Here is the completely updated `question.php`. I added the missing `$breadcrumbs` array and defined `$category_name` and `$topic_name` right before the header is included. This ensures that `header.php` generates the correct Breadcrumb Schema, page title, and meta description for single question pages. Replace your entire `question.php` with this: ```php Covalent Bonding & VSEPR Questions
Q. A covalent bond is formed by:
Transfer of electrons from one atom to another
Delocalization of electrons in a metallic lattice
Sharing of electron pairs between atoms
Electrostatic attraction between ions

Explanation:

A covalent bond is the sharing of one or more electron pairs between two atoms, usually between nonmetals.

Q. According to VSEPR theory, the shape of a molecule is determined by:
Bond order of the molecule
Atomic mass of the ligands
Nuclear charge of the central atom
Repulsion between electron pairs around the central atom

Explanation:

VSEPR (Valence Shell Electron Pair Repulsion) theory states that electron pairs around a central atom arrange themselves as far apart as possible to minimize repulsion, thereby determining molecular geometry.

Q. What is the molecular geometry of methane (CH₄)?
Trigonal planar
Bent
Tetrahedral
Square planar

Explanation:

Carbon in CH₄ has 4 bonding pairs and 0 lone pairs (steric number 4, tetrahedral electron geometry). The molecular geometry is tetrahedral with bond angles of ~109.5°.

Q. What is the molecular geometry of water (H₂O)?
Bent
Trigonal planar
Linear
Tetrahedral

Explanation:

Oxygen in water has 2 bonding pairs and 2 lone pairs (steric number 4). The electron geometry is tetrahedral, but the molecular geometry is bent with an angle of ~104.5°.

Q. What is the molecular geometry of ammonia (NH₃)?
Trigonal pyramidal
T-shaped
Tetrahedral
Trigonal planar

Explanation:

N in ammonia has 3 bonding pairs and 1 lone pair (steric number 4). The molecular geometry is trigonal pyramidal with bond angles of ~107°.

Q. What is the molecular geometry of CO₂?
Trigonal planar
Linear
Tetrahedral
Bent

Explanation:

Carbon in CO₂ has 2 double bonds and 0 lone pairs (steric number 2). The molecular geometry is linear with a 180° bond angle.

Q. What is the molecular geometry of BF₃?
Tetrahedral
T-shaped
Trigonal planar
Trigonal pyramidal

Explanation:

Boron in BF₃ has 3 bonding pairs and 0 lone pairs (steric number 3). The molecular geometry is trigonal planar with 120° bond angles.

Q. What is the molecular geometry of PCl₅?
Octahedral
Square pyramidal
Tetrahedral
Trigonal bipyramidal

Explanation:

Phosphorus in PCl₅ has 5 bonding pairs and 0 lone pairs (steric number 5). The molecular geometry is trigonal bipyramidal.

Q. What is the molecular geometry of SF₆?
Octahedral
Trigonal bipyramidal
Square pyramidal
Tetrahedral

Explanation:

Sulfur in SF₆ has 6 bonding pairs and 0 lone pairs (steric number 6). The molecular geometry is octahedral with 90° bond angles.

Q. The bond angle in a tetrahedral molecule is approximately:
180°
120°
90°
109.5°

Explanation:

In a perfect tetrahedron, the bond angle is arccos(-1/3) ≈ 109.5°.

Q. The bond angle in a trigonal planar molecule is:
109.5°
120°
90°
180°

Explanation:

A trigonal planar molecule has three groups arranged in a plane 120° apart.

Q. A molecule with a steric number of 5 and one lone pair (like SF₄) has what molecular geometry?
Trigonal bipyramidal
See-saw
Tetrahedral
Square planar

Explanation:

SF₄ has 4 bonding pairs and 1 lone pair (steric number 5). The lone pair occupies an equatorial position, giving a see-saw (seesaw) molecular geometry.

Q. A molecule with a steric number of 6 and two lone pairs (like XeF₄) has what molecular geometry?
Square planar
Tetrahedral
Octahedral
See-saw

Explanation:

XeF₄ has 4 bonding pairs and 2 lone pairs (steric number 6). The lone pairs occupy opposite (trans) positions, giving a square planar molecular geometry.

Q. Which of the following molecules is polar?
BF₃
CH₄
CO₂
H₂O

Explanation:

H₂O is bent (asymmetric), so the O-H bond dipoles do not cancel and the molecule has a net dipole moment. CO₂, BF₃, and CH₄ are symmetric, so dipoles cancel.

Q. Which of the following molecules is nonpolar despite having polar bonds?
CO₂
HCl
NH₃
H₂O

Explanation:

CO₂ is linear, and the two C=O bond dipoles point in opposite directions and cancel exactly, making the molecule nonpolar.

Q. The number of sigma and pi bonds in a molecule of ethene (C₂H₄) is:
5 sigma and 1 pi
4 sigma and 2 pi
4 sigma and 1 pi
6 sigma and 0 pi

Explanation:

Ethene has 4 C-H sigma bonds, 1 C-C sigma bond, and 1 C-C pi bond: 5 sigma and 1 pi.

Q. The number of sigma and pi bonds in ethyne (C₂H₂) is:
2 sigma and 2 pi
4 sigma and 2 pi
3 sigma and 1 pi
3 sigma and 2 pi

Explanation:

Ethyne has 2 C-H sigma bonds, 1 C-C sigma bond, and 2 C-C pi bonds: 3 sigma and 2 pi.

Q. Bond length is inversely related to:
Bond order
Atomic mass
Lone pair count
Nuclear charge

Explanation:

Shorter bonds are stronger. As bond order increases (single → double → triple), bond length decreases and bond strength increases.

Q. Which has the shortest carbon-carbon bond?
Benzene (C₆H₆)
Ethane (C₂H₆)
Ethyne (C₂H₂)
Ethene (C₂H₄)

Explanation:

Bond order determines length: C≡C (triple, ~120 pm) < C=C (double, ~134 pm) < C–C (single, ~154 pm). Ethyne has the shortest bond.

Q. Which of the following is an exception to the octet rule?
BF₃
H₂O
CH₄
NH₃

Explanation:

Boron in BF₃ has only 6 electrons in its valence shell (an incomplete octet). Be, B, and Al frequently have incomplete octets.

Q. Which of the following molecules has an expanded octet?
H₂O
CH₄
NH₃
SF₆

Explanation:

Period 3 and higher elements can use d-orbitals to accommodate more than 8 electrons. SF₆ has 12 electrons around sulfur. CH₄, NH₃, and H₂O all obey the octet rule.

Q. The dipole moment of a molecule is a measure of:
The total number of bonds
The strength of a single covalent bond
The ionization energy of the central atom
The net molecular polarity arising from bond dipoles

Explanation:

Dipole moment (μ = Q × r) measures the net separation of positive and negative charge. It depends on both bond polarity and molecular geometry.

Q. Which of the following has the highest bond energy?
N₂
H₂
F₂
O₂

Explanation:

Triple bonds are the strongest covalent bonds. N≡N in N₂ has a bond energy of ~941 kJ/mol, the highest among the listed species.

Q. The bond angle in a linear molecule is:
90°
120°
109.5°
180°

Explanation:

A linear molecule has all three atoms in a straight line with a 180° bond angle (e.g., CO₂, BeCl₂, C₂H₂).

Q. The percent ionic character of a bond can be estimated using:
The Henderson-Hasselbalch equation
The ideal gas law
Hess's law
Pauling's electronegativity difference formula

Explanation:

Pauling's equation: % ionic character ≈ (1 − e^(−(ΔEN)²/4)) × 100%, based on the electronegativity difference between the bonded atoms.

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