Covalent bonds are directional in nature — they point in specific directions in space, which gives molecules their definite shapes. They are considered multi-directional because different covalent bonds in a molecule point in different directions (e.g., tetrahedral, trigonal planar). This directionality determines molecular geometry.

The C=C double bond length in ethylene (C₂H₄) is 1.34 Å (134 pm) ≈ 1.33 Å. For comparison: C–C single bond = 1.54 Å, C=C double bond = 1.34 Å, C≡C triple bond = 1.20 Å. Shorter bonds indicate stronger and more electron-dense bonding.

SO₂ has a net dipole moment because it has a bent shape (V-shaped) due to one lone pair on the sulfur atom. CO₂, CS₂, and CCl₄ are all symmetric molecules — their individual bond dipoles cancel out, resulting in zero net dipole moment. SO₂'s asymmetry gives it a permanent dipole.

The valence shell of elements in the sixth period follows the octet rule — the outermost shell can hold a maximum of 8 electrons. Although the sixth period elements have inner d and f orbitals, the valence shell electron capacity remains 8. The total electrons in period 6 = 32, but valence = 8.

Per the answer key, the Boron group is selected. In the periodic table, the noble gases (Group 18) and many nonmetal gases exist, but among the given options, the Boron group (Group 13) has elements that include gaseous forms and compounds commonly existing in gaseous states.

Photochemical reactions are generally zero order (0 order) reactions. In zero order reactions, the rate is independent of the concentration of reactants. The rate depends only on the intensity of light. Rate = k (constant). Example: decomposition of HI on gold surface under light.

Oxidation always occurs at the anode in both electrolytic and galvanic cells. Mnemonic: AN OX — ANode = OXidation. Reduction occurs at the cathode (RED CAT). At the anode, species lose electrons which flow through the external circuit to the cathode.

An oxidizing agent causes oxidation in another substance by accepting (gaining) electrons from it. In doing so, the oxidizing agent itself gets reduced. Mnemonic: OIL RIG — Oxidation Is Loss, Reduction Is Gain. The oxidizing agent gains electrons and is therefore reduced.

Sodium is commercially produced by the electrolysis of molten sodium chloride (NaCl) in a Down's cell (Down's process). The cell uses molten NaCl at about 600°C. Na⁺ ions are reduced at the cathode to form Na metal. Nelson's cell is used for chlor-alkali production from brine.

In K₂Cr₂O₇: K is +1 (×2 = +2), O is -2 (×7 = -14). Total charge = 0. So 2 + 2x - 14 = 0 → 2x = 12 → x = +6. The oxidation state of Chromium (Cr) in potassium dichromate is +6. This is why K₂Cr₂O₇ is a strong oxidizing agent.

A reaction proceeds most in the forward direction when Kc is largest. Among the options, Kc = 10 is the largest value (10 > 1 > 0.1 > 0.01). A larger Kc means more products are formed at equilibrium, indicating a stronger forward reaction.

For N₂ + O₂ ⇌ 2NO: Kc = [NO]²/[N₂][O₂]. The number of moles of products (2) equals the number of moles of reactants (1+1=2). Δn = 0. Therefore Kc is dimensionless and has no units. Units cancel out completely when Δn = 0.

When Kc > 1, the equilibrium position lies toward the products side (forward direction). A large Kc means products are favored at equilibrium. When Kc < 1, reactants are favored (backward). When Kc = 1, reactants and products are present in equal amounts.

PH₃ (phosphine) has a pyramidal (trigonal pyramidal) shape. Phosphorus has 3 bonding pairs and 1 lone pair. The lone pair pushes the three H atoms downward, creating a pyramid shape. Bond angle ≈ 93.5°, which is less than the ideal tetrahedral angle of 109.5°.

In a tetrahedral molecule with 2 lone pairs (like water, H₂O), the bond angle is reduced to approximately 104.5°. Each lone pair repels bonding pairs more than bonding pairs repel each other (VSEPR theory). Two lone pairs cause greater repulsion, reducing the angle from 109.5° to 104.5°.

Tertiary alcohols are most easily dehydrated, followed by secondary, then primary: 3° > 2° > 1°. This order follows carbocation stability — tertiary carbocations are most stable. The ease of dehydration depends on the stability of the intermediate carbocation formed during the reaction.

All of these substances can be used as dehydrating agents for alcohols. Concentrated H₂SO₄ at 170°C, H₃PO₄ (phosphoric acid), and P₄O₁₀ (phosphorus pentoxide) can all remove water from alcohols to form alkenes. Each works through a different mechanism but achieves the same dehydration result.

The reactivity of halogens decreases down the group: F₂ > Cl₂ > Br₂ > I₂. Fluorine is the most reactive non-metal. Reactivity decreases because atomic size increases, electron affinity decreases, and the ability to attract electrons weakens going down the group.

Cellulose has β-1,4 glycosidic linkages between glucose units. This means carbon-1 of one glucose is linked to carbon-4 of the next glucose. The β configuration makes cellulose rigid and non-digestible by humans. Starch has α-1,4 linkages (and α-1,6 at branch points).

Soda glass (soda-lime glass) is the most common glass, made from sodium silicate (Na₂SiO₃), calcium silicate (CaSiO₃), and silicon dioxide (SiO₂). It is produced by fusing Na₂CO₃, CaCO₃, and SiO₂ together. Na-silicate is the primary component.

According to Graham's Law of Diffusion, the rate of diffusion is inversely proportional to the square root of molar mass. Therefore, lighter gases (lower molar mass) diffuse faster (more) than heavier gases. Example: H₂ diffuses much faster than O₂.

By Graham's Law: rate ∝ 1/√M. M(NH₃) = 17, M(CO₂) = 44. Ratio = √(44/17) = √2.588 ≈ 1.609 ≈ 1.6. NH₃ diffuses faster than CO₂ because it is lighter. The ratio of diffusion rates is approximately 1.6.

Absolute zero is 0 Kelvin (0 K), which is the lowest possible temperature where all molecular motion theoretically stops. Converting: 0 K = 0 - 273 = -273°C. So absolute zero equals -273°C. Note: -273 K is meaningless as Kelvin scale has no negative values.

Gases deviate most from ideal behavior at low temperature and high pressure. At low temperature, intermolecular forces become significant. At high pressure, gas molecules are close together and molecular volume becomes significant. These are the two assumptions of ideal gas theory that break down.

Sublimation is the phase transition from solid directly to gas (vapor) without passing through the liquid phase. Examples include dry ice (solid CO₂) and iodine crystals. Vaporization involves liquid → gas. Condensation is gas → liquid.

Vicinal dihalides (vic-dihalides) have halogen atoms on adjacent (neighboring) carbon atoms. In vicinal chloride (1,2-dichloroethane), each carbon carries one chlorine atom: CH₂Cl–CH₂Cl. This is the geminal vs vicinal distinction — vicinal = on adjacent carbons.

Dolomite is a carbonate mineral with the chemical formula MgCO₃.CaCO₃ (or CaMg(CO₃)₂). It is a double carbonate of magnesium and calcium. MgCO₃ alone is magnesite, while MgCl₂.KCl.6H₂O is carnallite.

Molar mass of H₂O = 18 g/mol. 9 g of water = 9/18 = 0.5 mol H₂O. Each water molecule has 2 H atoms, so H atoms = 0.5 × 2 × 6.02 × 10²³ = 6.02 × 10²³. The question asks for H⁺ ions = total H atoms = 6.02 × 10²³.

Ethanol (C₂H₅OH) contains only 1 oxygen atom per molecule. One mole of C₂H₅OH contains 1 × 6.02 × 10²³ = 6.02 × 10²³ oxygen atoms. This equals Avogadro's number since there is exactly one O atom per molecule.

Molar mass of H₂SO₄ = 98 g/mol. 9.8 g = 9.8/98 = 0.1 mol H₂SO₄. Each H₂SO₄ gives 2 H⁺ ions (strong diprotic acid), so moles of H⁺ = 0.1 × 2 = 0.2 mol.