v

1. Nature and Classification of Matter

Matter: Anything that has mass and occupies space.
- Physical Classification:
- Solid: Definite shape and definite volume.
- Liquid: Definite volume but no definite shape (takes the shape of the container).
- Gas: Neither definite shape nor definite volume.
- Chemical Classification:
- Pure Substances: Fixed composition and distinct chemical properties.
  - Elements: Consist of only one type of particle (atoms or molecules), such as $Cu$ , $Fe$ , $H_2$ , $O_2$ .
  - Compounds: Formed when two or more atoms of different elements combine in a fixed ratio, such as $H_2O$ , $CO_2$ .
- Mixtures: Contain two or more substances present in any ratio.
  - Homogeneous Mixtures: Uniform composition throughout (e.g., sugar solution, air).
  - Heterogeneous Mixtures: Non-uniform composition throughout (e.g., sand in water, oil in water).

2. Properties of Matter and Their Measurement

SI Units of Fundamental Quantities:
- Length: meter ( $m$ )
- Mass: kilogram ( $kg$ )
- Time: second ( $s$ )
- Electric current: ampere ( $A$ )
- Thermodynamic temperature: kelvin ( $K$ )
- Amount of substance: mole ( $mol$ )
- Luminous intensity: candela ( $cd$ )
Temperature Conversions:
- $^{\circ}F = \frac{9}{5}(^{\circ}C) + 32$
- $K = ^{\circ}C + 273.15$
Precision vs. Accuracy:
- Precision: Closeness of various measurements for the same quantity.
- Accuracy: Agreement of a particular value to the true value of the result.
Significant Figures: Meaningful digits known with certainty plus one estimated digit.
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros are not significant (e.g., $0.0025$ has $2$ significant figures).
- Trailing zeros after a decimal point are significant (e.g., $4.500$ has $4$ significant figures).

3. Laws of Chemical Combinations

Law of Conservation of Mass (Antoine Lavoisier, 1789):
- Matter can neither be created nor destroyed in a chemical reaction.
Law of Definite Proportions (Joseph Proust, 1799):
- A given compound always contains exactly the same proportion of elements by weight, regardless of its source.
Law of Multiple Proportions (John Dalton, 1803):
- If two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.
Gay-Lussac’s Law of Gaseous Volumes (1808):
- Gases combine or are produced in a chemical reaction in a simple ratio by volume, provided all gases are at the same temperature and pressure.
Avogadro’s Law (1811):
- Equal volumes of all gases at the same temperature and pressure contain an equal number of molecules.

4. Dalton's Atomic Theory

Matter consists of indivisible atoms.
All atoms of a given element have identical properties and mass.
Compounds are formed when atoms of different elements combine in a fixed, simple whole-number ratio.
Chemical reactions involve reorganization of atoms; atoms are neither created nor destroyed in a chemical reaction.

5. Atomic, Molecular, and Formula Masses

Atomic Mass Unit ( $amu$ or unified mass, $u$ ): Defined as a mass exactly equal to one-twelfth ( $\frac{1}{12}$ ) of the mass of one carbon-12 atom.
- $1\,u = 1.66056 \times 10^{-24}\,g$
Average Atomic Mass: Calculated by multiplying the fractional abundance of each isotope by its isotopic mass and summing the values:
- $\bar{A} = \sum (\text{fractional abundance} \times \text{isotopic mass})$
Molecular Mass: Sum of atomic masses of the elements present in a molecule.
Formula Mass: Used for ionic substances that do not exist as discrete molecules (e.g., $NaCl$ ).

6. Mole Concept and Molar Mass

Mole: One mole is the amount of substance that contains as many entities as there are atoms in exactly $12\,g$ of the $^{12}C$ isotope.
- Avogadro Constant ( $N_A$ ): $6.022 \times 10^{23}\,mol^{-1}$
Molar Mass: Mass of one mole of a substance in grams ( $g\,mol^{-1}$ ).
Number of Moles ( $n$ ):
- $n = \frac{\text{Mass in grams } (m)}{\text{Molar mass } (M)}$
- $n = \frac{\text{Number of particles } (N)}{N_A}$
- $n = \frac{\text{Volume of gas at STP in } dm^3}{22.7\,dm^3\,mol^{-1}}$

7. Percentage Composition, Empirical and Molecular Formulas

Mass Percentage of an Element:
- $\text{Mass } \% = \frac{\text{Mass of that element in the compound}}{\text{Molar mass of the compound}} \times 100$
Empirical Formula: Simplest whole-number ratio of various atoms present in a compound.
Molecular Formula: Exact number of different types of atoms present in a molecule of a compound.
- $\text{Molecular Formula} = n \times (\text{Empirical Formula})$
- $n = \frac{\text{Molar mass}}{\text{Empirical formula mass}}$

8. Stoichiometry and Stoichiometric Calculations

Limiting Reagent: The reactant that is completely consumed first in a reaction and limits the amount of product formed.
Concentration of Solutions:
- Mass Percent ( $w/w\%$ ):
- $\text{Mass } \% = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100$
- Mole Fraction ( $\chi$ ): Ratio of number of moles of a particular component to the total number of moles of the solution.
- $\chi_A = \frac{n_A}{n_A + n_B}$
- $\chi_A + \chi_B = 1$
- Molarity ( $M$ ): Number of moles of solute dissolved in $1\,dm^3$ ( $1\text{ liter}$ ) of solution.
- $M = \frac{n_{\text{solute}}}{V_{\text{solution}}\,(dm^3)}$
- Units: $mol\,dm^{-3}$
- Dependent on temperature.
- Molality ( $m$ ): Number of moles of solute present in $1\,kg$ of solvent.
- $m = \frac{n_{\text{solute}}}{W_{\text{solvent}}\,(kg)}$
- Units: $mol\,kg^{-1}$
- Independent of temperature.

Chapter 2: Structure of Atom

Subatomic Particles and Atomic Models:
- Electron: Discovered by J.J. Thomson via cathode ray discharge tube experiments; charge-to-mass ratio ( $e/m$ ) is $1.758820 \times 10^{11}\,C\,kg^{-1}$ .
- Charge on Electron: Determined by R.A. Millikan via oil drop experiment ( $e = -1.6022 \times 10^{-19}\,C$ ; mass $m_e = 9.1094 \times 10^{-31}\,kg$ ).
- Rutherford’s Nuclear Model: Alpha-particle scattering experiment established the presence of a small, dense, positively charged nucleus with electrons orbiting around it. Failed to explain atomic stability and line spectra.
Developments Leading to the Bohr Model:
- Dual Nature of Electromagnetic Radiation: Exhibits wave-like and particle-like properties.
- Wave Character: $c = \nu \lambda$ $\bar{\nu} = \frac{1}{\lambda}$
- Planck’s Quantum Theory: Radiant energy is emitted or absorbed in discrete packets called quanta. $E = h\nu$ $h = 6.626 \times 10^{-34}\,J\,s$
- Photoelectric Effect: Emission of electrons from a metal surface when light of suitable frequency hits it. $h\nu = h\nu_0 + \frac{1}{2}m_e v^2$
- Line Spectrum of Hydrogen: $\bar{\nu} = 109677 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)\,cm^{-1}$
- Lyman series: $n_1 = 1$ , $n_2 = 2, 3, \dots$ (Ultraviolet region)
- Balmer series: $n_1 = 2$ , $n_2 = 3, 4, \dots$ (Visible region)
- Paschen series: $n_1 = 3$ , $n_2 = 4, 5, \dots$ (Infrared region)
- Brackett series: $n_1 = 4$ , $n_2 = 5, 6, \dots$ (Infrared region)
- Pfund series: $n_1 = 5$ , $n_2 = 6, 7, \dots$ (Infrared region)
Bohr’s Model for Hydrogen Atom:
- Quantization of angular momentum: $m_e v r = \frac{n h}{2\pi}$
- Radius of the $n$ -th stationary orbit: $r_n = 52.9 \times \frac{n^2}{Z}\,pm$
- Energy of the stationary state: $E_n = -2.18 \times 10^{-18} \left(\frac{Z^2}{n^2}\right)\,J$
Quantum Mechanical Model of the Atom:
- de Broglie’s Relation: Dual behavior of matter. $\lambda = \frac{h}{p} = \frac{h}{m v}$
- Heisenberg’s Uncertainty Principle: It is impossible to simultaneously determine both the exact position and momentum of a subatomic particle. $\Delta x \times \Delta p \ge \frac{h}{4\pi}$
- Quantum Numbers:
- Principal ( $n$ ): Shell and size/energy ( $n = 1, 2, 3, \dots$ ).
- Azimuthal ( $l$ ): Subshell and orbital shape ( $l = 0$ to $n - 1$ ; $s=0$ , $p=1$ , $d=2$ , $f=3$ ).
- Magnetic ( $m_l$ ): Orientation of orbitals in space ( $m_l = -l$ to $+l$ ).
- Spin ( $m_s$ ): Orientation of electron spin ( $+\frac{1}{2}$ or $-\frac{1}{2}$ ).
- Rules for Electronic Configuration:
- Aufbau Principle: Orbitals are filled in order of increasing energies according to the $(n + l)$ rule.
- Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers; a single orbital holds a maximum of two electrons with opposite spins.
- Hund’s Rule of Maximum Multiplicity: Pairing in degenerate orbitals does not begin until each subshell contains one electron with parallel spins.

Chapter 3: Classification of Elements and Periodicity in Properties

Modern Periodic Law:
- The physical and chemical properties of the elements are periodic functions of their atomic numbers ( $Z$ ).
Division of the Periodic Table:
- $s$ -Block: Groups 1 and 2, valence configuration $ns^1$ to $ns^2$ .
- $p$ -Block: Groups 13 to 18, valence configuration $ns^2 np^{1-6}$ .
- $d$ -Block (Transition Elements): Groups 3 to 12, outer configuration $(n-1)d^{1-10} ns^{0-2}$ .
- $f$ -Block (Inner Transition Elements): Lanthanoids ( $4f$ ) and Actinoids ( $5f$ ), outer configuration $(n-2)f^{1-14} (n-1)d^{0-1} ns^2$ .
Periodic Trends in Physical Properties:
- Atomic and Ionic Radii: Decrease across a period due to increasing effective nuclear charge ( $Z_{\text{eff}}$ ). Increase down a group due to the addition of outer electron shells.
- Isoelectronic Species: Species with the same number of electrons. Radius decreases with increasing positive nuclear charge (e.g., radius order: $Al^{3+} < Mg^{2+} < Na^+ < F^- < O^{2-} < N^{3-}$ ).
- Ionization Enthalpy ( $\Delta_i H$ ): Minimum energy required to remove the most loosely bound electron from an isolated gaseous atom.
- Increases across a period; decreases down a group.
- Anomalies: $Be > B$ (due to penetration and stability of fully filled $2s$ ) and $N > O$ (due to stability of half-filled $2p$ orbitals).
- Electron Gain Enthalpy ( $\Delta_{eg} H$ ): Enthalpy change when an electron is added to an isolated neutral gaseous atom.
- Becomes more negative across a period; becomes less negative down a group.
- Anomaly: Chlorine has a more negative $\Delta_{eg} H$ than Fluorine due to strong interelectronic repulsions in the compact $2p$ subshell of Fluorine.
- Electronegativity: The ability of an atom in a compound to attract shared electron pairs toward itself. Increases across a period; decreases down a group.
Periodic Trends in Chemical Properties:
- Second-period elements exhibit anomalous behavior compared to heavier group congeners due to small size, high charge-to-radius ratio, high electronegativity, and absence of vacant $d$ -orbitals.

Chapter 4: Chemical Bonding and Molecular Structure

Octet Rule and Lewis Structures:
- Atoms combine by sharing or transferring electrons to attain a noble-gas octet.
- Formal Charge (FC): $\text{FC} = V - L - \frac{1}{2}B$ where $V$ is valence electrons in the free atom, $L$ is non-bonding electrons (lone pairs), and $B$ is total bonding electrons.
- Limitations: Incomplete octet ( $LiCl$ , $BeH_2$ , $BF_3$ ), odd-electron molecules ( $NO$ , $NO_2$ ), and expanded octet ( $PF_5$ , $SF_6$ , $H_2SO_4$ ).
Dipole Moment ( $\mu$ ):
- Measure of bond or molecular polarity. $\mu = Q \times r$
- Expressed in Debye ( $D$ ), where $1\,D = 3.33564 \times 10^{-30}\,C\,m$ .
Valence Shell Electron Pair Repulsion (VSEPR) Theory:
- Electron pairs around a central atom repel each other and position themselves to minimize repulsion.
- Order of repulsive strength: $\text{lone pair - lone pair} > \text{lone pair - bond pair} > \text{bond pair - bond pair}$
- Geometries (bonding pairs, lone pairs):
- Linear: $2$ bond pairs, $0$ lone pairs (e.g., $BeCl_2$ )
- Trigonal Planar: $3$ bond pairs, $0$ lone pairs (e.g., $BF_3$ ); Bent if $1$ lone pair (e.g., $SO_2$ )
- Tetrahedral: $4$ bond pairs, $0$ lone pairs (e.g., $CH_4$ ); Trigonal Pyramidal if $1$ lone pair (e.g., $NH_3$ ); Bent if $2$ lone pairs (e.g., $H_2O$ )
- Trigonal Bipyramidal: $5$ bond pairs, $0$ lone pairs (e.g., $PCl_5$ )
- Octahedral: $6$ bond pairs, $0$ lone pairs (e.g., $SF_6$ )
Valence Bond Theory (VBT) and Hybridization:
- Sigma ( $\sigma$ ) Bond: Formed by axial/end-to-end overlap; stronger bond.
- Pi ( $\pi$ ) Bond: Formed by lateral/sideways overlap; weaker bond.
- Hybridization: Mixing of atomic orbitals to form identical hybrid orbitals.
- $sp$ : Linear, angle $180^{\circ}$ (e.g., $C_2H_2$ , $BeCl_2$ )
- $sp^2$ : Trigonal planar, angle $120^{\circ}$ (e.g., $C_2H_4$ , $BCl_3$ )
- $sp^3$ : Tetrahedral, angle $109.5^{\circ}$ (e.g., $CH_4$ )
- $sp^3d$ : Trigonal bipyramidal, angles $90^{\circ}$ and $120^{\circ}$ (e.g., $PCl_5$ )
- $sp^3d^2$ : Octahedral, angle $90^{\circ}$ (e.g., $SF_6$ )
Molecular Orbital Theory (MOT):
- Linear combination of atomic orbitals (LCAO) produces bonding ( $\sigma$ , $\pi$ ) and antibonding ( $\sigma^*$ , $\pi^*$ ) orbitals.
- Bond Order: $\text{Bond Order} = \frac{N_b - N_a}{2}$ where $N_b$ is the number of bonding electrons and $N_a$ is the number of antibonding electrons.
- If $\text{Bond Order} > 0$ , the molecule exists stably; if $\text{Bond Order} \le 0$ , it is unstable.
- Magnetic Character: Diamagnetic if all electrons are paired; paramagnetic if one or more unpaired electrons are present (e.g., $O_2$ is paramagnetic with $2$ unpaired electrons).
Hydrogen Bonding:
- Electrostatic attraction between hydrogen covalently bound to a highly electronegative atom ( $F$ , $O$ , $N$ ) and an electronegative atom of another or the same molecule.
- Intermolecular H-bonding: Between different molecules (e.g., $HF$ , $H_2O$ , $C_2H_5OH$ ); elevates boiling points.
- Intramolecular H-bonding: Within the same molecule (e.g., o-nitrophenol).

Octet Rule and Lewis Structures:
- Kössel-Lewis Approach: Atoms combine either by transfer of valence electrons or by sharing of electrons in order to achieve a stable noble-gas configuration (octet of electrons, or duplet for helium).
- Formal Charge (FC):

$\text{FC} = V - L - \frac{1}{2}B$

where $V$ is the number of valence electrons in the free atom, $L$ is the number of non-bonding valence electrons (lone pairs), and $B$ is the total number of bonding electrons.

- **Limitations of the Octet Rule:**

    - **Incomplete octet:** Central atom has fewer than eight valence electrons (e.g.,  $LiCl$ ,  $BeH_2$ ,  $BF_3$ ).

    - **Odd-electron molecules:** Molecules with an odd number of electrons cannot satisfy the octet rule for all atoms (e.g.,  $NO$ ,  $NO_2$ ).

    - **Expanded octet:** Central atom has more than eight valence electrons due to available vacant  $d$ -orbitals in elements of the third period onwards (e.g.,  $PF_5$ ,  $SF_6$ ,  $H_2SO_4$ ).

    - Fails to explain the shape of molecules and relative stabilities.

Ionic Bonding and Lattice Enthalpy:
- Ionic Bond Formation: Favored by low ionization enthalpy of the metallic element, high negative electron gain enthalpy of the non-metallic element, and high lattice enthalpy of the resulting crystal.
- Lattice Enthalpy: The energy required to completely separate one mole of a solid ionic compound into its gaseous constituent ions.

Bond Parameters:
- Bond Length: Equilibrium distance between the nuclei of two bonded atoms in a molecule.
- Bond Angle: Angle between orbitals containing bonding electron pairs around the central atom.
- Bond Enthalpy: Amount of energy required to break one mole of bonds of a particular type between two atoms in a gaseous state. Stronger bonds have higher bond enthalpies.
- Bond Order: Number of covalent bonds between two atoms in a molecule. Stability increases and bond length decreases with increasing bond order.
- Resonance: When a single Lewis structure cannot accurately depict a molecule, multiple contributing structures (canonical forms) are averaged into a resonance hybrid (e.g., $O_3$ , $CO_3^{2-}$ ).

Dipole Moment and Bond Polarity:
- Dipole Moment ( $\mu$ ): Product of the magnitude of charge ( $Q$ ) and the distance between the centers of positive and negative charges ( $r$ ):

$\mu = Q \times r$

- Expressed in Debye ( $D$ ), where  $1\,D = 3.33564 \times 10^{-30}\,C\,m$ .

- For polyatomic molecules, the net dipole moment is the vector sum of individual bond moments (e.g.,  $\mu = 0$  for symmetrical linear  $CO_2$  and planar  $BF_3$ ;  $NH_3$  has a higher dipole moment ( $1.47\,D$ ) than  $NF_3$  ( $0.24\,D$ ) because lone-pair dipole reinforces bond dipoles in  $NH_3$  but opposes them in  $NF_3$ ).

- **Fajan's Rules:** Covalent character in ionic compounds increases with smaller cation size, larger anion size, and higher ionic charges.

Valence Shell Electron Pair Repulsion (VSEPR) Theory:
- Postulates that electron pairs surrounding a central atom repel each other and adopt an orientation that minimizes electrostatic repulsions.
- Repulsive Interaction Strength:

$\text{lone pair - lone pair} > \text{lone pair - bond pair} > \text{bond pair - bond pair}$

- **Molecular Geometries:**

    - ** $2$  Bond Pairs,  $0$  Lone Pairs:** Linear (e.g.,  $BeCl_2$ 

    - ** $3$  Bond Pairs,  $0$  Lone Pairs:** Trigonal planar (e.g.,  $BF_3$ 

    - ** $2$  Bond Pairs,  $1$  Lone Pair:** Bent / Angular (e.g.,  $SO_2$ 

    - ** $4$  Bond Pairs,  $0$  Lone Pairs:** Tetrahedral (e.g.,  $CH_4$ 

    - ** $3$  Bond Pairs,  $1$  Lone Pair:** Trigonal pyramidal (e.g.,  $NH_3$ 

    - ** $2$  Bond Pairs,  $2$  Lone Pairs:** Bent / V-shaped (e.g.,  $H_2O$ 

    - ** $5$  Bond Pairs,  $0$  Lone Pairs:** Trigonal bipyramidal (e.g.,  $PCl_5$ 

    - ** $4$  Bond Pairs,  $1$  Lone Pair:** See-saw (e.g.,  $SF_4$ 

    - ** $3$  Bond Pairs,  $2$  Lone Pairs:** T-shaped (e.g.,  $ClF_3$ 

    - ** $2$  Bond Pairs,  $3$  Lone Pairs:** Linear (e.g.,  $XeF_2$ 

    - ** $6$  Bond Pairs,  $0$  Lone Pairs:** Octahedral (e.g.,  $SF_6$ 

    - ** $5$  Bond Pairs,  $1$  Lone Pair:** Square pyramidal (e.g.,  $BrF_5$ 

    - ** $4$  Bond Pairs,  $2$  Lone Pairs:** Square planar (e.g.,  $XeF_4$

Valence Bond Theory (VBT) and Orbital Overlap:
- Covalent bonds form via the overlapping of half-filled atomic orbitals with opposite spins.
- Sigma ( $\sigma$ ) Bond: Formed by head-on/axial overlap of orbitals along the internuclear axis ( $s-s$ , $s-p$ , or $p_z-p_z$ ). Stronger bond with cylindrical electron symmetry.
- Pi ( $\pi$ ) Bond: Formed by sideways/lateral overlap of atomic orbitals perpendicular to the internuclear axis. Weaker bond due to lower extent of overlap.

Hybridization:
- Concept of intermixing orbitals of slightly different energies in an atom to produce equivalent hybrid orbitals with identical energy, shape, and directional properties.
- Types of Hybridization:
  - $sp$ Hybridization: Mixing of one $s$ and one $p$ orbital; linear geometry with bond angle $180^{\circ}$ (e.g., $BeCl_2$ , $C_2H_2$ ).
  - $sp^2$ Hybridization: Mixing of one $s$ and two $p$ orbitals; trigonal planar geometry with bond angle $120^{\circ}$ (e.g., $BCl_3$ , $C_2H_4$ ).
  - $sp^3$ Hybridization: Mixing of one $s$ and three $p$ orbitals; tetrahedral geometry with bond angle $109.5^{\circ}$ (e.g., $CH_4$ , $NH_3$ , $H_2O$ ).
  - $sp^3d$ Hybridization: Trigonal bipyramidal geometry with equatorial angles of $120^{\circ}$ and axial angles of $90^{\circ}$ (e.g., $PCl_5$ ; axial bonds are longer and weaker than equatorial bonds due to greater repulsions).
  - $sp^3d^2$ Hybridization: Octahedral geometry with bond angles of $90^{\circ}$ (e.g., $SF_6$ ).

Molecular Orbital Theory (MOT):
- Formed by the Linear Combination of Atomic Orbitals (LCAO) of comparable energies and proper symmetry.
- Generates Bonding Molecular Orbitals ( $\sigma$ , $\pi$ ; lower energy, stabilizes molecule) and Antibonding Molecular Orbitals ( $\sigma^*$ , $\pi^*$ ; higher energy, destabilizes molecule).
- Energy Order of Molecular Orbitals:
  - For elements with $\le 14$ electrons (e.g., $B_2$ , $C_2$ , $N_2$ ):

$\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < (\pi 2p_x = \pi 2p_y) < \sigma 2p_z < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z$

    - For elements with  $> 14$  electrons (e.g.,  $O_2$ ,  $F_2$ ):

$\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \sigma 2p_z < (\pi 2p_x = \pi 2p_y) < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z$

- **Bond Order:**

$\text{Bond Order} = \frac{N_b - N_a}{2}$

where $N_b$ is the number of bonding electrons and $N_a$ is the number of antibonding electrons.

    - If  $\text{Bond Order} > 0$ , the molecule is stable; if  $\text{Bond Order} \le 0$ , the molecule does not exist.

- **Magnetic Character:** Paramagnetic if unpaired electrons exist in MOs (e.g.,  $O_2$  has  $2$  unpaired electrons in  $\pi^* 2p$ ); diamagnetic if all electrons are paired (e.g.,  $N_2$ ).

Hydrogen Bonding:
- Attractive dipole-dipole force occurring when hydrogen is covalently bound to strongly electronegative atoms ( $F$ , $O$ , $N$ ).
- Intermolecular Hydrogen Bonding: Formed between distinct molecules of the same or different compounds (e.g., $HF$ , $H_2O$ , $C_2H_5OH$ ); leads to higher boiling points and increased viscosity.
- Intramolecular Hydrogen Bonding: Formed between hydrogen and an electronegative atom within the same molecule (e.g., o-nitrophenol, salicylaldehyde); prevents intermolecular association and results in lower boiling points.