Physical Chemistry Cheat Sheet - IIT-JEE MAINS 2027

Welcome to the ultimate chapter-wise reference guide and cheat sheet for IIT-JEE MAINS 2027 Physical Chemistry. Designed following the LibreTexts modular textbook format, this comprehensive resource covers critical formulas, fundamental laws, and high-yield concepts mapped strictly to the latest NTA exam pattern. Utilize this guide for rapid revision, concept strengthening, and solving past year questions (PYQs).

Table of Contents

• 1. Thermodynamics & Thermochemistry
• 2. Chemical & Ionic Equilibrium
• 3. Chemical Kinetics
• 4. Structure & Organic-Physical Interface
• 5. NTA Pattern & Chapter Weightage Analysis
• 6. Frequently Asked Questions (FAQ)

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1. Thermodynamics & Thermochemistry

Thermodynamics forms the backbone of Physical Chemistry in the IIT-JEE Mains syllabus. Questions typically focus on state functions, work done in various processes, and spontaneity conditions.

1.1 First Law of Thermodynamics

The First Law states the conservation of energy: \(\Delta U = q + w\).

Pressure-Volume Work is defined as: \[w = -\int P_{\text{ext}} dV\]

• Reversible Isothermal Process: \[w = -nRT \ln\bigl(\frac{V_2}{V_1}\bigr)\]
• Irreversible Isothermal Process: \[w = -P_{\text{ext}}(V_2 - V_1)\]
• Adiabatic Process (\(q = 0\)): \[w = \Delta U = n C_v \Delta T\]
• Reversible Adiabatic Condition: \[P V^\gamma = \text{constant}, \quad \gamma = \frac{C_p}{C_v}\]

1.2 Enthalpy & Heat Capacity

Enthalpy (\(H\)) is given by \(H = U + PV\). For an ideal gas, Mayer's relation states \(C_p - C_v = R\).

Heat capacity equations: \[\Delta H = n C_p \Delta T, \quad \Delta U = n C_v \Delta T\]

1.3 Entropy & Gibbs Free Energy

The Second Law of Thermodynamics introduces entropy: \[dS = \frac{dq_{\text{rev}}}{T}, \quad \Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \ge 0\]

Entropy change for an ideal gas: \[\Delta S_{\text{ideal gas}} = n C_v \ln\bigl(\frac{T_2}{T_1}\bigr) + n R \ln\bigl(\frac{V_2}{V_1}\bigr)\]

Gibbs Free Energy determines process spontaneity: \[G = H - TS \implies \Delta G = \Delta H - T \Delta S\]

At standard state equilibrium: \[\Delta G^\circ = -RT \ln K_{\text{eq}}\]

A process is thermodynamically spontaneous when \(\Delta G < 0\).

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2. Chemical & Ionic Equilibrium

Equilibrium topics test numerical accuracy regarding reversible reactions, pH calculations, and solubility limits.

2.1 Chemical Equilibrium

Relation between equilibrium constants: \[K_p = K_c (RT)^{\Delta n_g}\]

Temperature dependence is governed by the van 't Hoff Equation: \[\frac{d \ln K}{dT} = \frac{\Delta H^\circ}{RT^2} \implies \ln\bigl(\frac{K_2}{K_1}\bigr) = -\frac{\Delta H^\circ}{R}\bigl(\frac{1}{T_2} - \frac{1}{T_1}\bigr)\]

2.2 Ionic Equilibrium & pH

Logarithmic scale definitions: \[\text{pH} = -\log[\text{H}^+], \quad \text{pOH} = -\log[\text{OH}^-], \quad \text{pH} + \text{pOH} = 14\]

Ostwald Dilution Law for weak electrolytes: \[K_a = \frac{C \alpha^2}{1-\alpha} \approx C\alpha^2 \quad \text{for } \alpha \ll 1\]

2.3 Buffer Solutions & Solubility Product

Henderson-Hasselbalch Equations:

• Acidic Buffer: \[\text{pH} = pK_a + \log\bigl(\frac{[\text{Salt}]}{[\text{Acid}]}\bigr)\]
• Basic Buffer: \[\text{pOH} = pK_b + \log\bigl(\frac{[\text{Salt}]}{[\text{Base}]}\bigr)\]

Solubility Product Constant (\(K_{sp}\)) for sparse salt $A_x B_y leftharpoons x A^{y+} + y B^{x-}$: \[K_{sp} = x^x y^y S^{x+y}\]

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3. Chemical Kinetics

Chemical Kinetics focuses on reaction velocity, rate laws, order of reaction, and temperature activation barriers.

3.1 Integrated Rate Laws

• Zero-Order Reaction: \[k = \frac{[A]_0 - [A]_t}{t}, \quad t_{1/2} = \frac{[A]_0}{2k}\]
• First-Order Reaction: \[k = \frac{2.303}{t}\log\bigl(\frac{[A]_0}{[A]_t}\bigr), \quad t_{1/2} = \frac{0.693}{k}\]

3.2 Arrhenius Equation

Temperature sensitivity of rate constants: \[k = A e^{-E_a / RT} \implies \ln\bigl(\frac{k_2}{k_1}\bigr) = \frac{E_a}{R}\bigl(\frac{1}{T_1} - \frac{1}{T_2}\bigr)\]

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4. Structure & Organic-Physical Interface

Physical chemistry principles frequently overlap with organic structure stability and reaction energetics. Understanding functional group geometry is crucial for spatial awareness problems in competitive exams.

For example, consider the structural parameters and functional group interplay in acetylsalicylic acid given below:

```smiles CC(=O)Oc1ccccc1C(=O)O ```

Understanding the thermochemical stability, solubility product derivative in buffer systems, and hydrolysis kinetics of such aromatic ester derivatives is a common testing point in advanced NTA problems.

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5. NTA Pattern & Chapter Weightage Analysis

Analysis of recent trends in NTA-conducted IIT-JEE Mains papers indicates a consistent distribution across Physical Chemistry modules.

PYQ Analysis & Weightage Breakdown

• Thermodynamics & Thermochemistry: 2-3 Questions per shift. High weightage on numerical problems regarding path functions vs. state functions and $\Delta G$ calculations.
• Ionic & Chemical Equilibrium: 1-2 Questions per shift. Frequently tested via multi-stage buffer pH determination or precipitate formation conditions using $K_{sp}$.
• Chemical Kinetics: 1 Question per shift. Focuses heavily on first-order decay kinetics, graphical rate determination, and Arrhenius activation energy calculations.

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6. Frequently Asked Questions (FAQ)