Understanding the calculation of relative atomic mass and molecular mass is fundamental in the study of chemistry, particularly within the scope of mass spectrometry. These concepts enable chemists to determine the composition of substances, predict reaction outcomes, and analyze molecular structures. For students pursuing the AS & A Level in Chemistry (9701), mastering these calculations is essential for both academic success and practical applications in various scientific fields.

Key Concepts

Relative Atomic Mass (Ar)

Relative Atomic Mass (Ar) is a dimensionless quantity that represents the average mass of atoms of an element compared to one-twelfth of the mass of a carbon-12 atom. It accounts for the natural isotopic distribution of elements. The formula to calculate the relative atomic mass is:

$$Ar = \sum (f_i \times m_i)$$

where $ f_i $ is the fractional abundance of isotope $ i $ and $ m_i $ is the mass of isotope $ i $.

For example, consider Chlorine, which has two main isotopes: $ ^{35}Cl $ with a mass of 34.969 amu and $ ^{37}Cl $ with a mass of 36.966 amu. The relative atomic mass is calculated as:

$$Ar_{Cl} = (0.7576 \times 34.969) + (0.2424 \times 36.966) = 26.47 + 8.97 = 35.44$$

This value of 35.44 is the relative atomic mass of chlorine as it naturally occurs on Earth.

Molecular Mass

Molecular mass (Mm) is the sum of the relative atomic masses of all atoms in a molecule. It is expressed in unified atomic mass units (amu) or grams per mole (g/mol). The formula for molecular mass is:

$$Mm = \sum (n_i \times Ar_i)$$

where $ n_i $ is the number of atoms of element $ i $ in the molecule and $ Ar_i $ is the relative atomic mass of element $ i $.

For instance, the molecular mass of water (H$_2$O) is calculated as:

$$Mm_{H_2O} = (2 \times 1.008) + (1 \times 16.00) = 2.016 + 16.00 = 18.016 \text{ g/mol}$$

This calculation is crucial for stoichiometric analyses and determining the proportions of reactants and products in chemical reactions.

Molecular Formula Determination

Determining the molecular formula of a compound involves knowing both the empirical formula and the molecular mass. The empirical formula represents the simplest whole-number ratio of atoms in a compound, while the molecular formula shows the actual number of atoms of each element in a molecule.

The relationship between molecular mass and empirical formula mass (Ef) is given by:

$$Molecular\ Formula = (n \times Ef)$$

where $ n $ is an integer.

For example, if the empirical formula mass of a compound is 50 g/mol and the molecular mass is 200 g/mol, then:

$$n = \frac{200}{50} = 4$$

Therefore, the molecular formula is four times the empirical formula.

Isotopic Abundance

Isotopic abundance refers to the relative percentage of different isotopes of an element present in a natural sample. It plays a significant role in calculating the relative atomic mass. Accurate determination of isotopic abundance requires precise mass spectrometric measurements.

For example, Carbon exists mainly as two isotopes: $ ^{12}C $ (98.93%) and $ ^{13}C $ (1.07%). The relative atomic mass of carbon is calculated as:

$$Ar_{C} = (0.9893 \times 12.000) + (0.0107 \times 13.003) = 11.872 + 0.139 = 12.011 \text{ amu}$$

This reflects the weighted average mass of carbon atoms in nature.

Mass Spectrometry

Mass spectrometry is an analytical technique used to measure the masses of atoms and molecules. It ionizes chemical species, sorts the ions based on their mass-to-charge ratios, and detects them, providing precise measurements of molecular and atomic masses. This technique is invaluable for determining isotopic compositions and molecular structures.

The basic components of a mass spectrometer include the ion source, mass analyzer, and detector. The ionization process can involve methods like Electron Ionization (EI) or Electrospray Ionization (ESI), depending on the sample type.

Example Problems

Problem 1: Calculate the relative atomic mass of chlorine given that $ ^{35}Cl $ is 75.76% abundant and $ ^{37}Cl $ is 24.24% abundant.

Solution:

$$Ar_{Cl} = (0.7576 \times 34.969) + (0.2424 \times 36.966) = 35.44 \text{ amu}$$

Problem 2: Determine the molecular mass of sulfuric acid (H$_2$SO$_4$).

Solution:

$$Mm_{H_2SO_4} = (2 \times 1.008) + (32.07) + (4 \times 16.00) = 2.016 + 32.07 + 64.00 = 98.086 \text{ g/mol}$$

Advanced Concepts

Theoretical Derivations

The calculation of relative atomic mass involves summing the products of isotopic masses and their respective natural abundances. Mathematically, this can be expressed as:

$$Ar = \sum_{i=1}^{n} (f_i \times m_i)$$

where $ n $ is the number of naturally occurring isotopes, $ f_i $ is the fractional abundance of isotope $ i $, and $ m_i $ is the mass of isotope $ i $.

This formula is derived from the definition of relative atomic mass as an average value that accounts for the presence of various isotopes in nature.

Isotopic Mass Spectra Interpretation

Mass spectrometry produces isotopic mass spectra that display peaks corresponding to different isotopes of an element or molecule. Each peak's position indicates the mass-to-charge ratio (m/z), while the peak's height reflects the relative abundance.

Interpreting these spectra involves identifying the peaks, determining their m/z ratios, and calculating the relative abundance of each isotope. For example, the mass spectrum of bromine ($ ^{79}Br $ and $ ^{81}Br $) shows two peaks with nearly equal intensities, reflecting its almost 1:1 isotopic abundance ratio.

Understanding isotopic mass spectra is crucial for analyzing complex mixtures and identifying unknown compounds based on their unique isotopic signatures.

Complex Problem-Solving

Problem 3: A compound has a molecular mass of 180.16 g/mol and an empirical formula of C$_2$H$_6$O. Determine the molecular formula.

Solution:

1. Calculate the empirical formula mass (Ef): $$Ef = (2 \times 12.01) + (6 \times 1.008) + (16.00) = 24.02 + 6.048 + 16.00 = 46.068 \text{ g/mol}$$ 2. Determine the ratio of molecular mass to empirical formula mass: $$n = \frac{180.16}{46.068} \approx 3.91 \approx 4$$ 3. Multiply the empirical formula by $ n $: $$Molecular\ Formula = (C_2H_6O)_4 = C_8H_{24}O_4$$

Interdisciplinary Connections

The principles of relative atomic mass and molecular mass calculations extend beyond chemistry into fields like pharmacology, environmental science, and materials engineering. For example, in pharmacology, determining the molecular mass of drug compounds is essential for dosage calculations and understanding pharmacokinetics. In environmental science, analyzing pollutant molecular masses helps in assessing their distribution and impact. Moreover, materials engineering relies on precise molecular mass determinations to design and synthesize new materials with desired properties.

Additionally, these calculations are foundational in biochemistry for understanding biomolecular structures and interactions, such as proteins and nucleic acids, which are critical for life sciences research and biotechnology applications.

Mathematical Techniques in Mass Calculations

Advanced mass calculations often require solving systems of equations, especially when dealing with natural isotopic distributions. For instance, determining the exact isotopic composition from mass spectra data can involve simultaneous equations to account for overlapping isotopic peaks.

Another mathematical technique involves the use of logarithms and exponential functions in complex molecular mass determinations, particularly when extrapolating data from experimental measurements or modeling dynamic chemical systems.

Applications in Forensic Science

In forensic science, precise molecular mass calculations aid in identifying substances found at crime scenes. Mass spectrometry can detect and quantify trace amounts of substances, such as drugs or explosives, by comparing their molecular masses to known standards. This application underscores the practical importance of mastering relative atomic mass and molecular mass calculations for legal and investigative processes.

Comparison Table

Aspect	Relative Atomic Mass (Ar)	Molecular Mass (Mm)
Definition	Average mass of atoms of an element compared to 1/12th of a Carbon-12 atom.	Sum of the relative atomic masses of all atoms in a molecule.
Units	Dimensionless	grams per mole (g/mol) or amu
Calculation Basis	Natural isotopic abundance	Empirical formula and number of atoms
Application	Determining atomic composition	Stoichiometry in chemical reactions
Example	Chlorine: 35.44 amu	Water (H₂O): 18.016 g/mol

Summary and Key Takeaways

Relative Atomic Mass (Ar) represents the average mass of an element's isotopes.
Molecular Mass (Mm) is the total mass of atoms in a molecule.
Mass spectrometry is essential for precise mass determinations.
Advanced calculations involve isotopic abundance and molecular formula derivations.
Understanding these concepts is crucial for applications across various scientific disciplines.

Examiner Tip

Tips

To remember the difference between relative atomic mass and molecular mass, think "Ar" for Atomic and "Mm" for Molecular. Use the mnemonic "A Re Molecule Masses" to recall that Ar is atomic, and Mm is molecular. Additionally, always double-check your isotopic abundances add up to 1 (or 100%) before performing calculations to avoid errors on exams.

Did You Know

Did you know that the concept of relative atomic mass was pivotal in the early development of the periodic table? Additionally, mass spectrometry has been instrumental in identifying extraterrestrial compounds, such as those found in meteorites, providing insights into the formation of our solar system. Moreover, the precise calculation of molecular mass is essential in the development of new pharmaceuticals, ensuring the effectiveness and safety of medications.

Common Mistakes

Mistake 1: Ignoring the fractional abundance of isotopes when calculating relative atomic mass.
Incorrect: Summing only whole number isotopic masses.
Correct: Multiplying each isotopic mass by its fractional abundance and summing the results.

Mistake 2: Confusing empirical and molecular formulas.
Incorrect: Assuming the empirical formula is the same as the molecular formula.
Correct: Calculating the molecular formula by determining the ratio of molecular mass to empirical formula mass.

FAQ

What is the difference between relative atomic mass and molecular mass?

Relative atomic mass is the average mass of an element's isotopes compared to 1/12th of a Carbon-12 atom, while molecular mass is the sum of the relative atomic masses of all atoms in a molecule.

How is relative atomic mass calculated?

It is calculated by summing the products of each isotope's mass and its fractional abundance.

Why is mass spectrometry important in calculating molecular mass?

Mass spectrometry provides precise measurements of the masses of atoms and molecules, allowing accurate determination of molecular and atomic masses.

Can molecular mass be expressed in grams per mole?

Yes, molecular mass can be expressed in grams per mole (g/mol) or atomic mass units (amu).

How do you determine the molecular formula from the empirical formula?

Divide the molecular mass by the empirical formula mass to find the multiplier, then multiply the subscripts in the empirical formula by this integer to obtain the molecular formula.

What common errors should be avoided when calculating molecular mass?

Avoid mistakes such as overlooking the correct number of atoms for each element in the molecule and neglecting to use the accurate relative atomic masses.

1. Group 17

1.1 Physical Properties of the Group 17 Elements

1.1.1 Trends in Bond Strength of Halogen Molecules

1.1.2 Volatility Explained by Intermolecular Forces

1.1.3 Colours and Volatility of Chlorine, Bromine and Iodine

1.2 The Chemical Properties of the Halogen Elements and the Hydrogen Halides

1.2.1 Relative Reactivity of Halogen Elements as Oxidising Agents

1.2.2 Reactions of Halogens with Hydrogen

1.2.3 Thermal Stability of Hydrogen Halides

1.3 Some Reactions of the Halide Ions

1.3.1 Relative Reactivity of Halide Ions as Reducing Agents

1.3.2 Reactions of Halide Ions with Aqueous Silver Ions and Ammonia

1.3.3 Reactions of Halide Ions with Concentrated Sulfuric Acid

1.4 The Reactions of Chlorine

1.4.1 Reaction of Chlorine with Aqueous Sodium Hydroxide (Cold and Hot)

1.4.2 Use of Chlorine in Water Purification

2. Electrochemistry

2.1 Redox Processes: Electron Transfer and Changes in Oxidation Number

2.1.1 Calculating Oxidation Numbers

2.1.2 Using Oxidation Numbers to Balance Equations

2.1.3 Redox, Oxidation, Reduction, Disproportionation: Definitions

2.1.4 Oxidising and Reducing Agents: Definitions

2.1.5 Indicating Oxidation Numbers Using Roman Numerals

3. Chemical Energetics

3.1 Enthalpies of Solution and Hydration

3.1.1 Calculations Involving Solution and Hydration Energies

3.1.2 Effect of Ionic Charge and Radius on Hydration Enthalpy

3.1.3 Definition and Use of Enthalpy Change of Solution and Hydration

3.1.4 Construction and Use of Energy Cycles for Solution and Hydration

3.2 Entropy Change ΔS

3.2.1 Definition of Entropy

3.2.2 Prediction and Explanation of Entropy Changes

3.2.3 Calculation of Entropy Change for Reactions

3.3 Gibbs Free Energy Change ΔG

3.3.1 Gibbs Free Energy Equation

3.3.2 Calculations Using ΔG = ΔH – TΔS

3.3.3 Prediction of Reaction Feasibility

3.3.4 Effect of Temperature on Reaction Feasibility

3.4 Lattice Energy and Born–Haber Cycles

3.4.1 Definition and Use of Enthalpy Change of Atomisation and Lattice Energy

3.4.2 First Electron Affinity and Trends in Electron Affinity

3.4.3 Construction and Use of Born–Haber Cycles

3.4.4 Calculations Involving Born–Haber Cycles

3.4.5 Effect of Ionic Charge and Radius on Lattice Energy

4. Group 2

4.1 Magnesium to Barium, and Their Compounds

4.1.1 Variation in Solubility and Enthalpy Change of Solution of Hydroxides and Sulfates

4.1.2 Trend in Thermal Stability of Group 2 Nitrates and Carbonates

4.1.3 Effect of Ionic Radius on Polarisation of Large Anions

5. Atoms, Molecules and Stoichiometry

5.1 Formulas

5.1.1 Using Appropriate State Symbols

5.1.2 Empirical and Molecular Formulas: Definitions

5.1.3 Anhydrous, Hydrated and Water of Crystallisation

5.1.4 Calculation of Empirical and Molecular Formulas

5.1.5 Writing Ionic Compound Formulas from Ionic Charges and Oxidation Numbers

5.1.6 Predicting Ionic Charges from Periodic Table Positions

5.1.7 Common Ions: Names and Formulas

5.1.8 Writing and Balancing Chemical and Ionic Equations

5.2 Reacting Masses and Volumes (of Solutions and Gases)

5.2.1 Calculations Involving Reacting Masses and Percentage Yield

5.2.2 Calculations Involving Volumes of Gases

5.2.3 Calculations Involving Volumes and Concentrations of Solutions

5.2.4 Limiting Reagent and Excess Reagent Calculations

5.2.5 Deducing Stoichiometric Relationships from Calculations

5.3 Relative Masses of Atoms and Molecules

5.3.1 Unified Atomic Mass Unit

5.3.2 Relative Atomic Mass (Ar)

5.3.3 Relative Isotopic Mass

5.3.4 Relative Molecular Mass (Mr)

5.3.5 Relative Formula Mass

5.4 The Mole and the Avogadro Constant

5.4.1 Definition and Use of the Mole

5.4.2 Understanding the Avogadro Constant

6. Nitrogen Compounds

6.1 Primary and Secondary Amines

6.1.1 Production of Primary and Secondary Amines from Halogenoalkanes

6.1.2 Reduction of Amides and Nitriles to Amines

6.1.3 Reaction of Amines with Acyl Chlorides

6.1.4 Basicity of Aqueous Solutions of Amines

6.2 Phenylamine and Azo Compounds

6.2.1 Preparation of Phenylamine from Nitrobenzene

6.2.2 Reactions of Phenylamine with Bromine and Diazotisation

6.2.3 Relative Basicities of Ammonia, Ethylamine and Phenylamine

6.2.4 Formation and Use of Azo Compounds as Dyes

6.3 Amides

6.3.1 Production of Amides from Acyl Chlorides and Ammonia/Amines

6.3.2 Hydrolysis of Amides with Acids or Alkalis

6.3.3 Reduction of Amides to Amines

6.3.4 Weak Basic Nature of Amides

6.4 Amino Acids

6.4.1 Acid–Base Properties and Zwitterions

6.4.2 Formation of Peptide Bonds Between Amino Acids

6.4.3 Electrophoresis of Amino Acids and Peptides

7. Halogen Compounds

7.1 Halogenoalkanes

7.1.1 Elimination Reactions of Halogenoalkanes

7.1.2 SN1 and SN2 Mechanisms of Nucleophilic Substitution

7.1.3 Reactivity of Halogenoalkanes and Bond Strength

7.1.4 Production of Halogenoalkanes: Free-Radical Substitution and Electrophilic Addition

7.1.5 Classification of Halogenoalkanes: Primary, Secondary, Tertiary

7.1.6 Nucleophilic Substitution Reactions of Halogenoalkanes

7.1.7 Identification of Halogens by Reaction with Silver Nitrate

8. Chemistry of Transition Elements

8.1 General Physical and Chemical Properties of the First Row of Transition Elements

8.1.1 Titanium to Copper: Definition of Transition Elements

8.1.2 Titanium to Copper: Sketching 3dxy and 3dz² Orbitals

8.1.3 Titanium to Copper: General Properties: Variable Oxidation States, Catalytic Behavior, Formation of

8.1.4 Titanium to Copper: Explanation of Variable Oxidation States and Catalysis

8.2 General Characteristic Chemical Properties of the First Set of Transition Elements

8.2.1 Formation of Complexes and Ligand Types

8.2.2 Shapes and Coordination Numbers of Complexes

8.2.3 Ligand Exchange Reactions

8.2.4 Redox Reactions Involving Transition Elements

8.2.5 Redox Calculations Using E° Values

8.3 Colour of Complexes

8.3.1 Degenerate and Non-Degenerate d Orbitals

8.3.2 Splitting of d Orbitals in Octahedral and Tetrahedral Complexes

8.3.3 Explanation of Colour Based on Light Absorption

8.3.4 Effect of Ligand Types on Colour

8.4 Stereoisomerism in Transition Element Complexes

8.4.1 Geometrical (cis-trans) and Optical Isomerism in Complexes

8.4.2 Deduction of Overall Polarity of Complexes

8.5 Stability Constants

8.5.1 Definition and Expression of Stability Constants (Kstab)

8.5.2 Ligand Exchange and Kstab Values

9. Hydroxy Compounds

9.1 Alcohols

9.1.1 Production of Alcohols: Steam Addition, Oxidation, Reduction and Hydrolysis

9.1.2 Reactions of Alcohols: Combustion, Substitution, Oxidation, Dehydration, Esterification

9.1.3 Classification of Alcohols: Primary, Secondary, Tertiary

9.1.4 Tri-iodomethane Test for CH₃CH(OH)– Group

9.1.5 Acidity of Alcohols Compared to Water

10. Equilibria

10.1 Chemical Equilibria: Reversible Reactions and Dynamic Equilibrium

10.1.1 Reversible Reactions and Dynamic Equilibrium

10.1.2 Le Chatelier’s Principle

10.1.3 Effect of Temperature, Concentration, Pressure and Catalysts on Equilibrium

10.1.4 Equilibrium Constant Expressions (Kc)

10.1.5 Mole Fraction and Partial Pressure

10.1.6 Equilibrium Constant Expressions (Kp)

10.1.7 Calculations Using Kc and Kp

10.1.8 Changes Affecting the Value of Equilibrium Constants

10.1.9 Industrial Applications: Haber Process and Contact Process

10.2 Brønsted–Lowry Theory of Acids and Bases

10.2.1 Common Acids and Alkalis: Names and Formulas

10.2.2 Brønsted–Lowry Theory: Acids and Bases

10.2.3 Strong and Weak Acids and Bases

10.2.4 pH Scale and Differences Between Strong and Weak Acids

10.2.5 Neutralisation and Salt Formation

10.2.6 Acid–Base Titration Curves

10.2.7 Choosing Suitable Indicators for Titrations

11. Nitrogen and Sulfur

11.1 Nitrogen and Sulfur

11.1.1 Lack of Reactivity of Nitrogen Explained by Bond Strength and Polarity

11.1.2 Basicity of Ammonia and Structure of the Ammonium Ion

11.1.3 Displacement of Ammonia from Ammonium Salts

11.1.4 Natural and Man-made Sources of Nitrogen Oxides

11.1.5 Role of Nitrogen Oxides in Photochemical Smog Formation

11.1.6 Role of Nitrogen Oxides in Acid Rain Formation

12. Carbonyl Compounds

12.1 Aldehydes and Ketones

12.1.1 Production of Aldehydes and Ketones by Oxidation of Alcohols

12.1.2 Reduction of Aldehydes and Ketones

12.1.3 Reaction of Aldehydes and Ketones with Hydrogen Cyanide

12.1.4 Mechanism of Nucleophilic Addition Reactions

12.1.5 Detection of Carbonyl Compounds Using 2, 4-DNPH

12.1.6 Distinguishing Aldehydes from Ketones Using Fehling’s and Tollens’ Tests

12.1.7 Tri-iodomethane Test for CH₃CO– Group

13. Chemical Bonding

13.1 Electronegativity and Bonding

13.1.1 Definition of Electronegativity

13.1.2 Factors Affecting Electronegativity

13.1.3 Trends in Electronegativity Across a Period and Down a Group

13.1.4 Predicting Bond Type Using Electronegativity Differences

13.2 Ionic Bonding

13.2.1 Definition of Ionic Bonding

13.2.2 Ionic Bonding Examples: Sodium Chloride, Magnesium Oxide, Calcium Fluoride

13.3 Metallic Bonding

13.3.1 Definition of Metallic Bonding

13.4 Covalent Bonding and Coordinate (Dative Covalent) Bonding

13.4.1 Definition of Covalent Bonding

13.4.2 Covalent Bonding in Common Molecules (H₂, O₂, N₂, Cl₂, HCl, CO₂, NH₃, CH₄, C₂H₆, C₂H₄)

13.4.3 Expanded Octet in Period 3 Elements (SO₂, PCl₅, SF₆)

13.4.4 Definition of Coordinate (Dative Covalent) Bonding

13.4.5 Coordinate Bonding in NH₄⁺ and Al₂Cl₆

13.4.6 Sigma (σ) and Pi (π) Bonds: Orbital Overlap

13.4.7 Hybridisation: sp, sp² and sp³ Orbitals

13.4.8 Bond Energy and Bond Length Concepts

13.5 Shapes of Molecules

13.5.1 Shapes and Bond Angles Using VSEPR Theory (Examples: BF₃, CO₂, CH₄, NH₃, H₂O, SF₆, PF₅)

13.5.2 Predicting Shapes and Bond Angles of Similar Molecules and Ions

13.6 Intermolecular Forces, Electronegativity and Bond Properties

13.6.1 Hydrogen Bonding: Examples in Water and Ammonia

13.6.2 Anomalous Properties of Water Due to Hydrogen Bonding

13.6.3 Bond Polarity and Dipole Moments

13.6.4 Van der Waals' Forces: Instantaneous Dipole–Induced Dipole and Permanent Dipole–Dipole Forces

13.6.5 Comparison of Bond Strengths: Ionic, Covalent, Metallic vs. Intermolecular Forces

13.7 Dot-and-Cross Diagrams

13.7.1 Using Dot-and-Cross Diagrams to Represent Ionic, Covalent and Coordinate Bonding

14. Electrochemistry

14.1 Electrolysis

14.1.1 Prediction of Products During Electrolysis

14.1.2 Faraday Constant and Relationship with Avogadro Constant and Electron Charge

14.1.3 Calculations Involving Charge, Mass and Volume in Electrolysis

14.1.4 Determination of Avogadro Constant by Electrolysis

14.2 Standard Electrode Potentials and the Nernst Equation

14.2.1 Definition of Standard Electrode Potential and Standard Cell Potential

14.2.2 Description of the Standard Hydrogen Electrode

14.2.3 Measurement of Standard Electrode Potentials

14.2.4 Calculation of Standard Cell Potentials

14.2.5 Deduction of Electron Flow and Reaction Feasibility Using Electrode Potentials

14.2.6 Reactivity Predictions Using E° Values

14.2.7 Construction of Redox Equations from Half-Equations

14.2.8 Variation of Electrode Potential with Concentration

14.2.9 Using the Nernst Equation for Electrode Potentials

14.2.10 Relationship Between ΔG° and E°cell

15. Introduction to Organic Chemistry

15.1 Formulas, Functional Groups and the Naming of Organic Compounds

15.1.1 Definition of Hydrocarbons

15.2 Formulas

15.2.1 Functional Groups and Physical/Chemical Properties

15.2.2 Interpretation of General, Structural, Displayed and Skeletal Formulas

15.2.3 Systematic Nomenclature of Simple Aliphatic Organic Compounds

15.2.4 Deducing Molecular and Empirical Formulas

15.3 Characteristic Organic Reactions

15.3.1 Terminology of Organic Reactions: Homologous Series, Saturated/Unsaturated, Fission, Radicals, Nucle

15.3.2 Types of Organic Reactions: Addition, Substitution, Elimination, Hydrolysis, Condensation, Oxidation

15.3.3 Mechanisms of Organic Reactions: Free Radical Substitution, Electrophilic Addition, Nucleophilic Sub

15.4 Shapes of Organic Molecules; σ and π Bonds

15.4.1 Shapes and Bond Angles in Organic Molecules

15.4.2 Sigma (σ) and Pi (π) Bond Arrangements

15.4.3 Planarity in Organic Molecules

15.5 Isomerism: Structural Isomerism and Stereoisomerism

15.5.1 Types of Structural Isomerism: Chain, Positional, Functional Group

15.5.2 Types of Stereoisomerism: Geometrical (cis-trans) and Optical

15.5.3 Geometrical Isomerism in Alkenes

15.5.4 Chirality and Optical Isomerism

15.5.5 Identifying Chiral Centres and Isomer Types

16. Genetic technology

16.1 Genetically modified organisms in agriculture

16.1.1 GM crops and animals and their implications

16.2 Primary Amines

16.2.1 Production of Primary Amines by Reaction of Halogenoalkanes with Ammonia

16.3 Nitriles and Hydroxynitriles

16.3.1 Production of Nitriles by Reaction of Halogenoalkanes with KCN

16.3.2 Production of Hydroxynitriles by Reaction of Aldehydes and Ketones with HCN

16.3.3 Hydrolysis of Nitriles to Produce Carboxylic Acids

17. Atomic Structure

17.1 Particles in the Atom and Atomic Radius

17.1.1 Structure of the Atom: Nucleus and Electron Shells

17.1.2 Subatomic Particles: Protons, Neutrons, Electrons

17.1.3 Atomic Number, Proton Number, Mass Number, Nucleon Number

17.1.4 Mass and Charge Distribution in Atoms

17.1.5 Deflection of Charged Particles in Electric Fields

17.1.6 Calculations Involving Protons, Neutrons, Electrons

17.1.7 Trends in Atomic and Ionic Radii Across Periods and Down Groups

17.2 Isotopes

17.2.1 Definition and Notation of Isotopes

17.2.2 Chemical Properties of Isotopes

17.2.3 Physical Properties of Isotopes: Mass and Density Differences

17.3 Electrons

17.3.1 Energy Levels, and Atomic Orbitals: Shells, Sub-shells and Orbitals

17.3.2 Energy Levels,and Atomic Orbitals: Principal Quantum Number (n) and Ground State Configurations

17.3.3 Energy Levels and Atomic Orbitals: Order of Sub-shell Energy Levels (s, p, d)

17.3.4 Energy Levels and Atomic Orbitals: Full and Shorthand Electronic Configurations

17.3.5 Energy Levels and Atomic Orbitals: Electron Box Diagrams

17.3.6 Energy Levels and Atomic Orbitals: Shapes of s and p Orbitals

17.3.7 Energy Levels and Atomic Orbitals: Free Radicals and Unpaired Electrons

17.4 Ionisation Energy

17.4.1 First Ionisation Energy: Definition and Equations

17.4.2 Trends in Ionisation Energy Across Periods and Down Groups

17.4.3 Successive Ionisation Energies and Electron Shells

17.4.4 Factors Affecting Ionisation Energy: Nuclear Charge, Radius, Shielding

17.4.5 Deducing Electronic Configurations Using Ionisation Energy Data

17.4.6 Position of Elements Using Ionisation Energy Patterns

18. Polymerisation (Condensation Polymers)

18.1 Condensation Polymerisation

18.1.1 Formation of Polyesters from Diols and Dicarboxylic Acids or Dioyl Chlorides

18.1.2 Formation of Polyamides from Diamines and Dicarboxylic Acids or Dioyl Chlorides

18.1.3 Formation of Polymers from Amino Acids

18.2 Predicting the Type of Polymerisation

18.2.1 Identifying the Type of Polymerisation from Monomers or Polymer Structure

18.3 Degradable Polymers

18.3.1 Chemical Inertness and Disposal of Poly(alkenes)

18.3.2 Biodegradability of Polyesters and Polyamides

18.3.3 Degradation by Light

19. Carboxylic Acids and Derivatives

19.1 Carboxylic Acids

19.1.1 Production of Carboxylic Acids: Oxidation, Hydrolysis of Nitriles and Esters

19.1.2 Reactions of Carboxylic Acids with Metals, Alkalis and Carbonates

19.1.3 Esterification Reactions with Alcohols

19.1.4 Reduction of Carboxylic Acids

19.1.5 Relative Acidity of Carboxylic Acids, Phenols and Alcohols

19.1.6 Acidity of Chlorine-Substituted Carboxylic Acids

19.2 Esters

19.2.1 Production of Esters by Condensation of Carboxylic Acids and Alcohols

19.2.2 Hydrolysis of Esters with Acid or Alkali

20. Introduction to A Level Organic Chemistry

20.1 Formulas, Functional Groups and the Naming of Organic Compounds

20.1.1 Functional Groups in Aromatic and Extended Organic Molecules

20.1.2 Use of Structural, Displayed and Skeletal Formulas

20.1.3 Systematic Nomenclature for Aliphatic and Aromatic Molecules

20.2 Characteristic Organic Reactions

20.2.1 Electrophilic Substitution and Addition–Elimination Mechanisms

20.3 Shapes of Aromatic Organic Molecules; σ and π Bonds

20.3.1 Shape and Bonding in Benzene: sp² Hybridisation and Delocalised π System

20.4 Isomerism: Optical

20.4.1 Physical and Biological Properties of Optical Isomers

20.4.2 Concepts: Optically Active Compounds, Racemic Mixtures, Chiral Catalysts

21. Reaction Kinetics

21.1 Rate of Reaction

21.1.1 Definition of Rate of Reaction

21.1.2 Collision Theory: Effective and Non-Effective Collisions

21.1.3 Effect of Concentration and Pressure on Reaction Rate

21.1.4 Calculating Reaction Rate from Experimental Data

21.2 Effect of Temperature on Reaction Rates and the Concept of Activation Energy

21.2.1 Definition of Activation Energy

21.2.2 Boltzmann Distribution and Activation Energy

21.2.3 Effect of Temperature on Reaction Rate and Collision Frequency

21.3 Homogeneous and Heterogeneous Catalysts

21.3.1 Definition and Mechanism of Catalysis

21.3.2 Catalysts Lowering Activation Energy

21.3.3 Reaction Pathway Diagrams With and Without Catalysts

22. Organic Synthesis

22.1 Organic Synthesis

22.1.1 Identification of Functional Groups in Organic Molecules

22.1.2 Prediction of Properties and Reactions of Organic Molecules

22.1.3 Designing Multi-Step Synthetic Routes

22.1.4 Analysis of Synthetic Routes and Possible By-products

23. Hydrocarbons (Arenes)

23.1 Arenes

23.1.1 Substitution Reactions of Benzene and Methylbenzene

23.1.2 Mechanism of Electrophilic Substitution in Arenes

23.1.3 Predicting Halogenation: Side-Chain vs. Aromatic Ring

23.1.4 Directing Effects of Substituents in Electrophilic Substitution

24. Equilibria

24.1 Acids and Bases

24.1.1 Conjugate Acids and Bases

24.1.2 pH, Ka, pKa and Kw: Definitions and Calculations

24.1.3 Calculations of pH for Strong Acids, Strong Alkalis and Weak Acids

24.1.4 Definition and Formation of Buffer Solutions

24.1.5 Buffer Solutions in pH Control and Blood Chemistry

24.1.6 Calculations Involving Buffer Solutions

24.1.7 Solubility Product (Ksp) and Calculations

24.1.8 Common Ion Effect and Solubility Calculations

24.2 Partition Coefficients

24.2.1 Definition and Calculation of Partition Coefficient (Kpc)

24.2.2 Factors Affecting Partition Coefficients Based on Solute and Solvent Polarity

25. Analytical Techniques

25.1 Thin-Layer Chromatography

25.1.1 Terms and Interpretation: Stationary Phase, Mobile Phase, Rf Value, Solvent Front, Baseline

25.1.2 Explanation of Differences in Rf Values

25.2 Gas / Liquid Chromatography

25.2.1 Terms and Interpretation: Stationary Phase, Mobile Phase, Retention Time

25.2.2 Composition Analysis and Retention Time Explanation

25.3 Carbon-13 NMR Spectroscopy

25.3.1 Interpretation of C-13 NMR Spectra

25.3.2 Prediction of Number and Type of C Environments

25.4 Proton (¹H) NMR Spectroscopy

25.4.1 Interpretation of ¹H NMR Spectra: Chemical Shifts, Peak Areas, Splitting Patterns (n+1 Rule)

25.4.2 Prediction of Spectral Features

25.4.3 Use of TMS and Deuterated Solvents

25.4.4 Identification of O–H and N–H Protons by D₂O Exchange

26. Halogen Compounds (Arenes)

26.1 Halogen Compounds

26.1.1 Production of Halogenoarenes by Substitution

26.1.2 Reactivity Comparison: Halogenoalkanes vs. Halogenoarenes

27. Hydroxy Compounds (Phenol)

27.1 Alcohols

27.1.1 Reaction of Alcohols with Acyl Chlorides to Form Esters

27.2 Phenol

27.2.1 Directing Effects of Hydroxyl Group in Phenol Reactions

27.2.2 Reactions of Phenol with Bases, Sodium and Diazonium Salts

27.2.3 Nitration and Bromination of Phenol

27.2.4 Acidity of Phenol Compared to Water and Ethanol

27.2.5 Different Reaction Conditions for Phenol vs. Benzene

27.2.6 Production of Phenol from Diazonium Salts

28. Polymerisation

28.1 Addition Polymerisation

28.1.1 Description of Addition Polymerisation

28.1.2 Deduction of Repeat Units from Monomers

28.1.3 Identification of Monomers from Polymer Structures

28.1.4 Challenges of Disposal: Non-biodegradability and Harmful Combustion Products

29. Hydrocarbons

29.1 Alkanes

29.1.1 Production of Alkanes: Hydrogenation and Cracking

29.1.2 Combustion of Alkanes: Complete and Incomplete

29.1.3 Free-Radical Substitution of Alkanes

29.1.4 Mechanism of Free-Radical Substitution: Initiation, Propagation, Termination

29.1.5 Cracking for Useful Alkanes and Alkenes

29.1.6 Environmental Impact of Alkane Combustion

29.2 Alkenes

29.2.1 Production of Alkenes: Elimination and Dehydration Reactions

29.2.2 Electrophilic Addition Reactions of Alkenes

29.2.3 Oxidation of Alkenes: Cold Dilute and Hot Concentrated KMnO₄

29.2.4 Test for C=C Bond Using Aqueous Bromine

29.2.5 Mechanism of Electrophilic Addition in Alkenes

29.2.6 Stability of Carbocations and Markovnikov’s Rule

30. States of Matter

30.1 The Gaseous State: Ideal and Real Gases and pV = nRT

30.1.1 Origin of Pressure in Gases

30.1.2 Ideal Gas Assumptions

30.1.3 Ideal Gas Equation: pV = nRT

30.1.4 Applications of the Ideal Gas Equation

30.2 Bonding and Structure

30.2.1 Lattice Structures of Crystalline Solids

30.2.2 Structures and Bonding: Effect on Physical Properties

30.2.3 Deducing Structure and Bonding from Data

31. The Periodic Table: Chemical Periodicity

31.1 Periodicity of Physical Properties of the Elements in Period 3

31.1.1 Trends in Atomic Radius, Ionic Radius, Melting Point and Electrical Conductivity

31.1.2 Explanation of Melting Point and Conductivity Based on Structure and Bonding

31.2 Periodicity of Chemical Properties of the Elements in Period 3

31.2.1 Reactions of Elements with Oxygen, Chlorine and Water

31.2.2 Oxidation Numbers of Oxides and Chlorides

31.2.3 Reactions of Oxides with Water and pH of Solutions

31.2.4 Acid-Base Behaviour of Oxides and Hydroxides

31.2.5 Reactions of Chlorides with Water and pH of Solutions

31.2.6 Trends Explained by Bonding and Electronegativity

31.2.7 Bonding Types from Chemical and Physical Properties

31.3 Chemical Periodicity of Other Elements

31.3.1 Predicting Properties Based on Group Trends

31.3.2 Deducing Element Identity from Physical and Chemical Data

32. Organic Synthesis

32.1 Organic Synthesis

32.1.1 Identification of Organic Functional Groups

32.1.2 Predicting Properties and Reactions

32.1.3 Designing Multi-Step Synthetic Routes

32.1.4 Analyzing Synthetic Routes and Identifying By-products

33. Reaction Kinetics

33.1 Simple Rate Equations, Orders of Reaction and Rate Constants

33.1.1 Terms: Rate Equation, Order of Reaction, Overall Order, Rate Constant, Half-life, Rate-determining S

33.1.2 Deducing Orders from Graphs or Experimental Data

33.1.3 Interpretation of Concentration–Time and Rate–Concentration Graphs

33.1.4 Calculating Initial Rate from Data

33.1.5 Half-life of First-Order Reactions and Calculations

33.1.6 Calculating Rate Constants Using Different Methods

33.1.7 Predicting Reaction Mechanisms and Rate-Determining Steps

33.1.8 Identifying Catalysts and Intermediates from Mechanisms

33.1.9 Effect of Temperature on Rate Constants

33.2 Homogeneous and Heterogeneous Catalysts

33.2.1 Mode of Action of Heterogeneous Catalysts (Adsorption and Desorption)

33.2.2 Examples of Industrial Heterogeneous Catalysis

33.2.3 Mode of Action of Homogeneous Catalysts

33.2.4 Examples of Homogeneous Catalysis in Atmospheric Chemistry

34. Analytical Techniques

34.1 Infrared Spectroscopy

34.1.1 Analysis of Infrared Spectra to Identify Functional Groups

34.2 Mass Spectrometry

34.2.1 Interpretation of Mass Spectra: m/e Values and Isotopic Abundances

34.2.2 Calculation of Relative Atomic Mass and Molecular Mass

34.2.3 Identification of Molecules by Fragmentation Patterns

34.2.4 Determination of Carbon Atom Number Using [M+1]+ Peak

34.2.5 Detection of Bromine and Chlorine Atoms Using [M+2]+ Peak

35. Chemical Energetics

35.1 Enthalpy Change ΔH

35.1.1 Exothermic and Endothermic Reactions

35.1.2 Reaction Pathway Diagrams: Enthalpy Change and Activation Energy

35.1.3 Standard Conditions and Standard Enthalpy Changes

35.1.4 Enthalpy Changes: Reaction, Formation, Combustion, Neutralisation

35.1.5 Energy Transfer in Breaking and Making Bonds

35.1.6 Calculations Using Bond Energies

35.1.7 Calculations Using Experimental Data: q = mcΔT and ΔH = –mcΔT/n

35.2 Hess’s Law

35.2.1 Application of Hess’s Law to Construct Energy Cycles

35.2.2 Calculations Using Hess’s Law and Bond Energy Data

36. Group 2

36.1 Magnesium to Barium, and their Compounds

36.1.1 Reactions of Group 2 Elements with Oxygen, Water and Acids

36.1.2 Reactions of Group 2 Oxides, Hydroxides and Carbonates with Water and Acids

36.1.3 Thermal Decomposition of Group 2 Nitrates and Carbonates

36.1.4 Trends in Physical and Chemical Properties

36.1.5 Variation in Solubility of Hydroxides and Sulfates

37. Carboxylic Acids and Derivatives (Aromatic)

37.1 Esters

37.1.1 Production of Esters from Alcohols and Acyl Chlorides

37.2 Acyl Chlorides

37.2.1 Comparison of Hydrolysis of Acyl Chlorides, Alkyl Chlorides and Aryl Chlorides

37.2.2 Production of Acyl Chlorides from Carboxylic Acids

37.2.3 Addition–Elimination Mechanism of Acyl Chlorides

37.2.4 Reactions of Acyl Chlorides with Water, Alcohols, Phenols, Ammonia and Amines

37.3 Carboxylic Acids

37.3.1 Further Oxidation of Methanoic Acid and Ethanedioic Acid

37.3.2 Reactions of Carboxylic Acids with PCl₃, PCl₅ and SOCl₂

37.3.3 Effect of Chlorine Substitution on Acid Strength

37.3.4 Relative Acidities of Carboxylic Acids, Phenols and Alcohols

37.3.5 Production of Benzoic Acid from Alkylbenzene

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Calculation of Relative Atomic Mass and Molecular Mass

Introduction

Key Concepts

Relative Atomic Mass (Ar)

Molecular Mass

Molecular Formula Determination

Isotopic Abundance

Mass Spectrometry

Example Problems

Advanced Concepts

Theoretical Derivations

Isotopic Mass Spectra Interpretation

Complex Problem-Solving

Interdisciplinary Connections

Mathematical Techniques in Mass Calculations

Applications in Forensic Science

Comparison Table

Summary and Key Takeaways

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