IIT-JEE MAINS 2027 Physical Chemistry Formula Sheet & Chapter Breakdown

Welcome to the ultimate LibreTexts-style interactive guide for Physical Chemistry (IIT-JEE MAINS 2027). This comprehensive study resource covers fundamental thermodynamic laws, chemical kinetics rate equations, and quantum electrochemistry principles designed in accordance with the NTA testing pattern.

Table of Contents

• Chapter 1: Thermodynamics & Thermochemistry
• Chapter 2: Chemical Kinetics & Reaction Kinetics
• Chapter 3: Quantum Chemistry & Electrochemistry
• NTA Pattern & PYQ Analysis
• People Also Ask (FAQs)

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Chapter 1: Thermodynamics & Thermochemistry

1.1 The First Law of Thermodynamics

The fundamental mathematical formulation of the First Law expresses the conservation of internal energy \(U\) in terms of heat added to the system \(q\) and work done on/by the system \(w\):

\[\Delta U = q + w\]

1.2 Isothermal Reversible Expansion of an Ideal Gas

For an ideal gas undergoing a reversible, isothermal expansion from an initial volume \(V_1\) to a final volume \(V_2\) at temperature \(T\), the work done \(w\) is derived as:

\[w = -nRT \ln\bigl(\frac{V_2}{V_1}\bigr)\]

1.3 Enthalpy and Heat Capacities

Enthalpy \(H\) is defined via internal energy and state variables as \(H = U + PV\). For dynamic state changes, the differential enthalpy equation is given by:

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

The relation between constant pressure heat capacity \(C_p\) and constant volume heat capacity \(C_v\) for an ideal gas follows Mayer's relation:

\(C_p - C_v = R\)

1.4 Second Law, Entropy, and Gibbs Free Energy

Entropy change \(\Delta S\) for a reversible process and the total universe entropy change are governed by:

\[\Delta S = \int \frac{dq_{\text{rev}}}{T}, \quad \Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \ge 0\]

Gibbs Free Energy \(G\) measures system spontaneity under constant pressure and temperature:

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

At standard conditions, the equilibrium constant \(K\) relates directly to standard free energy:

\[\Delta G^\circ = -RT \ln K\]

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Chapter 2: Chemical Kinetics & Reaction Kinetics

2.1 Rate Laws & Differential Rate Equations

For a general stoichiometric reaction \(aA \to \text{Products}\), the instant rate of reaction is written as:

\[\text{rate} = -\frac{1}{a}\frac{d[A]}{dt} = k[A]^n\]

2.2 Integrated Rate Equations by Order

Understanding integrated rate laws allows calculation of remaining reactant concentrations \([A]_t\) at time \(t\) and the reaction half-life \(t_{1/2}\):

• Zero-Order Kinetics (\(n=0\)):
  \[[A]_t = -kt + [A]_0, \quad t_{1/2} = \frac{[A]_0}{2k}\]
• First-Order Kinetics (\(n=1\)):
  \[\ln[A]_t = -kt + \ln[A]_0, \quad t_{1/2} = \frac{\ln 2}{k}\]
• Second-Order Kinetics (\(n=2\)):
  \[\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}, \quad t_{1/2} = \frac{1}{k[A]_0}\]

2.3 Temperature Dependence & Arrhenius Equation

The rate constant \(k\) dependence on temperature is modeled using activation energy \(E_a\):

\[k = A e^{-E_a / RT}\]

Expressing two different temperatures \(T_1\) and \(T_2\) yields the integrated differential form:

\[\ln\bigl(\frac{k_2}{k_1}\bigr) = \frac{E_a}{R} \bigl(\frac{T_2 - T_1}{T_1 T_2}\bigr)\]

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Chapter 3: Quantum Chemistry & Electrochemistry

3.1 Quantum Mechanics Fundamentals

Energy quantization and wave-particle duality form the core foundation of modern atomic physics and chemistry:

• Schrödinger Wave Equation: \(\hat{H}\psi = E\psi\)
• Planck's Energy Relation: \(E = h u = \frac{hc}{\lambda}\)
• De Broglie Wavelength Equation: \(\lambda = \frac{h}{p} = \frac{h}{mv}\)

3.2 Electrochemistry & Cell Potential

The non-standard electromotive force \(E\) of an electrochemical cell is computed using the Nernst Equation:

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

At standard atmospheric room temperature (\(25^\circ\text{C}\) / \(298\text{ K}\)):

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

3.3 Electrical Thermodynamics & Kohlrausch's Law

The maximum non-PV work available from a cell corresponds to the standard Gibbs free energy change:

\(\Delta G^\circ = -nFE^\circ\)

For limiting molar conductivity \(\Lambda_m^\circ\) at infinite dilution, Kohlrausch's law of independent migration of ions dictates:

\[\Lambda_m^\circ = u_+ \lambda_+^\circ + u_- \lambda_-^\circ\]

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Spatial Organic Structure Visualization

Physical chemistry principles, such as reaction rates and thermodynamic stability, directly apply to conjugated organic molecules. Consider the spatial configuration given below:

```smiles CC(=C(C)C) ```

This molecule represents 2-methylbut-2-ene, which exhibits both hyperconjugation effects and specific thermodynamic stability governed by double-bond substitution patterns.

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NTA Pattern & PYQ Analysis

In recent years, the National Testing Agency (NTA) has placed increased emphasis on multi-concept questions in Physical Chemistry. A significant weightage in IIT-JEE MAINS is allocated to:

• Thermodynamics & Thermochemistry: Frequently combined with state functions, path functions, and non-ideal gas expansions (1-2 questions per shift).
• Electrochemistry & Kinetics: Numerical-value questions frequently combine Nernst equation calculations with first-order decay or half-life metrics (2 questions per shift).
• Chapter Weightage: Physical chemistry accounts for approximately 33-35% of the total Chemistry paper in JEE Mains, with a major focus on numerical integer-type section questions.

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People Also Ask (FAQs)

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