Physical Chemistry Formula Sheet & Chapterwise Quick-Reference - IIT-JEE MAINS 2027

Mastering Physical Chemistry for IIT-JEE MAINS 2027 requires a crystal-clear understanding of core mathematical relations, thermodynamic parameters, chemical kinetics equations, and electrochemistry state functions. Based on recent NTA question trends and PYQ weightage, Physical Chemistry contributes approximately 30-35% of the total Chemistry marks in JEE Main, with numerical value questions heavily emphasizing core formulas.

1. Thermodynamics & Thermochemistry

Thermodynamics forms the backbone of Physical Chemistry in JEE Main. NTA frequently combines First Law energy balances with Gibbs free energy criteria to test multi-concept numericals.

Core Formulas & Relations

First Law of Thermodynamics:

\[\Delta U = q + w\]

For expansion work against a constant external pressure \(P_{ext}\):

\[w = -P_{ext}\Delta V\]

Enthalpy Functions:

\[H = U + PV\] \[\Delta H = \Delta U + \Delta(PV)\]

For ideal gas reactions at constant temperature:

\[\Delta H = \Delta U + \Delta n_g RT\]

Heat Capacities & Phase Entropy:

\[C_p - C_v = R\] \[q = n C \Delta T\] \[\Delta S = \int \frac{dq_{rev}}{T}\]

For phase transition at constant transition temperature \(T_{trans}\):

\[\Delta S = \frac{\Delta H_{trans}}{T_{trans}}\]

Gibbs Free Energy & Spontaneity:

\[G = H - TS\] \[\Delta G = \Delta H - T\Delta S\]

Spontaneity criteria at constant temperature and pressure:

• \(\Delta G < 0\): Spontaneous process
• \(\Delta G = 0\): System at equilibrium
• \(\Delta G > 0\): Non-spontaneous process

Temperature Dependence of Equilibrium Constant (van 't Hoff Equation):

\[\Delta G^\circ = -RT \ln K\] \[\ln\bigl(\frac{K_2}{K_1}\bigr) = \frac{\Delta H^\circ}{R}\bigl(\frac{1}{T_1} - \frac{1}{T_2}\bigr)\]

2. Quantum Chemistry & Atomic Structure

Modern physics and physical chemistry overlap significantly in quantum theory. Understanding wave mechanics and probability density functions is vital for conceptual multiple-choice questions.

Key Energy & Wave Equations

Planck-Einstein & De Broglie Wavelength:

\[E = h u = \hbar\omega\] \[\lambda = \frac{h}{p} = \frac{h}{mv}\]

Heisenberg Uncertainty Principle:

\[\Delta x \cdot \Delta p_x \ge \frac{\hbar}{2}\] \[\Delta E \cdot \Delta t \ge \frac{\hbar}{2}\]

Schrödinger Wave Mechanics & Particle in a 1D Box:

\[\hat{H}\psi = E\psi\]

Wavefunction for a particle trapped in a 1D potential well of length \(L\):

\[\psi_n(x) = \sqrt{\frac{2}{L}}\sin\bigl(\frac{n\pi x}{L}\bigr)\] \[E_n = \frac{n^2 h^2}{8mL^2}, \quad n = 1, 2, 3, \dots\]

3. Chemical Kinetics & Rate Laws

Chemical kinetics questions in JEE Main test order determination, half-life formulas, and temperature coefficient calculations via Arrhenius plots.

Integrated Rate Laws & Half-Life Summary

\[\text{Differential Rate Law: } \text{Rate} = k[A]^m[B]^n\]

• Zero-Order Reaction: \([A]_t = [A]_0 - kt\), half-life \(t_{1/2} = \frac{[A]_0}{2k}\)
• First-Order Reaction: \(\ln[A]_t = \ln[A]_0 - kt\), half-life \(t_{1/2} = \frac{\ln 2}{k} \approx \frac{0.693}{k}\)
• Second-Order Reaction: \(\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt\), half-life \(t_{1/2} = \frac{1}{k[A]_0}\)

Arrhenius Equation & Temperature Dependence:

\[k = A e^{-E_a / RT}\] \[\ln\bigl(\frac{k_2}{k_1}\bigr) = \frac{E_a}{R}\bigl(\frac{T_2 - T_1}{T_1 T_2}\bigr)\]

4. Electrochemistry & Conductance

Electrochemistry carries high weightage in JEE Main Section B (numerical entry). Practice applying the Nernst equation for concentration cells and Kohlrausch's law for weak electrolytes.

Galvanic Cells & Electrolytic Conductance

Nernst Equation:

\[E = E^\circ - \frac{RT}{nF} \ln Q\]

At standard temperature \(298\text{ K}\):

\[E = E^\circ - \frac{0.0591}{n} \log Q\]

Thermodynamic Relation & Cell Equilibrium:

\[\Delta G^\circ = -nFE^\circ\] \[\log K = \frac{n E^\circ}{0.0591} \quad (\text{at } 298\text{ K})\]

Conductance & Kohlrausch's Law:

\[\Lambda_m = \frac{\kappa \cdot 1000}{c}\] \[\Lambda_m^\circ = u_+ \lambda_+^\circ + u_- \lambda_-^\circ\]

5. Solutions & Colligative Properties

Colligative properties depend on the number of solute particles in solution. The van 't Hoff factor \(i\) accounts for dissociation or association of ionic and molecular solutes.

Raoult's Law & Colligative Equations

\[P_A = X_A P_A^0\] \[\Delta T_b = i K_b m\] \[\Delta T_f = i K_f m\] \[\Pi = iCRT\] \[i = 1 + \alpha(n - 1)\]

6. Gaseous State & Molecular Velocities

Understanding ideal and real gas deviations is essential for understanding critical constants and compressiblity factor \(Z\).

Gas Laws & Real Gas Corrections

Ideal Gas Law:

\[PV = nRT = N k_B T\]

van der Waals Equation for Real Gases:

\[\bigl(P + \frac{a n^2}{V^2}\bigr)(V - nb) = nRT\]

Where \(a\) accounts for intermolecular attractive forces and \(b\) represents co-volume (excluded volume of gas molecules).

7. NTA Pattern & PYQ Weightage Analysis

According to past 5-year PYQ analyses for JEE Main (2020-2026):

Chapter Topic	Avg Questions per Shift	Expected Question Type
Thermodynamics & Thermochemistry	1 - 2	Numerical Value / Formula Application
Electrochemistry	1 - 2	Nernst Equation / Conductance Units
Chemical Kinetics	1	Arrhenius Equation / First Order Half-life
Solutions & Colligative Properties	1	van 't Hoff Factor Calculation
Quantum Mechanics / Atomic Structure	1	de Broglie / Heisenberg Uncertainty

8. Frequently Asked Questions (People Also Ask)

---