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Class 12 Chemistry Conductance of Electrolytic Solutions - Complete Study Notes

Introduction:

Conductance of electrolytic solutions is a fundamental concept in Class 12 Chemistry Chapter 2 Electrochemistry that explains how ionic solutions conduct electricity. Unlike metallic conductors that use electrons, electrolytic solutions conduct current through the movement of ions dissolved in the solution. This topic is crucial for understanding electrochemical cells, battery technology, and various industrial applications.

The ability of an electrolyte to conduct electricity depends on several factors including the concentration of ions, temperature, nature of the electrolyte, and the degree of dissociation. Understanding these principles helps explain phenomena from simple salt solutions to complex electrochemical processes in biological systems.

Types of Conductivity in Electrolytic Solutions

Specific Conductivity (κ)

Specific conductivity or conductivity is defined as the conductance of a unit volume of solution placed between two electrodes with unit area of cross-section and unit distance apart. It represents the intrinsic ability of the solution to conduct electricity.

Formula: κ = G × (l/A) = G × K

Where:

κ = specific conductivity (S cm⁻¹)

G = conductance (S)

l = distance between electrodes (cm)

A = area of electrodes (cm²)

K = cell constant (cm⁻¹)

Key Points:

SI unit: S m⁻¹ (commonly expressed as S cm⁻¹)

Specific conductivity decreases with dilution due to fewer ions per unit volume.

Depends on the nature and concentration of electrolyte

Molar Conductivity (Λₘ)

Molar conductivity is defined as the conductance of all ions produced by one mole of an electrolyte dissolved in solution. It provides information about the efficiency of ionic conduction per mole of electrolyte.

Formula: Λₘ = κ × 1000/c

Where:

Λₘ = molar conductivity (S cm² mol⁻¹)

κ = specific conductivity (S cm⁻¹)

c = molar concentration (mol L⁻¹)

Behavior with Dilution:

Strong electrolytes: Molar conductivity increases slowly with dilution

Weak electrolytes: Molar conductivity increases sharply with dilution due to increased ionization.

Equivalent Conductivity (Λₑq)

Equivalent conductivity represents the conductance of all ions produced by one gram-equivalent of electrolyte.

Formula: Λₑq = κ × 1000/Cₑq

Where Cₑq is the equivalent concentration.

Relationship: Λₘ = n × Λₑq (where n is the valency)

Cell Constant and Conductivity Measurement

Cell Constant (K)

The cell constant is a geometric factor that depends only on the physical dimensions of the conductivity cell.

Formula: K = l/A

Where:

l = distance between electrodes (cm)

A = effective area of electrodes (cm²)

Important Features:

Independent of temperature, electrolyte type, or concentration

Must be determined by calibration using standard solutions

Different cell constants suit different conductivity ranges

Common Cell Constants:

K = 0.01 cm⁻¹: Ultrapure water, distilled water

K = 0.1 cm⁻¹: Drinking water, low conductivity solutions

K = 1.0 cm⁻¹: Industrial water, moderate conductivity

K = 10.0 cm⁻¹: High concentration electrolytes, concentrated solutions

Conductivity Measurement:

Specific Conductivity = Measured Conductance × Cell Constant

The conductometer measures conductance, which is then multiplied by the cell constant to obtain true conductivity.

Strong vs Weak Electrolytes

Strong Electrolytes

Strong electrolytes undergo complete or nearly complete ionization in solution.

Characteristics:

Complete dissociation into ions

High conductivity at all concentrations

Molar conductivity varies slightly with concentration

Examples: NaCl, KBr, HCl, NaOH, H₂SO₄

Variation with Dilution:

The relationship follows Kohlrausch's equation: Λₘ = Λ°ₘ - A√c

Where:

Λ°ₘ = limiting molar conductivity

A = constant depending on electrolyte type

c = concentration

Weak Electrolytes

Weak electrolytes undergo partial ionization in solution.

Characteristics:

Partial dissociation into ions

Lower conductivity compared to strong electrolytes

Molar conductivity increases sharply with dilution

Examples: CH₃COOH, NH₄OH, H₂CO₃

Degree of Dissociation:

α = Λₘ/Λ°ₘ

Where α represents the fraction of molecules dissociated.

Kohlrausch's Law of Independent Migration of Ions

Statement

Kohlrausch's law states that at infinite dilution, each ion migrates independently and contributes individually to the total molar conductivity, regardless of the nature of other ions present.

Mathematical Expression: Λ°ₘ = λ°₊ + λ°₋

Where:

Λ°ₘ = limiting molar conductivity of electrolyte

λ°₊ = limiting molar conductivity of cation

λ°₋ = limiting molar conductivity of anion

Applications of Kohlrausch's Law

1. Calculation of Limiting Molar Conductivity for Weak Electrolytes

For acetic acid (CH₃COOH): Λ°ₘ(CH₃COOH) = λ°(H⁺) + λ°(CH₃COO⁻)

This can be calculated using strong electrolytes: Λ°ₘ(CH₃COOH) = Λ°ₘ(HCl) + Λ°ₘ(CH₃COONa) - Λ°ₘ(NaCl)

2. Determination of Degree of Dissociation

For weak electrolytes: α = Λₘ/Λ°ₘ

3. Calculation of Dissociation Constant

For a weak electrolyte: Kₐ = (Cα²)/(1-α)

Where C is the initial concentration.

Factors Affecting Conductance

1. Concentration

Specific conductivity: Increases with concentration (more ions per unit volume)

Molar conductivity: Decreases with concentration due to inter-ionic interactions

2. Temperature

Higher temperature increases ionic mobility

Generally increases all types of conductivity

Enhanced kinetic energy overcomes inter-ionic forces

Nature of Electrolyte

Strong electrolytes show higher conductivity than weak electrolytes

Multivalent ions contribute more to conductivity

Size and charge of ions affect mobility

Solvent Properties

Dielectric constant affects degree of dissociation

Viscosity influences ionic mobility

Temperature affects solvent properties

Important Formulas and Relationships

Basic Relationships:

Conductance and Resistance: G = 1/R

Specific Conductivity: κ = G × K = G × (l/A)

Molar Conductivity: Λₘ = κ × 1000/c

Kohlrausch's Law: Λ°ₘ = λ°₊ + λ°₋

Degree of Dissociation: α = Λₘ/Λ°ₘ

For Strong Electrolytes: Λₘ = Λ°ₘ - A√c

Unit Conversions:

Conductivity: S m⁻¹ = 100 × S cm⁻¹

Molar conductivity: S m² mol⁻¹ = 10⁴ × S cm² mol⁻¹

Solved Examples:

Example 1: Calculate Molar Conductivity

Given: κ = 0.001 S cm⁻¹, c = 0.01 mol L⁻¹

Solution:

Λₘ = κ × 1000/c = 0.001 × 1000/0.01 = 100 S cm² mol⁻¹

Example 2: Degree of Dissociation

For 0.025 mol L⁻¹ methanoic acid with Λₘ = 46.1 S cm² mol⁻¹ Given: λ°(H⁺) = 349.6 S cm² mol⁻¹, λ°(HCOO⁻) = 54.6 S cm² mol⁻¹

Solution: Λ°ₘ(HCOOH) = 349.6 + 54.6 = 404.2 S cm² mol⁻¹ α = Λₘ/Λ°ₘ = 46.1/404.2 = 0.114 = 11.4%

Practical Applications:

1. Water Quality Testing

Conductivity measurements determine the purity of water and concentration of dissolved salts. Pure water has very low conductivity, while contaminated water shows higher values.

2. Battery Technology

Understanding electrolyte conductivity is crucial for designing efficient batteries and fuel cells. Higher ionic conductivity leads to better battery performance.

3. Chemical Analysis

Conductometric titrations use conductivity changes to determine end points and analyze solution composition.

4. Industrial Processes

Monitoring electrolyte conductivity ensures proper conditions in electroplating, water treatment, and chemical manufacturing.

Important Points for Examinations

Key Concepts to Remember

Conductivity decreases with dilution, but molar conductivity increases

Strong electrolytes show complete ionization; weak electrolytes show partial ionization

Kohlrausch's law applies only at infinite dilution

Cell constant is independent of solution properties

Degree of dissociation increases with dilution for weak electrolytes

Common Mistakes to Avoid

Confusing specific conductivity with molar conductivity

Forgetting the factor of 1000 in molar conductivity calculations

Mixing up units in problem solving

Not considering temperature effects in conductivity measurements

Conclusion:

The conductance of electrolytic solutions is a fundamental topic that bridges theoretical chemistry with practical applications. Understanding the different types of conductivity, the behavior of strong versus weak electrolytes, and Kohlrausch's law provides essential knowledge for electrochemistry. These concepts form the foundation for advanced topics in electrochemical cells, batteries, and analytical chemistry. Mastering this topic requires understanding the mathematical relationships, practicing numerical problems, and appreciating the real-world applications in technology and industry. The principles learned here apply directly to modern developments in energy storage, water treatment, and chemical analysis.

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Mechanical Properties of Solids: Stress and Strain VAVA Classes

Introduction:

Mechanical properties tell us how a solid responds to forces. Two core ideas are stress and strain. They help predict strength, elasticity, and failure. This guide from VAVA Classes explains definitions, types, formulas, the stress–strain curve, and real-world uses in clear language.

What Are Mechanical Properties of Solids?

These properties describe how materials behave under load: whether they are rigid, ductile, brittle, or tough. Key measures include elasticity, plasticity, strength, and toughness.

Stress:

Definition: Internal restoring force per unit area.

Formula: Stress = Force / Area

Types of Stress:

• Tensile Stress: stretching action • Compressive Stress: squeezing action • Shear Stress: tangential force causing layers to slide

Strain:

Definition: Relative deformation (dimensionless).

Formula: Strain = Change in dimension / Original dimension

Types of Strain:

• Longitudinal Strain: change in length per original length • Volumetric Strain: change in volume per original volume • Shear Strain: angular distortion

Hooke’s Law and Elastic Constants:

Within the elastic limit, stress is proportional to strain.

Formula: Stress ∝ Strain

Elastic Moduli:

• Young’s modulus (E): ratio of normal stress to longitudinal strain • Shear modulus (G): ratio of shear stress to shear strain • Bulk modulus (K): ratio of pressure change to volumetric strain • Poisson’s ratio (ν): lateral strain / longitudinal strain

Stress–Strain Curve:

1. Proportional limit: Hooke’s law holds 2. Elastic limit: end of reversibility 3. Yield point: start of plastic flow 4. Ultimate tensile strength: maximum stress 5. Fracture: necking and break

Applications and Examples:

• Bridges and buildings: beams using E and yield strength • Machine parts: torsion and shear modulus • Pressure vessels: hoop stress and bulk modulus • Sports gear: flexibility and strength tuning

Conclusion:

Stress and strain form the base of the mechanical behavior of solids. Know the definitions, types, key constants, and curve features, and you can solve most exam and design questions with confidence. Keep this page from VAVA Classes handy as a quick reference.

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Carcinogenicity and Toxicity – NCERT Class 11 Chemistry Notes

Introduction:

In Chemistry, it is not just about reactions and compounds, but also about their impact on living beings and the environment. The concepts of carcinogenicity and toxicity deal with the harmful effects of chemicals. Understanding these terms helps students stay aware of the safety and health risks associated with chemicals used in daily life. This topic is included in Chapter 14 – Environmental Chemistry of the Class 11 NCERT Chemistry textbook and is crucial for both academic knowledge and real-world awareness.

What is Toxicity?

Toxicity refers to the degree to which a substance can damage an organism. Toxic chemicals can affect the body in different ways depending on the dose, duration of exposure, route of exposure, and nature of the substance.

Examples of toxic substances:

• Carbon monoxide (CO) • Arsenic compounds • Mercury and its compounds • Pesticides like DDT

Types of Toxicity

Acute Toxicity: Results from a single or short-term exposure. Symptoms occur quickly. Example: Carbon monoxide inhalation. Chronic Toxicity: Results from prolonged or repeated exposure. Symptoms appear after months or years. Example: Arsenic-contaminated water.

What is Carcinogenicity?

Carcinogenicity refers to the ability of a substance to cause cancer. Carcinogens are substances that lead to uncontrolled cell growth and tumor formation.

Common Carcinogens

• Asbestos • Tobacco smoke • Formaldehyde • Aflatoxins • Industrial dyes and solvents

Classification of Carcinogens (IARC)

• Group 1 – Carcinogenic to humans • Group 2A – Probably carcinogenic • Group 2B – Possibly carcinogenic • Group 3 – Not classifiable

Impact on Health and Environment

Human Health: Organ damage, cancer, genetic mutations. Environment: Bioaccumulation, soil/water pollution.

Prevention and Safety Measures

• Use Personal Protective Equipment (PPE) • Proper chemical labeling and storage • Refer to Material Safety Data Sheets (MSDS) • Follow disposal protocols • Apply green chemistry principles

Summary Table

Conclusion:

Understanding carcinogenicity and toxicity is essential for every chemistry student. As future professionals, students must be aware of the potential hazards of chemicals and follow safety protocols to minimize risks.

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Class 11 Chemistry: Towards Quantum Mechanical Model & Quantum Mechanical Model of Atom

Introduction:

Understanding the structure of the atom has been a central focus in atomic theory. While Bohr’s model introduced the concept of quantized orbits, it failed to explain the behavior of multi-electron atoms and the fine structure of spectral lines. This led to the development of a more advanced theory — the Quantum Mechanical Model of the Atom, built upon the foundations laid by de Broglie, Heisenberg, and Schrödinger.

Towards Quantum Mechanical Model of the Atom:

Limitations of Bohr’s Model:

- Could not explain Zeeman and Stark effects. - Failed for atoms beyond hydrogen. - Treated electrons as particles only.

Dual Nature of Matter — de Broglie Hypothesis:

Proposed by Louis de Broglie. Matter exhibits both particle and wave nature. Equation: λ = h/mv

Heisenberg’s Uncertainty Principle:

It is impossible to determine the exact position and momentum of an electron simultaneously. Δx·Δp ≥ h/4π

Need for a New Model:

Particle nature alone couldn’t describe electron behavior. Wave mechanics needed to describe subatomic particles accurately.

Quantum Mechanical Model of Atom:

Schrödinger’s Wave Equation:

Developed a mathematical model for electron wave behavior. Time-independent equation: Ĥψ = Eψ

Wave Function and Its Significance:

ψ² gives probability density of finding an electron.

Atomic Orbitals:

Region in space with high probability of finding electrons. Described using quantum numbers.

Quantum Numbers:

1. Principal Quantum Number (n): Energy level 2. Azimuthal Quantum Number (l): Shape of orbital 3. Magnetic Quantum Number (m): Orientation 4. Spin Quantum Number (s): Spin direction of electron

Shapes of Orbitals:

s-orbital: Spherical p-orbital: Dumbbell d-orbital: Cloverleaf f-orbital: Complex shapes

Pauli Exclusion Principle:

No two electrons in an atom can have the same set of all four quantum numbers.

Hund’s Rule of Maximum Multiplicity:

Electrons occupy degenerate orbitals singly before pairing.

Aufbau Principle:

Electrons fill orbitals from lower to higher energy.

Conclusion:

The Quantum Mechanical Model of the Atom revolutionized atomic theory by incorporating wave-particle duality and uncertainty. It provides a probabilistic approach to understanding electron distribution, successfully explaining the structure and properties of even complex atoms — a foundational concept for chemistry and physics alike.

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National Doctor's Day: A Tribute and Motivation for Future Doctors

Introduction:

Every year on July 1st, India celebrates National Doctor’s Day to honor the invaluable contribution of doctors in saving lives and serving humanity. For NEET aspirants and students preparing for medical entrance exams, this day is more than a celebration — it is a source of deep motivation and purpose. At VAVA Classes, we take this opportunity to inspire the next generation of doctors to dream bigger and serve better.

Why is National Doctor's Day Celebrated?

Honoring Dr. Bidhan Chandra Roy:

National Doctor’s Day in India commemorates the birth and death anniversary of Dr. B.C. Roy, a renowned physician, freedom fighter, and former Chief Minister of West Bengal. His dedication to the field of medicine and public service is a beacon for medical aspirants across the country.

What Makes This Day Special for NEET Aspirants?

It’s a Day of Purpose

For students aiming for a seat in MBBS or other medical programs through NEET (National Eligibility cum Entrance Test), this day is a powerful reminder of the noble profession they aspire to join.

Motivation to Push Harder

Hearing stories of doctors who once were students battling textbooks and mock tests can boost your motivation, especially during times of stress or burnout.

Reinforcing the Dream

Doctor’s Day reinforces the reason behind those long study hours — to serve, to heal, and to make a difference.

How Can NEET Aspirants Celebrate Doctor's Day?

1. Learn from Real Stories

Watch documentaries, read biographies, or attend webinars where doctors share their journeys. These real-life experiences can guide your own path.

2. Recommit to Your NEET Goal

Take this day to set a new milestone in your preparation — revise a difficult topic, take a mock test, or organize your study plan.

3. Thank the Doctors Around You

If you or your family have ever been helped by a doctor, a small thank-you note or call can make their day.

4. Join a Special Session at VAVA Classes

At VAVA Classes, we often host motivational webinars and guest talks from doctors to help NEET aspirants see the real-world impact of their future profession.

Lessons from Doctor’s Day for Future Medical Students

Discipline and Dedication

Success in NEET and in medicine requires unwavering focus — something every successful doctor embodies.

Compassion is Key

Medicine is not just about knowledge but empathy. This value must be built during the student phase itself.

Conclusion

National Doctor’s Day is not just about honoring existing doctors — it’s about encouraging future ones too. If you’re a NEET aspirant, let this day ignite a stronger passion for your dream. At VAVA Classes, we believe that every doctor starts with a dream, and every dream needs the right guidance. Let us walk this journey with you — from books to white coats.

👉 Join VAVA Classes Today and take your NEET preparation to the next level. Let's make your dream of becoming a doctor come true!

📞 Call: 9090961010

🌐 Visit: www.vavaclasses.com

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Detailed Study Notes on Class 12 Chemistry: Proteins

Introduction:

Proteins are vital biological macromolecules essential for life. In Class 12 Chemistry (Chapter: Biomolecules), understanding proteins includes their structure, types, and functions. These notes help you grasp the key concepts easily for board exams and competitive preparation like NEET and JEE.

What Are Proteins?

Proteins are large, complex molecules made up of amino acids joined by peptide bonds. They play critical roles in almost all biological processes. Chemically, proteins are polymers of α-amino acids.

Amino Acids – Building Blocks of Proteins

Structure of α-Amino Acids: Each amino acid has a central α-carbon, an amino group (–NH₂), a carboxylic group (–COOH), a hydrogen atom, and a variable R group. General formula: NH₂–CH(R)–COOH Classification: - Essential Amino Acids (e.g., Valine, Leucine) - Non-Essential Amino Acids (e.g., Glycine, Alanine)

Formation of Peptides and Proteins

Peptide Bond: Formed when –COOH of one amino acid reacts with –NH₂ of another, releasing water. Types: - Dipeptide: 2 amino acids - Tripeptide: 3 amino acids - Polypeptide: Many amino acids - Protein: More than ~50 amino acids in a specific 3D structure

Structure of Proteins

1. Primary Structure: Linear sequence of amino acids. 2. Secondary Structure: α-Helix and β-Pleated Sheet (hydrogen bonds). 3. Tertiary Structure: 3D shape formed by R-group interactions. 4. Quaternary Structure: Multiple polypeptide chains (e.g., Hemoglobin).

Classification of Proteins

By Composition: - Simple Proteins: Only amino acids - Conjugated Proteins: With non-protein parts By Function: - Structural: Keratin, Collagen - Enzymatic: Pepsin, Amylase - Transport: Hemoglobin - Hormonal: Insulin

Denaturation of Proteins

Loss of structure and biological activity due to temperature, pH, or chemicals. Example: Cooking an egg – Albumin protein coagulates.

Functions of Proteins

- Structural: Build cells and tissues - Enzymatic: Catalyze reactions - Transport: Carry substances - Regulatory: Hormones - Protective: Antibodies

Protein Tests (Class 12 Practical Relevance)

Biuret Test: Purple color indicates proteins. Xanthoproteic Test: Yellow color shows aromatic amino acids.

Important Protein Examples for Board Exams

Hemoglobin – Oxygen transport Insulin – Blood sugar regulation Albumin – Osmotic pressure control Pepsin – Protein digestion

Conclusion

Understanding proteins in Class 12 Chemistry is crucial for exams and future studies. Focus on structure, classification, and functions. Use diagrams and tables for clarity.

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Carbohydrates Class 12 Chemistry Notes- Biomolecules Chapter Explained

Introduction to Carbohydrates

Carbohydrates are the most abundant organic compounds found in nature and are vital for life. They serve as a primary source of energy for living organisms. Chemically, carbohydrates are polyhydroxy aldehydes or ketones or compounds that yield them on hydrolysis. The general formula is Cn(H2O)n.

Classification of Carbohydrates

1. Monosaccharides

• Simplest form of carbohydrates. • Cannot be hydrolyzed further. • General formula: CnH2nOn • Examples: Glucose, Fructose

2. Oligosaccharides

• Contain 2–10 monosaccharide units. • Most important oligosaccharide: Disaccharides • Examples: Sucrose (Glucose + Fructose), Lactose (Glucose + Galactose), Maltose (Glucose + Glucose)

3. Polysaccharides

• Long chains of monosaccharide units. • Not sweet, insoluble in water. • Examples: Starch, Cellulose, Glycogen

Structure and Function of Monosaccharides

Monosaccharides are further classified based on: - Number of carbon atoms: Trioses, Tetroses, Pentoses, Hexoses - Functional group:   • Aldoses (with –CHO group)   • Ketoses (with –CO group) Glucose is an aldohexose with the formula C6H12O6. It exists in two cyclic forms: α-glucose and β-glucose.

Reducing and Non-Reducing Sugars

Reducing Sugars

• Can reduce Fehling’s or Tollen’s reagent. • Contain free aldehyde or ketone group. • Examples: Glucose, Maltose, Lactose

Non-Reducing Sugars

• Do not have a free –CHO or –CO group. • Example: Sucrose

Properties of Glucose

• Sweet, soluble in water • Undergoes oxidation and reduction • Does not react with Schiff’s reagent • Exists as α- and β- anomers in solution

Polysaccharides in Biological Systems

Starch

• Plant storage carbohydrate • Made of amylose and amylopectin

Glycogen

• Animal storage carbohydrate • Similar to amylopectin but more branched

Cellulose

• Structural polysaccharide in plants • Cannot be digested by humans

Tests for Carbohydrates

1. Molisch’s Test

• General test for carbohydrates (violet ring formation)

2. Benedict’s Test

• Detects reducing sugars (brick red precipitate)

3. Fehling’s Test

• Another test for reducing sugars (red ppt. of Cu2O)

Importance of Carbohydrates:

• Source of energy: 1 gram = 4 kcal • Storage: Glycogen in animals, starch in plants • Structural role: Cellulose in plant cell walls • Component of biomolecules: DNA, RNA (ribose, deoxyribose)

Conclusion

Carbohydrates are crucial biomolecules that play multiple roles in metabolism and structure. Understanding their classification, structure, and functions provides a strong foundation in organic chemistry and biology. In exams, focus on glucose structure, disaccharide linkages, and polysaccharide functions for scoring high.

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Integration by Parts – Class 12 Mathematics Notes

Introduction:

Integration by Parts is a crucial technique in integral calculus, especially useful when dealing with the integration of the product of two functions. It is derived from the product rule of differentiation and helps solve complex integrals that cannot be integrated directly. Understanding this method thoroughly will aid in solving various problems in CBSE Class 12 board exams and competitive exams like JEE Main.

Formula for Integration by Parts:

If u = f(x) and v = g(x), then:

∫ u·v dx = u ∫v dx - ∫ (du/dx · ∫v dx) dx

Or simply,

∫ u·v dx = uv - ∫ v·(du/dx) dx

Choosing u and v – ILATE Rule:

To select which function to differentiate and which to integrate, use the ILATE rule:

I: Inverse Trigonometric functions L: Logarithmic functions A: Algebraic functions T: Trigonometric functions E: Exponential functions

Solved Examples of Integration by Parts:

Evaluate ∫ x · e^x dx

Let u = x (Algebraic), dv = e^x dx Then, du = dx, and v = ∫ e^x dx = e^x Apply the formula: ∫ x·e^x dx = x·e^x - ∫ e^x dx = x·e^x - e^x + C Answer: ∫ x·e^x dx = e^x(x - 1) + C

Evaluate ∫ ln x dx

Let u = ln x, dv = dx Then, du = (1/x) dx, v = ∫ dx = x Apply the formula: ∫ ln x dx = x·ln x - ∫ x·(1/x) dx = x·ln x - ∫ 1 dx = x·ln x - x + C Answer: ∫ ln x dx = x(ln x - 1) + C

Evaluate ∫ x · sin x dx

Let u = x, dv = sin x dx Then, du = dx, v = ∫ sin x dx = -cos x Apply the formula: ∫ x·sin x dx = -x·cos x + ∫ cos x dx = -x·cos x + sin x + C Answer: ∫ x·sin x dx = -x·cos x + sin x + C

Special Cases and Tips:

Some integrals may require repeated application of the formula. For example: ∫ x^2 e^x dx

Practice Questions

1. ∫ x · cos x dx 2. ∫ x · ln x dx 3. ∫ x^2 · e^x dx 4. ∫ arctan x dx 5. ∫ ln x dx

Conclusion:

Integration by Parts is a powerful technique in calculus, especially when dealing with products of functions. Mastery of the ILATE rule and regular practice of varied problems ensures confidence and accuracy in the exams.

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Specific Heat Capacity – Class 11 Physics Notes

Introduction:

Thermodynamics is a vital part of Class 11 Physics that deals with heat, energy, and their transformation. One of the essential concepts in this chapter is Specific Heat Capacity. Understanding this topic helps explain how substances respond to heat and why different materials heat up or cool down at different rates.

What is Specific Heat Capacity?

Specific Heat Capacity (c) is defined as the amount of heat required to raise the temperature of one kilogram of a substance by one degree Celsius (or 1 Kelvin).

Formula: Q = mcΔT

Where: - Q = heat energy supplied (in joules) - m = mass of the substance (in kg) - c = specific heat capacity (in J/kg·K) - ΔT = change in temperature (in °C or K)

Unit and Dimensions of Specific Heat Capacity:

- SI Unit: Joule per kilogram per Kelvin (J/kg·K) - CGS Unit: Calorie per gram per degree Celsius (cal/g·°C) - Dimensions: [L² T⁻² Θ⁻¹]

Types of Heat Capacities:

1. Specific Heat at Constant Volume (Cv)

Heat required to raise the temperature at constant volume. Relevant for gases in rigid containers.

2. Specific Heat at Constant Pressure (Cp)

Heat required to raise the temperature at constant pressure. Higher than Cv due to additional work done during expansion.

Relationship for ideal gases: Cp - Cv = R

Molar Specific Heat Capacity:

The heat capacity of 1 mole of a substance. Units: J/mol·K

Factors Affecting Specific Heat Capacity:

1. Nature of the Material

Metals have low specific heat, water has high specific heat.

2. Phase of Substance

Solids, liquids, and gases have different specific heats.

3. Temperature Range

Specific heat can vary with temperature.

Applications of Specific Heat Capacity:

- Cooking utensils - Climate control - Automobile cooling systems - Calorimetry

Worked Examples:

Example 1

How much heat is needed to raise the temperature of 2 kg of water from 25°C to 75°C? Given: c = 4186 J/kg·K

Q = mcΔT = 2 × 4186 × (75 - 25) = 418600 J

Example 2

A 500 g metal requires 2000 J to raise its temperature by 10°C. Find its specific heat.

c = Q / (mΔT) = 2000 / (0.5 × 10) = 400 J/kg·K

Experimental Determination (Calorimetry Method)

Principle of Calorimetry:

Heat lost = Heat gained

Procedure:

Use a calorimeter, heat a substance, place it in the calorimeter, measure equilibrium temperature, and use the equation to solve.

Conclusion:

Specific Heat Capacity is a crucial thermodynamic concept that helps us understand the thermal behavior of different materials. It forms the foundation for real-world applications such as climate science, engineering, and even daily cooking.

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Method of Preparation of Diazonium Salts – Class 12 Chemistry Notes

Introduction:

Diazonium salts form an important category of organic compounds that are widely used in organic synthesis, especially in the manufacture of azo dyes, pharmaceuticals, and aromatic derivatives. These compounds are prepared primarily from aromatic amines and are characterized by the presence of the functional group –N₂⁺X⁻. In Class 12 Chemistry, the topic is covered under the chapter “Amines”, and it often carries significant weightage in CBSE Board exams and entrance exams like NEET and JEE.

What are Diazonium Salts?

Diazonium salts are organic compounds that contain a diazonium group (–N₂⁺) attached to an aryl group. The general formula is ArN₂⁺X⁻, where: - Ar = Aromatic group (usually derived from benzene) - X⁻ = Anion like Cl⁻, Br⁻, NO₃⁻, HSO₄⁻, etc.

Example: Benzenediazonium chloride (C₆H₅N₂⁺Cl⁻)

General Method of Preparation of Diazonium Salts

Diazonium salts are prepared by a chemical reaction known as diazotization, which involves the reaction of primary aromatic amines with nitrous acid (HNO₂) in an acidic medium under cold conditions (0–5°C).

General Reaction: ArNH₂ + HNO₂ + HX → ArN₂⁺X⁻ + 2H₂O

Example using Aniline: C₆H₅NH₂ + HNO₂ + HCl → C₆H₅N₂⁺Cl⁻ + 2H₂O

Laboratory Preparation of Diazonium Salts:

In the lab, nitrous acid is prepared in situ: NaNO₂ + HCl → HNO₂ + NaCl

Step-by-Step Procedure: 1. Prepare a cold solution of aniline in dilute HCl. 2. Cool to 0–5°C. 3. Add NaNO₂ solution slowly while stirring.

Conditions Required for Diazotization Reaction:

Temperature: 0°C to 5°C. Higher temperatures cause decomposition. Acidic Medium: Usually dilute HCl or H₂SO₄. Type of Amine: Only primary aromatic amines.

Mechanism of Diazotization Reaction:

Step 1: NaNO₂ + HCl → HNO₂ + NaCl Step 2: HNO₂ + H⁺ → NO⁺ + H₂O Step 3: ArNH₂ + NO⁺ → ArN₂⁺ + H₂O

Applications of Diazonium Salts:

1. Azo Dye Formation 2. Sandmeyer Reaction 3. Gattermann Reaction 4. Phenol Formation 5. Synthesis of Aromatic Compounds 6. Medicinal Chemistry Intermediates

Conclusion:

The preparation of diazonium salts via diazotization is a cornerstone topic in Class 12 Organic Chemistry. By understanding the conditions, mechanism, and practical importance of this reaction, students can master one of the most high-scoring sections of their board and entrance exams.

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Importance of Diazonium Salts in Synthesis of Aromatic Compounds

Introduction:

Diazonium salts play a vital role in synthetic organic chemistry, particularly in the preparation of aromatic compounds. Derived from aromatic primary amines, these salts serve as highly reactive intermediates for substitution and coupling reactions. Their importance lies in the ability to introduce functional groups like –OH, –Cl, –Br, –CN, and –NO₂ into aromatic rings, making them indispensable in both laboratory and industrial processes.

1. What are Diazonium Salts?

Diazonium salts are organic compounds with the general formula ArN₂⁺X⁻, where Ar is an aryl group and X⁻ is an anion such as Cl⁻, Br⁻, or BF₄⁻. They are typically formed by treating aromatic primary amines with nitrous acid at low temperatures (0–5°C).

Example:

Aniline + NaNO₂ + HCl → Benzene diazonium chloride + NaCl + H₂O

C₆H₅NH₂ + HNO₂ + HCl → C₆H₅N₂⁺Cl⁻ + 2H₂O

2. Importance of Diazonium Salts in Aromatic Synthesis:

Diazonium salts are versatile intermediates that allow:

- Substitution reactions without harsh conditions.

- Formation of a wide variety of aromatic derivatives.

- Introduction of functional groups not directly available via electrophilic substitution.

3. Replacement Reactions (Substitution Reactions):

a. Replacement by –OH (Phenol Formation):

C₆H₅N₂⁺Cl⁻ + H₂O → C₆H₅OH + N₂↑ + HCl

b. Replacement by Halogens (Sandmeyer Reaction):

C₆H₅N₂⁺Cl⁻ + CuCl → C₆H₅Cl + N₂

C₆H₅N₂⁺Br⁻ + CuBr → C₆H₅Br + N₂

Gattermann Reaction:

C₆H₅N₂⁺Cl⁻ + Cu/HCl → C₆H₅Cl + N₂

c. Replacement by –CN:

C₆H₅N₂⁺Cl⁻ + CuCN → C₆H₅CN + N₂

4. Coupling Reactions – Formation of Azo Compounds:

Diazonium salts undergo azo coupling with phenols or aromatic amines to form brightly colored azo dyes.

Example:

C₆H₅N₂⁺Cl⁻ + C₆H₅OH → C₆H₅–N=N–C₆H₄OH

Used extensively in:

- Textile industry

- Food colorants

- Indicator dyes

5. Applications in Industrial and Laboratory Synthesis:

- Manufacturing of azo dyes

- Synthesis of aromatic halides and phenols

- Production of pharmaceutical intermediates

- Use in agrochemical synthesis

- Preparation of complex organic compounds

6. Limitations and Precautions:

- Stability: Diazonium salts are unstable above 5°C and may decompose explosively.

- Fresh Preparation: Must be prepared fresh and used immediately.

- Safe Handling: Requires low-temperature conditions and proper lab safety protocols.

Conclusion:

Diazonium salts serve as powerful intermediates for the synthesis of aromatic compounds. Their ability to undergo a wide range of substitution and coupling reactions under mild conditions enhances their utility in organic synthesis. Whether it is the production of dyes, pharmaceuticals, or complex molecules, diazonium chemistry plays a central role in modern chemical practices.

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Class 12 Chemistry: Redox Reactions and Electrode Processes

Introduction:

Redox reactions (oxidation-reduction reactions) play a crucial role in chemistry, from industrial applications to biological systems. This topic is fundamental in electrochemistry, influencing processes like corrosion, energy storage, and electrode potentials. Understanding redox reactions and electrode processes helps students grasp essential concepts for competitive exams and practical applications.

Redox Reactions – An Overview:

Oxidation and Reduction

- Oxidation: Loss of electrons or increase in oxidation state.

- Reduction: Gain of electrons or decrease in oxidation state.

Oxidizing and Reducing Agents:

- Oxidizing agent: Gains electrons and gets reduced.

- Reducing agent: Loses electrons and gets oxidized.

Types of Redox Reactions:

- Combination Reactions: Two or more reactants form a single product.

- Decomposition Reactions: A compound breaks down into simpler substances.

- Displacement Reactions: One element replaces another in a compound.

- Disproportionation Reactions: The same element undergoes oxidation and reduction simultaneously.

Oxidation Number and Balancing Redox Reactions:

Oxidation Number Rules:

- The oxidation number of free elements is zero.

- Oxygen generally has an oxidation number of -2 (except in peroxides and superoxides).

- Hydrogen has an oxidation number of +1 (except in metal hydrides where it is -1).

Balancing Redox Reactions:

- Oxidation Number Method: Identify oxidation state changes and balance electrons.

- Ion-Electron Method: Divide reactions into oxidation and reduction half-reactions and balance them separately.

Electrode Processes and Electrochemical Cells:

Types of Electrochemical Cells:

- Galvanic (Voltaic) Cells: Convert chemical energy into electrical energy (e.g., Daniel cell).

- Electrolytic Cells: Use electrical energy to drive non-spontaneous reactions (e.g., electrolysis of water).

Standard Electrode Potential (E°):

- The potential difference between a metal electrode and its ion solution under standard conditions.

- Measured in volts and compared to the standard hydrogen electrode (SHE).

Nernst Equation:

- The Nernst equation calculates the electrode potential of a cell under non-standard conditions: E = E° - (RT/nF) ln Q Where: - E = electrode potential, - E° = standard electrode potential, - R = universal gas constant, - T = temperature, - n = number of electrons transferred, - F = Faraday’s constant, - Q = reaction quotient.

Applications of Redox Reactions and Electrode Processes:

Industrial Applications:

- Metallurgy: Extraction of metals using redox processes.

- Corrosion Prevention: Galvanization and cathodic protection.

- Electroplating: Coating metals to prevent rusting.

Biological Importance:

- Cellular Respiration: Energy production in living organisms.

- Photosynthesis: Redox reactions drive glucose synthesis in plants.

Batteries and Fuel Cells:

- Lithium-ion Batteries: Power electronic devices.

- Hydrogen Fuel Cells: Alternative energy sources.

Conclusion:

Redox reactions and electrode processes are integral to chemistry and real-world applications. Mastering oxidation-reduction concepts is crucial for understanding electrochemical cells, energy storage, and various industrial processes. A strong grasp of these principles will help students excel in their exams and practical applications in science and technology.

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AC Generator - Class 12 Physics Study Notes

Introduction:

An AC Generator (Alternating Current Generator) is an electrical machine that converts mechanical energy into electrical energy in the form of alternating current (AC). It operates on the principle of electromagnetic induction, discovered by Michael Faraday. AC generators are widely used in power stations and industries for generating electricity.

What is an AC Generator?

An AC Generator is a device that produces alternating current by rotating a coil within a magnetic field. The direction of the current reverses periodically due to the changing magnetic flux.

Principle of AC Generator:

The working of an AC Generator is based on Faraday’s Law of Electromagnetic Induction, which states: When a conductor moves through a magnetic field, an electromotive force (EMF) is induced in it, and if the circuit is closed, an electric current flows through it.

Formula for Induced EMF:

The induced EMF is given by: E = NBAω sin(ωt)

Construction of AC Generator:

An AC Generator consists of the following components:

(i) Armature Coil - A rectangular coil of wire wound around an iron core to enhance the magnetic effect.

(ii) Magnetic Field - Produced by permanent magnets or electromagnets to generate magnetic flux.

(iii) Slip Rings - Two metal rings connected to the coil ends, allowing free rotation.

(iv) Brushes - Carbon brushes press against slip rings to transfer current to the external circuit.

(v) External Load - Connected to the output terminals to utilize the generated AC power.

Working of AC Generator:

The AC Generator works in the following steps:

Step 1 - Coil Rotation: The coil rotates within the magnetic field due to an external mechanical force (turbines, engines, etc.).

Step 2 - Magnetic Flux Change: As the coil rotates, the magnetic flux linked with the coil changes, inducing EMF.

Step 3 - Direction of Induced Current: According to Fleming’s Right-Hand Rule, the direction of the induced current reverses every half rotation, producing alternating current (AC).

Step 4 - Output Voltage Variation: The AC voltage varies sinusoidally with time and follows the equation: E = E₀ sin(ωt).

Advantages of AC Generators:

Efficient Power Transmission – AC power is easily transmitted over long distances.

Simple Design – No commutator, making it more durable than DC generators.

Cost-Effective – Less maintenance and lower manufacturing cost.

High Power Output – Used in power plants for large-scale electricity generation.

Applications of AC Generators:

Power Stations – Generate electricity for homes, industries, and businesses.

Wind Turbines – Convert wind energy into electrical energy.

Hydroelectric Plants – Water turbines rotate AC generators to produce power.

Automobiles – Used in car alternators to charge batteries.

Difference Between AC and DC Generators:

Conclusion:

An AC Generator is a crucial electrical device that converts mechanical energy into electrical energy using the principle of electromagnetic induction. It is widely used for power generation due to its efficiency, simplicity, and low maintenance. Understanding its working, construction, and applications is essential for Class 12 Physics students preparing for exams.

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Representation of AC Current and Voltage by Rotating Vectors - Phasors

Introduction:

In alternating current (AC) circuits, the magnitude and direction of current and voltage vary sinusoidally with time. To simplify their analysis, the concept of rotating vectors, known as phasors, is used. Phasors allow us to represent sinusoidal quantities as rotating vectors in a complex plane, making the analysis of AC circuits easier and more intuitive.

Understanding Phasors:

What is a Phasor?

A phasor is a rotating vector that represents a sinusoidal quantity. The length of the phasor corresponds to the peak value of the sine wave, and its angular position represents the phase of the wave at any given time.

Mathematical Representation:

The general expression for an AC voltage or current is: V(t) = V₀ sin(ωt + φ) Where: - V₀ = Peak voltage - ω = Angular frequency - φ = Phase angle - t = Time In phasor notation, this can be represented as: V = V₀ e^(j(ωt + φ)) where j is the imaginary unit.

Advantages of Using Phasors:

1. Simplifies the addition and subtraction of sinusoidal waveforms. 2. Converts differential equations into simple algebraic equations. 3. Provides a visual representation of phase differences between waveforms.

Phasor Diagram:

How to Draw a Phasor Diagram:

1. Draw a reference axis. 2. Represent the voltage or current as a vector with magnitude V₀. 3. The angle between the phasor and the reference axis corresponds to the phase angle φ. 4. As time progresses, the phasor rotates counter-clockwise at an angular velocity ω.

Applications of Phasors in AC Circuits:

1. Analyzing series and parallel AC circuits. 2. Determining impedance and phase relationships. 3. Analyzing resonance in LCR circuits. 4. Calculating power in AC circuits.

Conclusion:

Phasors are an essential tool for understanding and analyzing alternating current circuits. By representing sinusoidal quantities as rotating vectors in the complex plane, phasors simplify the mathematical analysis of AC circuits and help in visualizing phase relationships.

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Temperature Dependence of the Rate of a Reaction Notes

Introduction:

The rate of a chemical reaction depends on various factors, including temperature. Generally, an increase in temperature results in an increase in the reaction rate. This is because higher temperatures provide more energy to reactant molecules, leading to more frequent and effective collisions. The relationship between temperature and reaction rate is quantitatively described by the Arrhenius equation.

Effect of Temperature on Reaction Rate:

The speed of a reaction increases with temperature due to:

• Increased kinetic energy of reactant molecules. • Higher collision frequency. • Greater fraction of molecules possessing energy equal to or greater than the activation energy.

The Arrhenius Equation:

The Arrhenius equation mathematically expresses how reaction rate constants vary with temperature:

k = A e^(-Ea/RT)

Where:

• k = rate constant • A = pre-exponential factor • Ea = activation energy • R = universal gas constant (8.314 J/mol·K) • T = temperature (in Kelvin)

Activation Energy and Temperature Relationship:

Activation energy (Ea) is the minimum energy required for reactants to convert into products. • At lower temperatures, fewer molecules have sufficient energy to overcome the activation barrier. • At higher temperatures, a larger proportion of molecules exceed the activation energy, resulting in a faster reaction.

Temperature Coefficient and Rule of Thumb:

The temperature coefficient expresses how much the reaction rate changes with a 10°C rise in temperature. Generally, for most reactions:

Rate at (T+10)°C ≈ 2-3 × Rate at T°C

This means that for every 10°C increase in temperature, the reaction rate approximately doubles or triples.

Graphical Representation of Arrhenius Equation:

A logarithmic form of the Arrhenius equation is: ln k = ln A - (Ea/R) × (1/T) Plotting ln k vs. 1/T results in a straight-line graph with slope -Ea/R, which helps determine the activation energy experimentally.

Practical Applications of Temperature Dependence of Reaction Rate:

• Industrial Reactions: Optimizing temperature conditions in chemical manufacturing (e.g., Haber process for ammonia production). • Biological Systems: Enzyme-catalyzed reactions are highly temperature-sensitive. • Storage of Medicines and Food: Lowering temperature slows down degradation reactions. • Explosives and Combustion: Reactions are accelerated at higher temperatures, leading to controlled or uncontrolled explosions.

Conclusion:

Temperature significantly affects reaction rates by influencing molecular energy and collision frequency. The Arrhenius equation provides a mathematical framework to understand this dependency. By controlling temperature, chemical processes can be optimized for efficiency in industrial and biological applications.

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Bonding in Metal Carbonyls - Class 12 Chemistry Notes with Explanation

Introduction:

Metal carbonyls are coordination compounds in which a transition metal is bonded to one or more carbonyl (CO) ligands. These compounds play a crucial role in organometallic chemistry due to their unique bonding characteristics, stability, and industrial applications. The bonding in metal carbonyls is explained using the synergic bonding model, involving both σ-donation and π-back donation interactions.

Bonding in Metal Carbonyls – Class 12 Chemistry:

Metal carbonyls exhibit fascinating bonding properties due to the presence of carbonyl ligands, which interact with the metal center through a combination of donation and back-donation mechanisms.

Structure and Composition of Metal Carbonyls:

- Metal carbonyls are composed of a transition metal center bonded to CO ligands. - The general formula is M(CO)x, where ‘M’ represents the metal, and ‘x’ denotes the number of CO ligands. - Examples: Ni(CO)4, Fe(CO)5, Cr(CO)6. - These compounds can be mononuclear or polynuclear.

Synergic Bonding in Metal Carbonyls:

The bonding in metal carbonyls follows a synergic interaction involving: 1. σ-Bonding: The carbonyl ligand donates electron density to the metal via the lone pair on carbon (M ← CO). 2. π-Back Bonding: The metal donates electron density from its d-orbitals into the empty π* (antibonding) orbitals of CO (M → CO).

Molecular Orbital Approach to Metal Carbonyl Bonding

- The metal-carbon bond is a result of molecular orbital interactions. - The carbonyl ligand acts as both a donor and acceptor, stabilizing the complex. - The strength of back bonding depends on:   - The oxidation state of the metal.   - The number of CO ligands.   - The nature of the metal (e.g., Fe, Ni, Cr).

Infrared Spectroscopy and Bonding in Metal Carbonyls

- The C≡O stretching frequency (νCO) in metal carbonyls helps determine the extent of π-back bonding. - Strong back bonding reduces the CO stretching frequency (lower νCO). - Examples:   - Free CO: ~2143 cm⁻¹   - Fe(CO)5: ~2000 cm⁻¹ (due to back bonding)

Applications of Metal Carbonyls

1. Catalysis:    - Used in industrial catalysts (e.g., hydroformylation and carbonylation). 2. Organic Synthesis:    - Metal carbonyls are precursors for many organometallic compounds. 3. Industrial Processing:    - Nickel carbonyl [Ni(CO)4] is used in metal refining. 4. Medical Applications:    - Some metal carbonyls are explored for drug development.

Conclusion

Metal carbonyls are essential coordination compounds exhibiting unique synergic bonding through σ-donation and π-back bonding. Their structural properties influence their stability, spectroscopic behavior, and industrial applications. Understanding these interactions provides deeper insights into transition metal chemistry.

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Bonding in Coordination Compounds Class 12 Detailed Study Notes

Introduction:

Coordination compounds play a crucial role in chemistry, especially in biological and industrial applications. Understanding their bonding is essential for predicting their structures and properties. The bonding theories, including Valence Bond Theory (VBT), Crystal Field Theory (CFT), and Molecular Orbital Theory (MOT), help explain how metal ions interact with ligands to form stable complexes.

Bonding Theories in Coordination Compounds:

Valence Bond Theory (VBT):

VBT explains coordination bonding based on hybridization and overlapping of orbitals.

Key points include:

- Metal ions use empty orbitals to accommodate ligands. - Hybridization (sp3, dsp2, d2sp3) determines geometry. - Inner and outer orbital complexes depend on the d-electron configuration.

Example:

[Co(NH3)6]³⁺ undergoes d2sp3 hybridization, forming an inner orbital complex (low spin).

[Ni(CN)4]²⁻ exhibits dsp2 hybridization, resulting in a square planar geometry.

Limitations of VBT:

- Does not explain color in complexes. - Fails to address magnetic properties effectively. - Cannot distinguish between strong and weak field ligands quantitatively.

Crystal Field Theory (CFT):

CFT considers the electrostatic interactions between metal cations and ligands. It assumes ligands are point charges or dipoles affecting the metal’s d-orbitals.

Key Features:

- Splitting of d-orbitals into eg and t2g levels. - Explains color due to d-d transitions. - Accounts for paramagnetism and diamagnetism.

Example:

[Fe(CN)6]⁴⁻: Strong field ligand, low spin, t2g⁶ eg⁰ (octahedral).

[Fe(H2O)6]²⁺: Weak field ligand, high spin, t2g⁴ eg² (octahedral).

Crystal Field Splitting in Different Geometries:

- Octahedral: d-orbitals split into t2g (lower) and eg (higher) levels. - Tetrahedral: d-orbitals split into eg (lower) and t2g (higher) levels. - Square Planar: Further splitting with significant energy gap.

Molecular Orbital Theory (MOT) in Coordination Compounds:

MOT explains bonding using linear combination of atomic orbitals (LCAO). It accounts for sigma and pi bonding interactions.

Key Aspects:

- Bonding molecular orbitals (BMO) and antibonding molecular orbitals (ABMO). - Ligand’s contribution to the metal’s electronic structure. - Predicts bond strength, stability, and electronic transitions.

Example:

In [Co(NH3)6]³⁺, ligand-to-metal bonding involves sigma donation, leading to strong-field stabilization.

Applications of Bonding Theories in Coordination Compounds:

Industrial and Biological Importance:

- Hemoglobin (Fe complex): Oxygen transport in the blood. - Chlorophyll (Mg complex): Photosynthesis in plants. - Catalysts: Platinum complexes in hydrogenation reactions. - Medicinal Chemistry: Cisplatin as an anticancer drug.

Conclusion:

Bonding in coordination compounds is fundamental to understanding their behavior. While VBT provides a basic understanding, CFT and MOT offer deeper insights into electronic structure, magnetism, and color. These theories help explain various biological and industrial applications of coordination chemistry.