📘 UNIT 1 – BASIC ENGINEERING MATHEMATICS & CHEMISTRY NOTES 📘

📘 UNIT 1 – BASIC ENGINEERING MATHEMATICS & CHEMISTRY NOTES

🧪 Chemistry – 1 Mark Questions (Detailed)

1. Define the term isotope.
Isotopes are atoms of the same element which have the same atomic number but different mass numbers. For example, 1H,2H,3H^1H, ^2H, ^3H are isotopes of hydrogen.

2. Define the term isobar.
Isobars are atoms of different elements that have the same mass number but different atomic numbers. For example, 40Ar^ {40}Ar and 40Ca^ {40}Ca are isobars.

3. Define metallic bond.
A metallic bond is the force of attraction between positively charged metal ions and the sea of delocalized free electrons around them. This bond gives metals properties like conductivity and malleability.

4. Define oxidation.
Oxidation is a chemical process in which an atom, ion, or molecule loses electrons, or gains oxygen, or loses hydrogen. Example: 2Mg+O2→2MgO2Mg + O_2 \rightarrow 2MgO.

5. What is meant by valency?
Valency is the combining capacity of an element, expressed by the number of electrons an atom can lose, gain, or share to form stable compounds. For example, the valency of oxygen is 2.

6. State Hund’s rule.
According to Hund’s rule, electrons fill degenerate orbitals singly with parallel spins before pairing takes place. This minimizes electron repulsion and gives maximum stability.

7. What is the electronic configuration of Cr?
The atomic number of chromium (Cr) is 24. Its electronic configuration is: 1s22s22p63s23p63d54s11s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^1 or in short form: [Ar] 3d⁵ 4s¹.

8. What is conjugate acid–base pair?
A conjugate acid–base pair consists of two species that differ only by one proton (H⁺). For example, HClHCl and Cl−Cl^- form a conjugate acid–base pair.

9. Define ionic product of water.
The ionic product of water (Kw)(K_w) is the product of the molar concentrations of hydrogen ions [H+][H^+] and hydroxyl ions [OH−][OH^-] in water. At 25°C, Kw=[H+][OH−]=1×10−14K_w = [H^+][OH^-] = 1 \times 10^{-14}.


🧪 Chemistry – 3 Marks Questions (Exam Length Answers)

1. State the charge and mass of fundamental particles.
An atom consists of three fundamental particles – electron, proton, and neutron.

  • Electron: charge = –1, mass ≈ 9.1 × 10⁻³¹ kg.

  • Proton: charge = +1, mass ≈ 1.67 × 10⁻²⁷ kg.

  • Neutron: charge = 0, mass ≈ 1.67 × 10⁻²⁷ kg.
    Thus, protons and neutrons are heavier, while electrons are very light.

2. State the demerits of Bohr’s theory.
Bohr’s theory explained hydrogen atom but failed for multi-electron atoms.
It could not explain the fine structure of spectral lines.
It also failed to explain Zeeman effect (splitting in magnetic field) and Stark effect (splitting in electric field).
Hence, it was replaced by quantum theory.

3. What is the significance of quantum numbers?
Quantum numbers describe the position and energy of an electron in an atom.

  • Principal number (n): shows the main energy level.

  • Azimuthal number (l): shows subshell and orbital shape.

  • Magnetic number (m): shows orientation of orbital in space.

  • Spin number (s): shows spin direction of electron.
    Together they give the full address of an electron.

4. State and explain Pauli’s principle.
Pauli’s exclusion principle states that no two electrons in the same atom can have the same set of four quantum numbers.
This means each orbital can hold a maximum of two electrons, and they must have opposite spins.
For example, in 1s orbital, if one electron has spin +½, the other will have spin –½.

5. State and explain Aufbau principle.
Aufbau principle explains the filling of electrons in an atom.
It states that electrons occupy orbitals in the order of increasing energy.
The sequence is: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p and so on.
Thus, lower energy orbitals fill first, then higher ones.

6. Write the set of quantum numbers for the differentiating electron of sodium.
Sodium (Z = 11) has electronic configuration: 1s² 2s² 2p⁶ 3s¹.
The last electron enters the 3s orbital.
Its quantum numbers are:

  • n = 3 (principal quantum number),

  • l = 0 (s-orbital),

  • m = 0 (only one orientation for s),

  • s = +½ (spin).

7. Outline the shapes of s and d orbitals.
The s-orbital is spherical in shape and symmetrical around the nucleus.
The size increases with increasing principal quantum number.
The d-orbitals are clover-leaf shaped with four lobes.
There are 5 d-orbitals, each oriented differently in space.

8. Explain covalent bond formation in nitrogen by Lewis method.
Nitrogen has atomic number 7 and electronic configuration 1s² 2s² 2p³.
Each nitrogen atom has 5 valence electrons.
To complete octet, two nitrogen atoms share three electrons each.
Thus, a triple bond (N≡N) is formed, making the molecule stable.

9. Outline the limitations of Arrhenius theory.
According to Arrhenius, acids produce H⁺ and bases produce OH⁻ in water.
But this theory is limited only to aqueous solutions.
It cannot explain acid–base behavior in non-aqueous solvents.
It also fails to explain how NH₃ acts as a base though it has no OH⁻ ions.

10. Explain neutralization by Lewis theory with example.
Lewis theory defines acids as electron pair acceptors and bases as electron pair donors.
In a neutralization reaction, the base donates its lone pair to the acid.
For example, NH3NH₃ donates a pair of electrons to BF3BF₃.
Thus, a coordinate covalent bond is formed, showing acid–base neutralization.

🧪 Chemistry – 5 Marks Questions (Exam Length Answers)

1. Explain anomalous configurations of Chromium and Copper
Normally, electron configuration should follow Aufbau’s principle.

  • Chromium (Z=24) expected: [Ar] 3d⁴ 4s²
    But actual: [Ar] 3d⁵ 4s¹ (half-filled 3d is stable).

  • Copper (Z=29) expected: [Ar] 3d⁹ 4s²
    But actual: [Ar] 3d¹⁰ 4s¹ (completely filled 3d is stable).
    Reason: Half-filled and fully filled d-orbitals give extra stability.

2. Differences between Ionic and Covalent Compounds

  • Ionic compounds are formed by transfer of electrons, covalent by sharing of electrons.

  • Ionic compounds are crystalline, hard, brittle; covalent are soft and exist as liquids or gases.

  • Ionic compounds conduct electricity in molten/aqueous state, covalent compounds are poor conductors.

  • Ionic compounds have high melting/boiling points; covalent compounds have low.
    Example: NaCl (ionic), H₂O (covalent).

3. Differences between Orbit and Orbital

  • Orbit: Fixed circular path of an electron around nucleus (Bohr’s model).

  • Orbital: A 3D region around nucleus where probability of finding electron is maximum.

  • Orbit shows exact path; orbital shows distribution of electron.

  • Orbit is a simple model; orbital concept is more advanced (Quantum mechanical).

4. Identify and explain the nature of bonding in MgO and HCl

  • MgO: Ionic bond. Magnesium loses 2e⁻ → Mg²⁺, Oxygen gains 2e⁻ → O²⁻, strong electrostatic force forms.

  • HCl: Covalent bond. H and Cl share one pair of electrons. However, HCl is polar covalent due to electronegativity difference.

5. Find oxidation numbers

  • In H₂SO₄: Let S = x. (2×+1) + x + (4×-2)=0 → x=+6.

  • In KMnO₄: Let Mn = x. (+1) + x + (4×-2)=0 → x=+7.

  • In K₂Cr₂O₇: 2(+1) + 2x + 7(-2)=0 → x=+6.
    So oxidation numbers are: S=+6, Mn=+7, Cr=+6.

6. Define pH. Find the pH of 0.5 M NaOH

  • Definition: pH = –log[H⁺], measures acidity/basicity.

  • For NaOH (strong base), [OH⁻] = 0.5 M.
    pOH = –log(0.5) ≈ 0.3.
    pH = 14 – 0.3 = 13.7.
    So solution is strongly basic.

7. Buffer solutions and applications

  • Definition: A buffer resists change in pH on addition of small amounts of acid/base.

  • Types: Acidic buffer (CH₃COOH + CH₃COONa), Basic buffer (NH₄OH + NH₄Cl).

  • Applications:

    1. Used in blood to maintain pH ~7.4.

    2. In pharmaceutical industries.

    3. In biochemical processes (enzymes need constant pH).

    4. In fermentation and electroplating.


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