🧬 NEET 2026  •  Physical Chemistry

NEET Chemistry
Formula Sheet2026

Complete Physical Chemistry formulas for NEET 2026 — all 10 major chapters, every formula you need, beautifully rendered.

Atomic Structure Stoichiometry Gaseous State Thermodynamics Equilibrium Ionic Eq. Electrochemistry Solutions Solid State Chemical Kinetics
🔍
⚛️

1. Atomic Structure

14 Formulas
Important
Closest Distance of Approach (α-particle)
\[ R = \frac{4KZe^2}{m_\alpha V_\alpha^2} \]
K = Coulomb's constant, Z = atomic number, e = charge, m_α = mass of α-particle
Radius of Nucleus
\[ R = R_0 A^{1/3} \text{ cm} \]
R₀ ≈ 1.2 × 10⁻¹³ cm; A = mass number
Key
Planck's Quantum Theory — Energy of Photon
\[ E = h\nu = \frac{hc}{\lambda} \]
h = 6.626×10⁻³⁴ J·s; c = 3×10⁸ m/s
Photoelectric Effect
\[ h\nu = h\nu_0 + \frac{1}{2}m_e v^2 \]
ν₀ = threshold frequency; ½mₑv² = kinetic energy of ejected electron
Key
Bohr's Model — Quantization of Angular Momentum
\[ mvr = n\frac{h}{2\pi} \]
n = principal quantum number (1,2,3…)
Important
Energy of Electron (Bohr Model)
\[ E_n = -\frac{E_1 z^2}{n^2} = -2.178\times10^{-18}\frac{z^2}{n^2}\ \text{J/atom} = -13.6\frac{z^2}{n^2}\ \text{eV} \]
E₁ = −13.6 eV for hydrogen; z = atomic number; n = orbit number
Radius of nth Orbit (Bohr)
\[ r_n = \frac{n^2}{Z} \times \frac{h^2}{4\pi^2 e^2 m} = \frac{0.529\,n^2}{Z}\ \text{Å} \]
Velocity of Electron (Bohr)
\[ v = \frac{2\pi ze^2}{nh} = \frac{2.18\times10^6\,z}{n}\ \text{m/s} \]
Key
de-Broglie Wavelength
\[ \lambda = \frac{h}{mc} = \frac{h}{p} \]
p = momentum; for particles: λ = h/mv
Rydberg Formula (Spectral Lines)
\[ \frac{1}{\lambda} = \bar{\nu} = Rz^2\!\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \]
R = Rydberg constant = 1.097×10⁷ m⁻¹
No. of Spectral Lines (from level n)
\[ \text{Lines} = \frac{n(n-1)}{2} \quad\text{(or }\ \frac{\Delta n(\Delta n+1)}{2}\text{)} \]
Heisenberg's Uncertainty Principle
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \quad;\quad m\Delta x\cdot\Delta v \geq \frac{h}{4\pi} \]
NEET Key
Orbital Angular Momentum
\[ L = \frac{h}{2\pi}\sqrt{\ell(\ell+1)} = \hbar\sqrt{\ell(\ell+1)} \]
ℓ = azimuthal quantum number (0,1,…,n−1)
Quantum Numbers Summary
Orbitals in subshell: \(2\ell+1\)
Max electrons in subshell: \(2(2\ell+1)\)
n: 1,2,3,… | ℓ: 0 to n−1 | mₗ: −ℓ to +ℓ | mₛ: ±½
⚖️

2. Stoichiometry & Concentration

15 Formulas
Relative Atomic Mass (RAM)
\[ \text{RAM} = \frac{\text{Mass of one atom of element}}{\frac{1}{12}\times\text{mass of }^{12}C} = \text{Total nucleons} \]
Important
Molarity (M)
\[ M = \frac{w \times 1000}{\text{Mol. wt of solute} \times V_{\text{mL}}} \]
w = mass of solute (g); V = volume of solution (mL)
Important
Molality (m)
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} = \frac{1000\,w_1}{M_1\,w_2} \]
w₁ = mass solute, M₁ = mol. wt solute, w₂ = mass solvent (g)
Mole Fraction
\[ x_1 = \frac{n}{n+N}\ \text{(solute)};\quad x_2 = \frac{N}{n+N}\ \text{(solvent)} \]
x₁ + x₂ = 1
% Calculations
\(\%\,w/w = \dfrac{\text{mass solute (g)}}{\text{mass solution (g)}}\times100\)

\(\%\,w/v = \dfrac{\text{mass solute (g)}}{\text{volume solution (mL)}}\times100\)
Vapour Density
\[ V.D. = \frac{M_{\text{gas}}}{2} \quad\Rightarrow\quad M_{\text{gas}} = 2\times V.D. \]
Average/Mean Atomic Mass
\[ A_x = \frac{a_1 x_1 + a_2 x_2 + \cdots + a_n x_n}{100} \]
xᵢ = % abundance; aᵢ = atomic mass of isotope
Mean Molar Mass
\[ M_{\text{avg}} = \frac{n_1 M_1 + n_2 M_2 + \cdots}{n_1 + n_2 + \cdots} \]
Normality (N)
\[ N = \frac{\text{No. of equivalents of solute}}{\text{Volume of solution (L)}} \]
Normality = Molarity × v.f. (valency factor)
Equivalent Weight
\[ E = \frac{\text{Atomic / Molecular weight}}{\text{Valency factor (n-factor)}} \]
Acid: n-factor = basicity | Base: n-factor = acidity | Redox: n-factor = e⁻ gained/lost
Key
At Equivalence Point
\[ N_1 V_1 = N_2 V_2 \quad;\quad n_1 M_1 V_1 = n_2 M_2 V_2 \]
Interconversion of Concentration Units
From → ToFormula
Mole fraction → Molarity\(M = \dfrac{x_2\rho\times1000}{x_1 M_1 + M_2 x_2}\)
Molarity → Mole fraction\(x_2 = \dfrac{MM_1\times1000}{\rho\times1000 - MM_2}\)
Mole fraction → Molality\(m = \dfrac{x_2\times1000}{x_1 M_1}\)
Molality → Molarity\(M = \dfrac{m\rho\times1000}{1000+mM_2}\)
Molarity → Molality\(m = \dfrac{M\times1000}{1000\rho - M\cdot M_2}\)
Volume Strength of H₂O₂
\(N = \dfrac{\text{Vol. strength}}{5.6}\)

\(M = \dfrac{\text{Vol. strength}}{11.2}\)
Hardness of Water (ppm)
\[ \text{Hardness (ppm)} = \frac{\text{mass of CaCO}_3}{\text{Total mass of water}}\times10^6 \]
💨

3. Gaseous State

18 Formulas
Boyle's Law (Constant T)
\[ P\propto\frac{1}{V} \quad\Rightarrow\quad P_1 V_1 = P_2 V_2 \]
Charles's Law (Constant P)
\[ V\propto T \quad\Rightarrow\quad \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Gay-Lussac's Law (Constant V)
\[ P\propto T \quad\Rightarrow\quad \frac{P_1}{T_1} = \frac{P_2}{T_2} \]
Key
Ideal Gas Equation
\[ PV = nRT \quad;\quad P = \frac{d}{M}RT \quad;\quad Pm = dRT \]
R = 8.314 J mol⁻¹ K⁻¹; d = density; M = molar mass
Dalton's Law of Partial Pressures
\[ P_{\text{total}} = P_1 + P_2 + P_3 + \cdots \]
Partial pressure = mole fraction × total pressure
Amagat's Law of Partial Volumes
\[ V = V_1 + V_2 + V_3 + \cdots \]
Important
Graham's Law of Diffusion
\[ r \propto \frac{1}{\sqrt{d}} \quad;\quad \frac{r_1}{r_2} = \sqrt{\frac{d_2}{d_1}} = \sqrt{\frac{M_2}{M_1}} \]
Kinetic Gas Equation
\[ PV = \frac{1}{3}mN\overline{U^2} \]
Average KE (per mole)
\[ KE = \frac{3}{2}RT = \frac{3}{2}KN_A T \]
K = Boltzmann constant = 1.38×10⁻²³ J/K
Key
Root Mean Square Speed
\[ U_{\text{rms}} = \sqrt{\frac{3RT}{M}} \]
M must be in kg/mol
Average Speed
\[ U_{\text{avg}} = \sqrt{\frac{8RT}{\pi M}} = \sqrt{\frac{8KT}{\pi m}} \]
Most Probable Speed
\[ U_{\text{mp}} = \sqrt{\frac{2RT}{M}} = \sqrt{\frac{2KT}{m}} \]
Speed Ratio
\[ U_{\text{mp}} : U_{\text{avg}} : U_{\text{rms}} = \sqrt{2} : \sqrt{\frac{8}{\pi}} : \sqrt{3} \approx 1 : 1.128 : 1.225 \]
Important
Van der Waals Equation
\[ \left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT \]
a = intermolecular attraction; b = volume correction (excluded volume)
Critical Constants
\[ V_c = 3b,\quad P_c = \frac{a}{27b^2},\quad T_c = \frac{8a}{27Rb} \]
Average Molecular Mass of Gas Mixture
\[ M_{\text{mix}} = \frac{n_1 M_1 + n_2 M_2 + n_3 M_3}{n_1 + n_2 + n_3} \]
Compressibility Factor
\[ Z = \frac{PV}{nRT} \]
Z = 1 ideal; Z > 1 repulsion dominant; Z < 1 attraction dominant
Temperature Conversion
\[ \frac{C-0}{100} = \frac{K-273}{100} = \frac{F-32}{180} \]
🔥

4. Thermodynamics

20 Formulas
Key
First Law of Thermodynamics
\[ \Delta U = q + w \quad;\quad \Delta U = q - P\Delta V \]
Work done ON system = +ve; work done BY system = −ve (IUPAC sign convention)
Degrees of Freedom & Internal Energy
\[ U = \frac{f}{2}nRT \quad;\quad \Delta E = \frac{f}{2}nR\Delta T \]
f = 3 (monoatomic); f = 5 (diatomic/linear); f = 6 (non-linear polyatomic)
Enthalpy
\[ H = U + PV \quad;\quad \Delta H = \Delta U + P\Delta V \]
H = state function, extensive property
Relation between Cp and Cv
\[ C_p - C_v = R \quad(\text{ideal gas}) \quad;\quad \gamma = \frac{C_p}{C_v} \]
Cp = γR/(γ−1) ; Cv = R/(γ−1)
Important
Work Done
Isothermal rev.: \(W = -nRT\ln\dfrac{V_2}{V_1}\)

Isobaric: \(W = -P(V_f - V_i)\)

Isochoric: \(W = 0\)
Adiabatic Reversible Process
\[ T_2 V_2^{\gamma-1} = T_1 V_1^{\gamma-1} \quad;\quad W = \frac{nR(T_2-T_1)}{\gamma-1} \]
Heat at Constant Volume / Pressure
\[ q_v = \Delta U = nC_v\Delta T \quad;\quad q_p = \Delta H = nC_p\Delta T \]
Key
Second Law — Entropy
\[ \Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0 \]
For spontaneous process ΔS_universe > 0
Entropy Change (Ideal Gas)
\[ \Delta S_{\text{system}} = nC_v\ln\frac{T_2}{T_1} + nR\ln\frac{V_2}{V_1} \]
Important
Gibbs Free Energy
\[ G = H - TS \quad;\quad \Delta G = \Delta H - T\Delta S \]
ΔG < 0 → spontaneous; ΔG = 0 → equilibrium; ΔG > 0 → non-spontaneous
Standard Free Energy Change
\[ \Delta G^\circ = -2.303\,RT\log K \quad;\quad \Delta G = \Delta G^\circ + 2.303RT\log Q \]
Kirchhoff's Equation
\[ \Delta H_2^\circ = \Delta H_1^\circ + \Delta C_p(T_2 - T_1) \]
ΔCp = Cp(products) − Cp(reactants)
Enthalpy from Bond Enthalpies
\[ \Delta H = \Sigma\,(\text{Bond enthalpy of reactants}) - \Sigma\,(\text{Bond enthalpy of products}) \]
Resonance Energy
\[ \Delta H_{\text{resonance}} = \Delta H_{f,\text{experimental}} - \Delta H_{f,\text{calculated}} \]
Process Summary
Isothermal: T = const; ΔT = 0  |  Isochoric: V = const; w = 0  |  Isobaric: P = const  |  Adiabatic: q = 0
⚡

5. Chemical Equilibrium

14 Formulas
Key
Equilibrium Constant (Kc)
\[ K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \quad\text{for }aA + bB \rightleftharpoons cC + dD \]
Equilibrium Constant (Kp)
\[ K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b} \]
Important
Relation between Kp and Kc
\[ K_p = K_c(RT)^{\Delta n} \]
Δn = moles of gaseous products − moles of gaseous reactants
Relation Kp and Kx
\[ K_p = K_x(P)^{\Delta n} \]
Van't Hoff Equation
\[ \log\frac{K_2}{K_1} = \frac{\Delta H}{2.303R}\!\left(\frac{1}{T_1} - \frac{1}{T_2}\right) \]
ΔG and Equilibrium Constant
\[ \Delta G^\circ = -2.303\,RT\log K \quad;\quad \Delta G = \Delta G^\circ + RT\ln Q \]
Reaction Quotient Q
\[ Q = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]
Q < K → forward; Q > K → backward; Q = K → equilibrium
Important
Degree of Dissociation (α)
\[ \alpha = \frac{\text{moles dissociated}}{\text{initial moles}} \]
% dissociation = α × 100
Observed Molecular Weight (Dissociation)
\[ \alpha = \frac{D-d}{(n-1)\times d} = \frac{M_T - M_0}{(n-1)M_0} \]
D = theoretical V.D.; d = observed V.D.; n = total moles after dissociation
Le Chatelier's Principle — Effect Summary
Factor ChangedEffect
↑ Reactant concentrationEquilibrium shifts forward
↑ Product concentrationEquilibrium shifts backward
↑ Pressure / ↓ VolumeShifts toward fewer moles of gas
↑ TemperatureShifts in endothermic direction (↑K if endothermic)
Inert gas at constant VNo effect
Inert gas at constant PShifts toward more moles of gas
🧪

6. Ionic Equilibrium

22 Formulas
Key
Ostwald Dilution Law — Weak Acid
\[ K_a = \frac{C\alpha^2}{1-\alpha} \approx C\alpha^2 \quad(\alpha\ll1) \]
α = degree of dissociation; C = concentration; Ka = acid dissociation constant
Degree of Dissociation
\[ \alpha = \sqrt{\frac{K_a}{C}} = \sqrt{K_a \times V} \quad;\quad \alpha_b = \sqrt{\frac{K_b}{C}} \]
Important
pH Scale
\(\text{pH} = -\log[H^+]\)
\(\text{pOH} = -\log[OH^-]\)
\(\text{pH} + \text{pOH} = 14 \quad(25°C)\)
Ionic Product of Water
\[ K_w = [H^+][OH^-] = 10^{-14} \quad(25°C) \]
pKa + pKb = pKw = 14 (conjugate acid-base pairs)
pH of Weak Acid (Monoprotic)
\[ [H^+] = \sqrt{K_a \cdot C} \quad\Rightarrow\quad \text{pH} = \frac{1}{2}(\text{p}K_a - \log C) \]
pH of Strong Acid/Base Mixtures
2 strong acids: \([H^+] = \dfrac{N_1V_1 + N_2V_2}{V_1+V_2}\)

Acid + Base: \([H^+] = \dfrac{N_1V_1 - N_2V_2}{V_1+V_2}\) (if acid excess)
pH of Mixture of Two Weak Acids
\[ [H^+] = \sqrt{K_{a1}C_1 + K_{a2}C_2 + K_w} \]
Key
Salt Hydrolysis — pH Summary
Salt TypeType of HydrolysispH
Weak acid + Strong baseAnionic\(7 + \frac{1}{2}\text{p}K_a + \frac{1}{2}\log C\)
Strong acid + Weak baseCationic\(7 - \frac{1}{2}\text{p}K_b - \frac{1}{2}\log C\)
Weak acid + Weak baseBoth\(7 + \frac{1}{2}\text{p}K_a - \frac{1}{2}\text{p}K_b\)
Strong acid + Strong baseNone7
Important
Henderson-Hasselbalch (Buffer)
Acidic buffer: \(\text{pH} = \text{p}K_a + \log\dfrac{[\text{Salt}]}{[\text{Acid}]}\)

Basic buffer: \(\text{pOH} = \text{p}K_b + \log\dfrac{[\text{Salt}]}{[\text{Base}]}\)
Buffer Capacity
\[ \beta = \frac{dx}{d(\text{pH})} = 2.303\frac{(a+x)(b-x)}{a+b} \]
Indicator pH
\[ \text{pH} = \text{p}K_{\text{HIn}} + \log\frac{[\text{In}^-]}{[\text{HIn}]} \]
NEET Key
Solubility Product (Ksp)
\[ K_{sp} = (xs)^x \cdot (ys)^y = x^x \cdot y^y \cdot s^{x+y} \]
For MₓYᵧ ⇌ xMʸ⁺ + yXˣ⁻; s = molar solubility
Condition for Precipitation
If \(K_{IP} > K_{SP}\) → precipitation occurs
If \(K_{IP} = K_{SP}\) → saturated solution
If \(K_{IP} < K_{SP}\) → unsaturated (no precipitate)
pH of Amphiprotic Anion (e.g. HCO₃⁻)
\[ \text{pH}(HCO_3^-) = \frac{\text{p}K_{a1} + \text{p}K_{a2}}{2} \]
Isoelectric Point
\[ [H^+] = \sqrt{K_{a1}\cdot K_{a2}} \quad\Rightarrow\quad \text{pH} = \frac{\text{p}K_{a1} + \text{p}K_{a2}}{2} \]
🔋

7. Electrochemistry

18 Formulas
Key
Cell EMF
\[ E_{\text{cell}} = E_{\text{cathode}}^{\text{SRP}} - E_{\text{anode}}^{\text{SRP}} \]
Anode = lower SRP; Cathode = higher SRP; Ecell always +ve
Gibbs Energy and EMF
\[ \Delta G = -nFE_{\text{cell}} \quad;\quad \Delta G^\circ = -nFE^\circ_{\text{cell}} \]
Important
Nernst Equation
\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF}\ln Q = E^\circ_{\text{cell}} - \frac{0.0591}{n}\log Q \quad(298\,K) \]
At Chemical Equilibrium
\[ E_{\text{cell}} = 0 \quad;\quad \log K_{eq} = \frac{nE^\circ_{\text{cell}}}{0.0591} \]
Electrode Potential (Nernst for Electrode)
\[ E_{M^{n+}/M} = E^\circ_{M^{n+}/M} - \frac{0.0591}{n}\log\frac{1}{[M^{n+}]} \]
Important
Faraday's First Law of Electrolysis
\[ w = ZIt = Z \cdot q \]
Z = electrochemical equivalent = E/96500 g/C
Faraday's Second Law
\[ \frac{W_1}{W_2} = \frac{E_1}{E_2} \quad;\quad \frac{W}{E} = \frac{it}{96500} \]
Current Efficiency
\[ \%\,\text{efficiency} = \frac{\text{actual mass deposited}}{\text{theoretical mass}}\times100 \]
Conductance & Resistance
\[ G = \frac{1}{R} \quad;\quad K = \frac{1}{\rho} = G\cdot\frac{l}{A} \]
K = specific conductance (conductivity)
Key
Molar Conductance
\[ \lambda_m = \frac{K\times1000}{\text{Molarity}} \quad\text{unit: ohm}^{-1}\text{cm}^2\text{mol}^{-1} \]
Equivalent Conductance
\[ \lambda_E = \frac{K\times1000}{\text{Normality}} \]
Kohlrausch's Law (Strong Electrolytes)
\[ \lambda_M^c = \lambda_M^\infty - b\sqrt{C} \]
Kohlrausch's Law (Limiting Conductance)
\[ \lambda_\infty = n_+\lambda_+^\infty + n_-\lambda_-^\infty \]
Degree of Dissociation (Conductometric)
\[ \alpha = \frac{\lambda_m^c}{\lambda_m^0} \quad;\quad K_{eq} = \frac{C\alpha^2}{1-\alpha} \]
Transport Number
\[ t_c = \frac{\mu_c}{\mu_c+\mu_a} \quad;\quad t_a = \frac{\mu_a}{\mu_c+\mu_a} \quad;\quad t_c+t_a=1 \]
Solubility from Conductance
\[ \lambda_M^c = K\times\frac{1000}{\text{solubility}} \quad;\quad K_{sp} = S^2 \]
🌊

8. Solutions & Colligative Properties

16 Formulas
Key
Raoult's Law (Volatile Liquids)
\[ P_A = x_A P_A^0 \quad;\quad P_T = x_A P_A^0 + x_B P_B^0 \]
Important
Relative Lowering of Vapour Pressure
\[ \text{RLVP} = \frac{P^0-P_s}{P^0} = x_{\text{solute}} = \frac{n}{n+N} \]
n = moles solute; N = moles solvent
RLVP (Approximate for Dilute Solutions)
\[ \frac{P^0-P_s}{P_s} = \frac{n}{N} \quad;\quad \frac{P^0-P_s}{P_s} = \text{molality}\times\frac{M_1}{1000} \]
Important
Elevation in Boiling Point
\[ \Delta T_b = iK_b m \quad;\quad K_b = \frac{RT_b^2 M_1}{1000\Delta H_{\text{vap}}} \]
i = Van't Hoff factor; m = molality; Kb (water) = 0.512 K·kg/mol
Important
Depression in Freezing Point
\[ \Delta T_f = iK_f m \quad;\quad K_f = \frac{RT_f^2 M_1}{1000\Delta H_{\text{fus}}} \]
Kf (water) = 1.86 K·kg/mol
Key
Osmotic Pressure
\[ \pi = iCRT = i\frac{n}{V}RT \]
π₁ = π₂ → isotonic; π₁ > π₂ → hypertonic; π₁ < π₂ → hypotonic
NEET Key
Van't Hoff Factor (i)
\[ i = \frac{\text{observed colligative property}}{\text{theoretical colligative property}} = \frac{\text{theoretical molar mass}}{\text{observed molar mass}} \]
i > 1 → dissociation; i < 1 → association
i and Degree of Dissociation (α)
\[ i = 1 + (n-1)\alpha \quad\text{where }n = x+y \text{ (total ions)} \]
i and Degree of Association (β)
\[ i = 1 + \left(\frac{1}{n}-1\right)\beta \]
Ideal vs Non-Ideal Solutions
PropertyIdealPositive DeviationNegative Deviation
Raoult's LawObeyedPexp > PidealPexp < Pideal
A–B InteractionA–A = A–B = B–BA–B < A–A, B–BA–B > A–A, B–B
ΔHmix0+ve−ve
ΔVmix0+ve−ve
ExampleC₆H₆ + C₇H₈EtOH + H₂OCHCl₃ + (CH₃)₂CO
💎

9. Solid State

12 Formulas
Key
Analysis of Cubic Systems
PropertySimple Cubic (SC)Body Centred (BCC)Face Centred (FCC)
Atoms per unit cell (Z)124
Coordination number6812
Atomic radius (r)\(a/2\)\(\frac{\sqrt{3}a}{4}\)\(\frac{a}{2\sqrt{2}}\)
Packing efficiency52.4%68%74%
Important
Density of Lattice Matter
\[ d = \frac{Z \cdot M}{N_A \cdot a^3} \]
Z = atoms/unit cell; M = molar mass; a = edge length; NA = Avogadro's number
Ionic Radii Ratio & Coordination Number
r₊/r₋ RangeCoordination NumberGeometry
0.155 – 0.2253Triangular Planar
0.225 – 0.4144Tetrahedral
0.414 – 0.7326Octahedral
0.732 – 1.0008Cubic (BCC type)
Seven Crystal Systems
Cubic | Orthorhombic | Tetragonal | Monoclinic | Rhombohedral | Triclinic | Hexagonal
14 Bravais lattices total across 7 crystal systems
NaCl (Rock Salt) Structure
\[ \text{CN} = 6:6 \quad;\quad a_{\text{FCC}} = 2(r_+ + r_-) \]
Na⁺ in octahedral voids of Cl⁻ FCC; 4 formula units/cell
CsCl Structure
\[ \text{CN} = 8:8 \quad;\quad a_{\text{SC}} = \frac{2}{\sqrt{3}}(r_+ + r_-) \]
ZnS (Zinc Blende) Structure
\[ \text{CN} = 4:4 \quad;\quad a_{\text{FCC}} = \frac{4}{\sqrt{3}}(r_{Zn^{2+}} + r_{S^{2-}}) \]
Bragg's Law (X-ray Diffraction)
\[ n\lambda = 2d\sin\theta \]
d = interplanar spacing; θ = angle of diffraction
⏱️

10. Chemical Kinetics & Radioactivity

18 Formulas
Key
Rate of Reaction
\[ r = -\frac{d[A]}{dt} = \frac{d[P]}{dt} \]
Unit: mol L⁻¹ s⁻¹
Rate Law
\[ r = k[A]^p[B]^q \]
p, q = orders; (p+q) = overall order; k = rate constant; Unit of k = (mol/L)^(1−n)·s⁻¹
Important
Integrated Rate Laws
OrderIntegrated LawHalf-life (t½)Unit of k
Zero\(C_t = C_0 - kt\)\(C_0/2k\)mol L⁻¹ s⁻¹
First\(k = \frac{2.303}{t}\log\frac{a}{a-x}\)\(0.693/k\)s⁻¹
Second (A+A)\(\frac{1}{a-x} - \frac{1}{a} = kt\)\(1/ka\)L mol⁻¹ s⁻¹
nth order—\(t_{1/2} \propto \frac{1}{[A_0]^{n-1}}\)(mol/L)^(1−n)·s⁻¹
NEET Key
First Order Half-life
\[ t_{1/2} = \frac{0.693}{k} \]
Independent of initial concentration — characteristic of 1st order reactions
Average Life (Mean Life)
\[ t_{\text{avg}} = \frac{1}{k} = 1.44\,t_{1/2} \]
Important
Arrhenius Equation
\[ k = A\,e^{-E_a/RT} \quad;\quad \ln k = \ln A - \frac{E_a}{RT} \]
A = frequency/pre-exponential factor; Ea = activation energy
Arrhenius (Two Temperatures)
\[ \log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\!\left(\frac{1}{T_1} - \frac{1}{T_2}\right) \]
Temperature Coefficient
\[ \mu = \frac{k_{T+10}}{k_T} \approx 2\text{ to }3 \]
Rate approximately doubles for every 10°C rise in temperature
Radioactive Decay
\[ N = N_0\,e^{-\lambda t} \quad;\quad t_{1/2} = \frac{0.693}{\lambda} \]
λ = decay constant; N₀ = initial number of atoms
Atoms Remaining After n Half-lives
\[ N = \frac{N_0}{2^n} \quad;\quad \text{time} = n\times t_{1/2} \]
Progress via Pressure (Gaseous Reactions)
\[ k = \frac{2.303}{t}\log\frac{P_0(n-1)}{nP_0 - P_t} \]
n = stoichiometric coefficient; P₀ = initial pressure
Pseudo First Order Reaction
\[ k' = kb \quad\Rightarrow\quad k = \frac{2.303}{t}\log\frac{a}{a-x} \]
When [B] is in large excess: b >> a; k' = pseudo 1st order rate constant