Degree of Unsaturation (DU) formula for organic compound

Step 1: Calculate DU

Formula: $DU = \frac{2C + 2 – H}{2}$

For C₆H₁₄O (ignore O in DU): $DU = \frac{2(6) + 2 – 14}{2} = \frac{12 + 2 – 14}{2} = 0$

Meaning of DU = 0

No double bond
No triple bond
No ring

So, all structures are open-chain saturated alcohols

Which is stronger acid in Picric acid and formic acid?

Picric acid has three –NO₂ groups which are strong electron-withdrawing groups.
These groups stabilize the conjugate base (picrate ion) by resonance and –I effect.
Formic acid has only one –COOH group, so its conjugate base is less stabilized.
Greater stabilization of conjugate base ⇒ higher acidity, so picric acid is stronger.

HCOOH (Picric Acid)

Picric acid is soluble in NaHCO₃ solution?

Picric acid (2,4,6-trinitrophenol) is a strong acid due to the presence of three –NO₂ groups, which strongly withdraw electrons and stabilize the phenoxide ion. Because of this high acidity, it can react even with a weak base like NaHCO₃.

Reaction:
Picric acid + NaHCO₃ → Sodium picrate (soluble) + CO₂ + H₂O

So, it dissolves in NaHCO₃ with effervescence of CO₂ gas.

Reimer Tiemann reaction mechanism

The Reimer–Tiemann reaction is used to introduce a –CHO (aldehyde) group into a phenol ring, usually at the ortho position (forming salicylaldehyde).

Overall reaction

Phenol + CHCl₃ + NaOH → o-hydroxybenzaldehyde (major) + p-hydroxybenzaldehyde (minor)

Key Points to Remember

Reagent: CHCl₃ + NaOH
Reactive intermediate: dichlorocarbene (:CCl₂)
Directing group: –O⁻ (phenoxide) → ortho/para directing
Major product: ortho-hydroxybenzaldehyde
Para product is minor due to intramolecular H-bonding stabilizing ortho product

How Niels Bohr found radius of hydrogen-like atom

According to Bohr, electrons move in stationary orbits where they do not radiate energy, hence energy of an orbit remains constant with time.

Bohr assumed stationary orbits (not proved mathematically) This explains atomic stability Energy is quantized and constant in each orbit.

Electrostatic force = Centripetal force

Step 1: Electron is attracted to nucleus, so: $\frac{mv^2}{r} = \frac{1}{4\pi \varepsilon_0} \cdot \frac{Z e^2}{r^2}$

Step 2 : Quantization of angular momentum

$mvr = \frac{nh}{2\pi}$

Step 3: Substitute v into Step 1

$m \left( \frac{nh}{2\pi mr} \right)^2 = \frac{1}{4\pi \varepsilon_0} \cdot \frac{Z e^2}{r}$

Step 4: Simplify

$\frac{n^2 h^2}{4\pi^2 m r^2} = \frac{1}{4\pi \varepsilon_0} \cdot \frac{Z e^2}{r}$

Step 5: Solve for radius r

$r = \frac{4\pi \varepsilon_0 n^2 h^2}{4\pi^2 m Z e^2}$

Simplify: $r = \frac{\varepsilon_0 h^2}{\pi m e^2} \cdot \frac{n^2}{Z}$

Final Result

$r_n = \frac{n^2 a_0}{Z}$

where, $a_0 = \frac{\varepsilon_0 h^2}{\pi m e^2} = 0.529 \, \text{Å}$

Key Results

$r_n \propto n^2$
$r_n \propto \frac{1}{Z}$
Valid for hydrogen-like species (H, He⁺, Li²⁺)

Bohr model, hydrogen-like atom, radius derivation, angular momentum quantization, electrostatic force

The limiting line (or limit) of a spectral series (like Lyman, Balmer..)

The line corresponding to the transition where the electron comes from an infinitely large orbit (n = ∞) to a fixed lower energy level.

🔹 What it means simply

When an electron falls from very high energy levels (n = very large), the spectral lines get closer and closer.
Finally, at n = ∞, they merge into one line → this is the series limit (limiting line).

🔹 Formula (Rydberg equation)

$\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} – \frac{1}{n_2^2} \right)$

For limiting line $\frac{1}{\lambda} = \frac{R}{n_1^2}$

Examples of limits

Lyman series (n₁ = 1)
- Limit: electron falls from ∞ → 1
- Region: Ultraviolet (UV)
Balmer series (n₁ = 2)
- Limit: ∞ → 2
- Region: Visible
Paschen series (n₁ = 3)
- Limit: ∞ → 3
- Region: Infrared

Limiting line = shortest wavelength (maximum energy) line of a series.

Lyman Alpha (α) Line

The Lyman α (alpha) line is the first spectral line of the Lyman series.

JEE/NEET-ready summary of acidic, basic, neutral, and amphoteric oxides with examples + trends:

1. Acidic Oxides

Definition: Oxides that react with water to form acids or react with bases to give salt + water.

Examples:

CO₂, SO₂, SO₃, P₂O₅, N₂O₅, Cl₂O₇
Non-metal oxides

Reactions:

CO₂ + H₂O → H₂CO₃
SO₃ + 2NaOH → Na₂SO₄ + H₂O

Trend:

Non-metallic character ↑ ⇒ acidity ↑
Across a period: acidity increases
Down a group: acidity decreases

2. Basic Oxides

Definition: Oxides that react with water to form bases or react with acids to give salt + water.

Examples:

Na₂O, CaO, MgO, K₂O
Mostly metal oxides

Reactions:

Na₂O + H₂O → 2NaOH
CaO + 2HCl → CaCl₂ + H₂O

Trend:

Metallic character ↑ ⇒ basicity ↑
Down a group: basicity increases
Across a period: basicity decreases

3. Amphoteric Oxides

Definition: Oxides that react with both acids and bases.

Examples (VERY IMPORTANT for exams):

Al₂O₃, ZnO, BeO, SnO, PbO, Cr₂O₃

Reactions:

ZnO + 2HCl → ZnCl₂ + H₂O (acts basic)
ZnO + 2NaOH → Na₂ZnO₂ + H₂O (acts acidic)

Trend:

Found near metal–nonmetal boundary
Small size + high charge density → amphoteric behavior

4. Neutral Oxides

Definition: Oxides that do not react with acids or bases.

Examples:

CO, NO, N₂O

Trend:

Mostly simple molecules
No acidic or basic nature

IMPORTANT PERIODIC TREND (MOST ASKED)

Across a period (Left → Right):

Basic → Amphoteric → Acidic

Example (Period 3):
Na₂O → MgO → Al₂O₃ → SiO₂ → P₂O₅ → SO₃ → Cl₂O₇

Key shift:

Metals → Non-metals
Basic → Acidic

QUICK REVISION TABLE

Type	Nature	Examples
Basic	Metal oxides	Na₂O, CaO
Amphoteric	Both	Al₂O₃, ZnO
Acidic	Non-metal oxides	SO₃, CO₂
Neutral	No reaction	CO, NO

EXAM TIPS

Al₂O₃, ZnO → always remember (amphoteric)
CO ≠ acidic (neutral!)
Higher oxidation state ⇒ more acidic oxide
- Example: SO₂ < SO₃ (acidity increases)

MCQs

Q1. Arrange in increasing acidic nature:

A. CO₂ < SiO₂ < SO₃
B. SiO₂ < CO₂ < SO₃
C. SO₃ < CO₂ < SiO₂
D. CO₂ < SO₃ < SiO₂

Q2. Arrange in decreasing basic strength:

A. Na₂O > MgO > Al₂O₃
B. Al₂O₃ > MgO > Na₂O
C. MgO > Na₂O > Al₂O₃
D. Na₂O > Al₂O₃ > MgO

Q3. Arrange in increasing amphoteric character:

A. Na₂O < MgO < Al₂O₃
B. Al₂O₃ < MgO < Na₂O
C. MgO < Na₂O < Al₂O₃
D. Na₂O < Al₂O₃ < MgO

Q4. Arrange in increasing acidic strength:

A. SO₂ < SO₃ < Cl₂O₇
B. Cl₂O₇ < SO₃ < SO₂
C. SO₃ < SO₂ < Cl₂O₇
D. SO₂ < Cl₂O₇ < SO₃

Q5. Arrange in increasing basic character:

A. CaO < MgO < Na₂O
B. Na₂O < MgO < CaO
C. MgO < CaO < Na₂O
D. CaO < Na₂O < MgO

Q6. Arrange in increasing acidic nature:

A. P₂O₅ < SO₃ < Cl₂O₇
B. Cl₂O₇ < SO₃ < P₂O₅
C. SO₃ < P₂O₅ < Cl₂O₇
D. P₂O₅ < Cl₂O₇ < SO₃

Q7. Arrange in increasing basic strength:

A. BeO < MgO < CaO
B. CaO < MgO < BeO
C. MgO < BeO < CaO
D. BeO < CaO < MgO

Q8. Arrange in increasing acidic character:

A. N₂O₃ < NO₂ < N₂O₅
B. N₂O₅ < NO₂ < N₂O₃
C. NO₂ < N₂O₃ < N₂O₅
D. N₂O₃ < N₂O₅ < NO₂

ANSWERS

B → SiO₂ < CO₂ < SO₃
A → Na₂O > MgO > Al₂O₃
A → Na₂O < MgO < Al₂O₃
A → SO₂ < SO₃ < Cl₂O₇
C → MgO < CaO < Na₂O
A → P₂O₅ < SO₃ < Cl₂O₇
A → BeO < MgO < CaO
A → N₂O₃ < NO₂ < N₂O₅

SHORT TRICKS (VERY IMPORTANT)

Across period: Basic ↓, Acidic ↑
Down group: Basic ↑
Higher oxidation state ⇒ more acidic
Metal oxides → basic
Non-metal oxides → acidic
Border elements (Be, Al, Zn) → amphoteric

Electronegativity — JEE/NEET Complete Concepts

🔹 Definition

Electronegativity is the tendency of an atom to attract the shared pair of electrons towards itself in a chemical bond.

Important Points

Applies only to bonded atoms
It is a relative (dimensionless) value
Most commonly used scale → Pauling scale

Trends in Periodic Table

Across a Period (→)

Increases

Reason: Increase in nuclear charge → stronger pull on electrons

Down a Group (↓)

Decreases

Reason: Increase in size → weaker attraction

🔹 Important Order

Fluorine (F) is the most electronegative element $\textbf{F > O > N > Cl > Br > I}$

Factors Affecting Electronegativity

Atomic Size
- Smaller atom → higher electronegativity
Nuclear Charge
- More protons → stronger attraction
Shielding Effect
- More shielding → lower electronegativity
Hybridisation
- sp > sp² > sp³

More s-character → electrons closer to nucleus

Important Exceptions

❗ Noble Gases

Usually no electronegativity
(Because they rarely form bonds)

Pauling Scale (Electronegativity) — JEE/NEET Concept

The Pauling scale is the most commonly used scale to measure electronegativity, proposed by Linus Pauling.

Basic Idea

Electronegativity is calculated based on:

✔ Bond energies (bond dissociation enthalpies)

If a bond A–B is stronger than expected, it means:
A and B have different electronegativities

Formula (Conceptual)

Pauling related electronegativity difference to bond energy: $\chi_A – \chi_B \propto \sqrt{D_{AB} – \frac{D_{AA} + D_{BB}}{2}}$

Where:

$D_{AB}$ = bond energy of A–B
$D_{AA}, D_{BB}$ = bond energies of A–A and B–B

Key Points

Fluorine is highest
- Value = 4.0 (maximum on scale)
Values are relative
- Not absolute, just comparison
Dimensionless
- No unit

🔹 Example Values

Element	Electronegativity
F	4.0
O	3.5
N	3.0
Cl	3.0
H	2.1

Important Applications

1. Predict Bond Type

ΔEN ≈ 0 → Non-polar covalent
ΔEN small → Polar covalent
ΔEN large → Ionic

2. Predict Polarity

Larger difference → more polar bond

Mulliken Scale — Electronegativity (JEE/NEET)

The Mulliken scale was proposed by Robert S. Mulliken.

Basic Idea

Electronegativity depends on:

✔ Ionisation Enthalpy (IE)
✔ Electron Gain Enthalpy (EGE / Electron Affinity)

So, it considers both:

Tendency to lose electron (IE)
Tendency to gain electron (EGE)

🔹 Formula

$\chi = \frac{\text{IE} + \text{EGE}}{2}$ (In some books, electron affinity is used instead of EGE)

🔹 Meaning

Higher IE → atom doesn’t lose electrons easily
More negative EGE → atom gains electrons easily

✔ So, higher value = higher electronegativity

🔹 Key Points

Absolute scale
- Based on measurable energies (unlike Pauling)
Applies to isolated atoms
- Not bond-based
Units initially in energy
- Often converted to dimensionless values

🔹 Comparison with Pauling Scale

Feature	Mulliken	Pauling
Based on	IE + EGE	Bond energy
Type	Absolute	Relative
Concept	Atomic property	Bond property

Basic Relation

The two scales are related approximately by: $\chi_{\text{Pauling}} \approx \frac{\chi_{\text{Mulliken}}}{2.8}$

Electron Gain Enthalpy (EGE) — JEE/NEET Complete Concepts

🔹 Definition

Electron Gain Enthalpy is the enthalpy change when an electron is added to an isolated gaseous atom.

Usually negative (energy released)
More negative = greater tendency to gain electron

🔹 Representation

$X(g) + e^- \rightarrow X^-(g)$

🔹 General Trends

Across a Period (Left → Right)

EGE becomes more negative

Reason:

Increase in nuclear charge → stronger attraction for incoming electron

Down a Group (Top → Bottom)

EGE becomes less negative

Reason:

Increase in size → electron added far from nucleus → less attraction

IMPORTANT EXCEPTIONS (Very Important for JEE/NEET)

❗ Exception 1: Be, Mg (Group 2)

EGE ≈ zero or slightly positive

Reason:

Stable ns² configuration
Incoming electron enters higher energy p-orbital

❗ Exception 2: N (Group 15)

EGE is less negative than expected

Reason:

Stable half-filled configuration (np³)
Adding electron causes electron-electron repulsion

❗ Exception 3: Noble Gases (Group 18)

EGE is positive

Reason:

Completely filled orbitals → very stable
Electron must enter new shell → requires energy

❗ Exception 4: Fluorine vs Chlorine

👉 Cl has more negative EGE than F ❗

❌ Expected: F > Cl
✅ Actual: Cl > F

Reason:

F is very small → strong electron-electron repulsion in 2p orbital
Cl has larger size → less repulsion → easier electron addition

🔹 Important Order Example

Among halogens:
Cl > F > Br > I

Successive Electron Gain Enthalpy

👉 Adding 2nd electron: $X^- + e^- \rightarrow X^{2-}$

❗ Always positive
Reason:

Electron added to already negative ion → strong repulsion

🔹 Elements in Group 16

Oxygen (O)
Sulfur (S)
Selenium (Se)
Tellurium (Te)
Polonium (Po)

Increases down the group
O < S < Se < Te

Why is the 2nd Electron Gain Enthalpy of Oxygen Positive?

Consider the process: $\text{O}^- (g) + e^- \rightarrow \text{O}^{2-} (g)$

🔹 Key Reason: Electron–Electron Repulsion

After gaining one electron:

Oxygen becomes O⁻ (negatively charged)

Now, adding another electron:

Incoming electron is repelled by the already negative ion

✔ So, energy must be supplied → EGE becomes positive

Isoelectronic Species (JEE/NEET Concept)

Isoelectronic species are:

Atoms, ions, or molecules that have the same number of electrons.

🔹 Examples

N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺

All of these have 10 electrons → so they are isoelectronic

How to identify?

Just count total electrons

Example:

O²⁻ → 8 + 2 = 10 electrons
F⁻ → 9 + 1 = 10 electrons
Na⁺ → 11 − 1 = 10 electrons

✔ Same electrons → Isoelectronic

🔹 Important Trend (VERY IMPORTANT for JEE/NEET)

In an isoelectronic series:

Size decreases as nuclear charge (Z) increases

Example Order of Size

For species with 10 electrons:

N³⁻ > O²⁻ > F⁻ > Ne > Na⁺ > Mg²⁺

Reason:

All have same electrons
But increasing protons (Z) pull electrons closer → size decreases

🔹 Key Exam Line

“Isoelectronic species have same number of electrons but different nuclear charge.”

Van der Waals radius (JEE/NEET Concept)

The Van der Waals radius is defined as:

Half of the distance between the nuclei of two non-bonded identical atoms when they are just touching each other.

Simple Understanding

When atoms are not chemically bonded (no covalent/ionic bond), they still can come close due to weak intermolecular forces.
The distance at this closest approach = Van der Waals distance
So,
Van der Waals radius = (Van der Waals distance) / 2

Example

If two neon atoms (not bonded) are 3.2 Å apart:

Van der Waals radius of neon = 3.2 / 2 = 1.6 Å

Correct Order of Atomic Radii:

Van der Waals radius > Metallic radius > Covalent radius

🔹 Why this order?

Covalent radius (smallest)
- Atoms are strongly bonded
- Nuclei pull shared electrons → atoms come closer
Metallic radius (middle)
- Metal atoms are packed in a lattice
- Bonding is weaker than covalent → atoms are slightly farther apart
Van der Waals radius (largest)
- No bonding, only weak attraction
- Atoms stay far apart

🔹 Comparison Table

Radius Type	Condition	Smaller/Larger
Covalent radius	Bonded atoms	Smaller
Metallic radius	Metal lattice	Medium
Van der Waals	Non-bonded atoms	Largest