar masses.

Memory trick: Raoult → X (mole), not m (mass).

Colligative properties

“Adding sugar to tea raises its boiling point just as adding salt does, because both increase the number of particles in the liquid.”

Boiling-point elevation, freezing-point depression and osmotic pressure are colligative: ΔT = K·m·i, Π = iMRT. They depend only on the total number of solute particles per kilogram of solvent, not on chemical nature. A common slip is using molarity instead of molality for ΔT.

Memory trick: Colligative = particle count only.

Colligative properties — common mistake

“A cup of sugar water and a cup of salt water at same concentration boil at the same temperature, showing identity doesn’t matter.”

The effect of a solute on colligative properties is governed solely by particle count (i·m). Assuming the solute’s identity changes ΔTb or ΔTf is wrong; even non-electrolytes and electrolytes follow the same rule once i is accounted for. Forgetting i is the classic error.

Memory trick: i·m counts, not solute type.

Van't Hoff factor

“When NaCl dissolves, each crystal splits into a sodium and a chloride ion, doubling the particles that affect colligative properties.”

The van’t Hoff factor i equals the number of particles a solute yields in solution; for NaCl, i≈2, so colligative effects roughly double. Toppers note that i is used in ΔT = K·m·i and Π = iMRT, and that it must be adjusted for real solutions.

Memory trick: i ≈ ions formed (NaCl → 2).

Van't Hoff factor — common mistake

“A concentrated NaCl solution doesn’t double the boiling-point rise because ions stick together, reducing the effective i.”

A frequent mistake is to take i as the ideal integer (e.g., 2 for NaCl) regardless of concentration. In concentrated electrolytes ion pairing lowers the effective i, so calculated ΔTb or Π will be too large if the ideal value is used.

Memory trick: i falls as solution gets concentrated.

Osmotic pressure

“Plant roots push water up because the solute inside creates osmotic pressure, like a tiny pump proportional to how many solute particles are present.”

Osmotic pressure Π = iMRT (or i c RT) is the pressure needed to stop solvent flow across a semipermeable membrane. It rises linearly with solute concentration and absolute temperature. Forgetting the i factor for electrolytes or mixing units (Pa vs atm) leads to wrong answers.

Memory trick: Π = iMRT – count × T.

Osmotic pressure — common mistake

“A fresh-water plant cell swells as water rushes through its membrane toward the sugary interior.”

Osmotic pressure π = iMRT (positive for the solution side). Solvent always moves from lower solute concentration (higher water activity) to higher solute concentration. In calculations the pure-solvent side is taken as zero; missing this sign convention gives a wrong net pressure.

Memory trick: Low solute → high water activity → out; high solute → low activity → in.

Ideal versus non-ideal solutions

“When 95 % ethanol is mixed with water it boils at 78 °C, lower than either pure ethanol or water, showing a minimum-boiling azeotrope.”

Positive deviation from Raoult’s law means A–B attractions are weaker than A–A and B–B, so total vapor pressure exceeds the ideal sum. The mixture reaches a minimum boiling point (azeotrope). The trap: assuming Raoult’s law at all compositions; always check deviation sign before using it for boiling-point calculations.

Memory trick: Positive dev → higher VP → lower BP.

Ideal versus non-ideal solutions — common mistake

“Adding table salt to ice water drops the freezing point more than the same mass of sugar because NaCl splits into Na⁺ and Cl⁻.”

Dissociation increases particle number (van’t Hoff factor i>1), so apparent molar mass M_app = M_true / i, giving a larger freezing-point depression than a non-electrolyte. The classic mistake is using i=1 for electrolytes, which underestimates ΔTf.

Memory trick: NaCl i≈2 → ΔTf doubles.

Henry's law

“Opening a soda releases CO₂ because the gas’s partial pressure drops, just like a balloon deflating when the room pressure falls.”

Henry’s law states C = k_H·P at constant temperature; the gas concentration in a liquid is directly proportional to its partial pressure above the liquid. The constant k_H is temperature-dependent, decreasing as temperature rises, so solubility falls. Trap: treating k_H as the same for all gases or ignoring its temperature variation.

Memory trick: CO₂ fizz → C ∝ P, drop P → fizz out.

Henry's law — common mistake

“Opening a chilled soda in a warm kitchen makes the fizz vanish quickly as CO₂ escapes.”

Henry’s law (NCERT) is C = k_H·P; k_H decreases with temperature for most gases because dissolution is exothermic. Hence, at higher T, k_H ↓ and C ↓ even if P is constant. The trap is mixing the two forms (C = k_H·P vs P = k_H·C) and assuming k_H always rises with T.

Memory trick: C = k·P, k falls as T rises → C falls.

Abnormal molar mass

“When acetic acid forms dimers in benzene, a cryoscopic experiment reports a molar mass twice the real one.”

Apparent molar mass from colligative data is M_app = M_true / i, where i is the van’t Hoff factor. Association reduces particle number (i<1) → M_app > M_true; dissociation increases particles (i>1) → M_app < M_true. The common pitfall is treating association as i>1.

Memory trick: i<1 → M_app larger; i>1 → M_app smaller.

Abnormal molar mass — common mistake

“In benzene, acetic acid molecules pair like dancing partners, so the solution seems to have twice the mass per particle.”

Association into n-mers reduces the number of particles; the apparent molar mass from colligative data is M_app = M_true /[1-(n-1)α/n]. For dimerization (n=2) this simplifies to M_app = M_true /(1-α/2). Ignoring the (n-1)/n factor gives a too-large mass error, a common trap.

Memory trick: Mapp = Mtrue ÷[1-(n-1)α/n]; dimer → ÷(1-α/2)

Delta T_b = i K_b m

“Adding salt to boiling water is like loading extra bricks onto a backpack; each ion lifts the boiling point higher.”

ΔT_b = i·K_b·m gives the boiling-point elevation for dilute solutions; i is the van’t Hoff factor (1 for non-electrolytes, total ions for strong electrolytes). The trap is using i=1 for electrolytes or ignoring that K_b is solvent-specific.

Delta T_b = i K_b m

Memory trick: i·K_b·m lifts the boil