Atoms and Molecules

Introduction to Atoms

• Atom: The smallest unit of matter that retains the properties of an element.
• Historical Perspective:
  • The term "atom" comes from the Greek word atomos, meaning indivisible.
  • Proposed by ancient Greek philosophers Democritus and Leucippus.

Structure of an Atom

1. Nucleus:

   • Small, dense central part of the atom.
   • Contains protons (positively charged) and neutrons (neutral particles).
   • Almost all the mass of an atom resides in the nucleus.

2. Electrons:

   • Negatively charged particles revolving around the nucleus in specific orbits (energy levels).
   • Negligible mass compared to protons and neutrons.

3. Subatomic Particles:

   Particle	Charge	Mass (in $u$)	Location
   Proton	$+1$	$1.007$	Nucleus
   Neutron	$0$	$1.009$	Nucleus
   Electron	$-1$	$0.00055$	Outside nucleus

---

Atomic Models

1. Dalton’s Atomic Theory (1803):

   • Atoms are indivisible particles.
   • Atoms of a given element are identical in mass and properties.
   • Atoms combine in whole-number ratios to form compounds.
   • Limitations:
     • Failed to explain the discovery of subatomic particles.
     • Could not explain isotopes and isobars.

2. Thomson’s Plum Pudding Model (1904):

   • Atom consists of a positively charged sphere with electrons embedded in it, like raisins in a pudding.
   • Limitations:
     • Could not explain atomic stability.

3. Rutherford’s Nuclear Model (1911):

   • Based on the famous gold foil experiment:
     • Most alpha particles passed through the foil (indicating an atom is mostly empty space).
     • Few were deflected (indicating a dense, positively charged nucleus).
   • Key features:
     • Atom has a small, dense nucleus containing protons and neutrons.
     • Electrons revolve around the nucleus.
   • Limitations:
     • Could not explain the stability of atoms or energy levels.

---

Molecules

• Definition: Molecules are groups of two or more atoms bonded together chemically.
• Types of Molecules:
  1. Molecules of Elements:
     • Contain atoms of the same element.
     • Examples: $\text{H}_2$, $\text{O}_2$, $\text{N}_2$.
  2. Molecules of Compounds:
     • Contain atoms of different elements.
     • Examples: $\text{H}_2\text{O}$, $\text{CO}_2$, $\text{CH}_4$.

---

Atomic Mass and Molecular Mass

1. Atomic Mass:

   • The mass of a single atom, expressed in atomic mass units ($u$).
   • 1 atomic mass unit ($u$) = $\frac{1}{12}$ the mass of a carbon-12 atom.
   • Example: Atomic mass of hydrogen = $1 \, u$, oxygen = $16 \, u$.

2. Molecular Mass:

   • The sum of atomic masses of all atoms in a molecule.
   • Example:
     • Molecular mass of $\text{H}_2\text{O}$: $\text{Mass} = (2 \times 1 \, u) + (1 \times 16 \, u) = 18 \, u$

---

Mole Concept

• Definition: One mole is the amount of substance containing $6.022 \times 10^{23}$ particles (atoms, molecules, or ions). This number is known as Avogadro’s Number ($N_A$).
• Molar Mass: The mass of one mole of a substance, expressed in grams per mole ($\text{g/mol}$).
  • Example:
    • Molar mass of oxygen ($\text{O}_2$) = $32 \, \text{g/mol}$.

---

Law of Conservation of Mass

• Statement: Mass is neither created nor destroyed in a chemical reaction.
• Example:
  • Reaction: $\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}$.
  • Total mass of reactants = Total mass of products.

Laws of Chemical Combination

The behavior of atoms and molecules in chemical reactions is governed by these fundamental laws:

1. Law of Definite Proportions (Proust’s Law):

   • Statement: A given compound always contains the same elements in the same proportion by mass, regardless of the source or preparation method.
   • Example:
     • Water ($\text{H}_2\text{O}$) always contains hydrogen and oxygen in the ratio $2:16$ by mass.

2. Law of Multiple Proportions:

   • Statement: When two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other are in a simple whole-number ratio.
   • Example:
     • Carbon and oxygen form two compounds:
       • $\text{CO}$: Carbon and oxygen combine in a $12:16$ ratio.
       • $\text{CO}_2$: Carbon and oxygen combine in a $12:32$ ratio.
       • Ratio of oxygen masses: $16:32 = 1:2$.

3. Gay-Lussac’s Law of Gaseous Volumes:

   • Statement: When gases react together at constant temperature and pressure, their volumes are in simple whole-number ratios.
   • Example:
     • Reaction: $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$.
     • Volume ratio: $2:1:2$.

4. Avogadro’s Hypothesis:

   • Statement: Equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules.
   • Application:
     • Forms the basis of the molar volume concept: $1 \, \text{mol}$ of any gas occupies $22.4 \, \text{L}$ at STP.

---

Atomic Number and Mass Number

1. Atomic Number ($Z$):

   • Number of protons in the nucleus of an atom.
   • Determines the chemical identity of an element.
   • Example: Hydrogen ($Z = 1$), Carbon ($Z = 6$).

2. Mass Number ($A$):

   • Sum of protons and neutrons in the nucleus. $A = Z + \text{Number of Neutrons}$
   • Example: For oxygen ($Z = 8$, neutrons = $8$), $A = 8 + 8 = 16$.

---

Isotopes, Isobars, and Isotones

1. Isotopes:

   • Atoms of the same element with the same atomic number ($Z$) but different mass numbers ($A$).
   • Example:
     • Hydrogen isotopes: Protium ($^1\text{H}$), Deuterium ($^2\text{H}$), Tritium ($^3\text{H}$).

2. Isobars:

   • Atoms of different elements with the same mass number ($A$) but different atomic numbers ($Z$).
   • Example:
     • $\text{C}^{14}_6$ and $\text{N}^{14}_7$.

3. Isotones:

   • Atoms of different elements with the same number of neutrons.
   • Example:
     • $\text{C}^{14}_6$ (neutrons = 8) and $\text{O}^{16}_8$ (neutrons = 8).

---

Molecule and Atomicity

1. Molecule:

   • A group of atoms bonded together, representing the smallest unit of a chemical compound.

2. Atomicity:

   • The number of atoms in a molecule.
   • Types:
     • Monoatomic: $\text{He}, \text{Ne}$
     • Diatomic: $\text{O}_2, \text{H}_2$
     • Triatomic: $\text{O}_3, \text{CO}_2$
     • Polyatomic: $\text{P}_4, \text{S}_8$

---

Empirical and Molecular Formulas

1. Empirical Formula:

   • Represents the simplest whole-number ratio of atoms in a compound.
   • Example:
     • Glucose: Empirical formula = $\text{CH}_2\text{O}$.

2. Molecular Formula:

   • Represents the actual number of atoms of each element in a molecule.
   • Related to the empirical formula by: $\text{Molecular formula} = n \times \text{Empirical formula}$
   • Example:
     • Glucose: Molecular formula = $\text{C}_6\text{H}_{12}\text{O}_6$.

Chemical Bonding in Molecules

Atoms combine to form molecules through chemical bonds. These bonds are of various types:

1. Ionic Bond:

   • Formed by the transfer of electrons from one atom to another.
   • One atom becomes a positively charged ion (cation), and the other becomes a negatively charged ion (anion).
   • Example:
     • Sodium chloride ($\text{NaCl}$): Sodium donates one electron to chlorine. $\text{Na} \rightarrow \text{Na}^+ + e^-$ $\text{Cl} + e^- \rightarrow \text{Cl}^-$

2. Covalent Bond:

   • Formed by the sharing of electrons between two atoms.
   • Example:
     • Water ($\text{H}_2\text{O}$): Each hydrogen atom shares one electron with oxygen.

3. Metallic Bond:

   • Formed by the attraction between a lattice of positive metal ions and a sea of delocalized electrons.
   • Example:
     • Metals like iron, copper.

4. Hydrogen Bond:

   • A weak bond formed between a hydrogen atom covalently bonded to a highly electronegative atom (e.g., oxygen, nitrogen) and another electronegative atom.
   • Example:
     • Hydrogen bonding in water molecules.

---

Mole Concept and Calculations

1. Relationship Between Mole, Mass, and Molar Mass: $n = \frac{m}{M}$ Where:

   • $n$ = Number of moles,
   • $m$ = Mass of substance (in grams),
   • $M$ = Molar mass (in $\text{g/mol}$).

2. Number of Particles in a Mole: $N = n \times N_A$ Where:

   • $N$ = Total number of particles,
   • $n$ = Number of moles,
   • $N_A$ = Avogadro’s number ($6.022 \times 10^{23}$).

3. Molar Volume of Gases:

   • At STP ($0^\circ \text{C}$, $1 \, \text{atm}$), 1 mole of any gas occupies $22.4 \, \text{L}$.

---

Chemical Reactions and Balancing Equations

1. Chemical Reaction:

   • A process in which one or more substances (reactants) are converted into one or more new substances (products).
   • Example: $\text{2H}_2 + \text{O}_2 \rightarrow \text{2H}_2\text{O}$

2. Balancing Chemical Equations:

   • Ensure the number of atoms of each element is the same on both sides of the equation.
   • Example:
     • Unbalanced: $\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}$.
     • Balanced: $\text{2H}_2 + \text{O}_2 \rightarrow \text{2H}_2\text{O}$.

---

Stoichiometry

1. Definition:

   • The calculation of quantities of reactants and products in a chemical reaction.

2. Steps for Stoichiometric Calculations:

   • Write the balanced chemical equation.
   • Convert the given quantity (mass/volume) into moles.
   • Use the mole ratio from the balanced equation.
   • Convert the result back to the required unit.

3. Example:

   • Reaction: $\text{2H}_2 + \text{O}_2 \rightarrow \text{2H}_2\text{O}$.
   • If $4 \, \text{mol}$ of $\text{H}_2$ reacts, how many moles of $\text{H}_2\text{O}$ are produced? $\text{Mole ratio: } \text{H}_2 : \text{H}_2\text{O} = 2:2$ $\text{Moles of } \text{H}_2\text{O} = 4 \, \text{mol}$

---

Empirical and Molecular Formula Calculation

1. Steps to Determine Empirical Formula:

   • Determine the mass or percentage composition of each element.
   • Convert masses to moles.
   • Divide by the smallest number of moles to get the simplest ratio.

2. Steps to Determine Molecular Formula:

   • Calculate the empirical formula mass.
   • Determine the ratio: $\text{Molecular Formula} = n \times \text{Empirical Formula}$ Where: $n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$

3. Example:

   • Compound: $40\% \, \text{C}$, $6.7\% \, \text{H}$, $53.3\% \, \text{O}$.
   • Molar mass: $180 \, \text{g/mol}$.
   • Empirical formula: $\text{CH}_2\text{O}$.
   • Empirical formula mass: $12 + 2(1) + 16 = 30 \, \text{g/mol}$.
   • Molecular formula: $n = \frac{180}{30} = 6$ $\text{Molecular formula} = \text{C}_6\text{H}_{12}\text{O}_6$

---

Summary Table of Key Concepts

Concept	Key Formula/Value	Example
Avogadro’s Number ($N_A$)	$6.022 \times 10^{23}$ particles/mol	Used in mole calculations
Molar Volume at STP	$22.4 \, \text{L}$	1 mole of $\text{O}_2$ occupies $22.4 \, \text{L}$
Empirical Formula	Simplest whole-number ratio of atoms	$\text{CH}_2\text{O}$
Molecular Formula	$n \times \text{Empirical Formula}$	$\text{C}_6\text{H}_{12}\text{O}_6$