# 3.5 Shapes of Molecules ## Valence Shell Electron Pair Repulsion (VSEPR) Theory The **Valence Shell Electron Pair Repulsion (VSEPR)** theory is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. The core principle is that electron pairs, being negatively charged, repel each other. They arrange themselves around the central atom in a way that maximizes the distance between them, thus minimizing the repulsive forces. The final shape of a molecule is determined by the number of *bonding pairs* (electrons shared in a covalent bond) and *lone pairs* (non-bonding electrons) around the central atom. ### Hierarchy of Electron Pair Repulsion Lone pairs have a more concentrated electron charge cloud than bonding pairs, leading to stronger repulsion. The order of repulsion strength is: * **Lone Pair - Lone Pair (LP-LP)** > **Lone Pair - Bonding Pair (LP-BP)** > **Bonding Pair - Bonding Pair (BP-BP)** This hierarchy explains why molecules with lone pairs often have distorted bond angles compared to idealized geometries. ### 3.5.1 Shapes of Molecules with Two Electron Pairs Molecules where the central atom is surrounded by two bonding pairs and no lone pairs ($AX_2$) adopt a **linear** shape with a bond angle of **$180^\circ$**. **Example: Beryllium Fluoride ($BeF_2$)** * The central beryllium atom contributes two valence electrons. * Each fluorine atom contributes one electron to the bond. * The Lewis structure shows two single bonds from Be to F. * To minimize repulsion, the two electron pairs are positioned on opposite sides of the central atom. ### 3.5.2 Shapes of Molecules with Three Electron Pairs #### Three Bonding Pairs ($AX_3$) Molecules with three bonding pairs and no lone pairs have a **trigonal planar** geometry with bond angles of **$120^\circ$**. **Example: Boron Trichloride ($BCl_3$)** * The central boron atom contributes three valence electrons. * The three bonding pairs repel each other equally, arranging themselves in a plane. **Example: Carbonate Ion ($CO_3^{2-}$)** * The central carbon atom is bonded to three oxygen atoms. The overall structure is trigonal planar. #### Two Bonding Pairs and One Lone Pair ($AX_2E$) Molecules with two bonding pairs and one lone pair have an electron geometry that is trigonal planar, but the molecular shape is **bent** or **V-shaped**. The bond angle is less than $120^\circ$ due to the stronger repulsion from the lone pair. **Example: Sulfur Dioxide ($SO_2$)** * The central sulfur atom has three electron domains: two double bonds and one lone pair. * The lone pair-bonding pair (LP-BP) repulsion is greater than the bonding pair-bonding pair (BP-BP) repulsion, pushing the bonding pairs closer together. ### 3.5.3 Shapes of Molecules with Four Electron Pairs #### Four Bonding Pairs ($AX_4$) Molecules with four bonding pairs and no lone pairs have a **tetrahedral** geometry with bond angles of **$109.5^\circ$**. **Example: Methane ($CH_4$)** * The central carbon atom is surrounded by four bonding electron pairs. #### Three Bonding Pairs and One Lone Pair ($AX_3E$) Molecules with three bonding pairs and one lone pair have a **trigonal pyramidal** shape. The bond angle is less than $109.5^\circ$ (around $107^\circ$). **Example: Ammonia ($NH_3$)** * The central nitrogen atom has one lone pair and three bonding pairs. * The lone pair repels the bonding pairs, reducing the H-N-H bond angle. #### Two Bonding Pairs and Two Lone Pairs ($AX_2E_2$) Molecules with two bonding pairs and two lone pairs have a **bent** or **V-shaped** geometry. The bond angle is significantly less than $109.5^\circ$ (around $104.5^\circ$) due to strong LP-LP and LP-BP repulsions. **Example: Water ($H_2O$)** * The central oxygen atom has two lone pairs and two bonding pairs. * The two lone pairs exert a strong repulsive force, compressing the H-O-H bond angle. ### 3.5.4 Shapes of Molecules with Five Electron Pairs ($AX_5$) Molecules with five bonding pairs and no lone pairs have a **trigonal bipyramidal** geometry. This shape has two different bond angles: * **Axial positions:** Two positions at $90^\circ$ to the equatorial plane. * **Equatorial positions:** Three positions in a plane at $120^\circ$ to each other. **Example: Phosphorus Pentachloride ($PCl_5$)** ### 3.5.5 Shapes of Molecules with Six Electron Pairs ($AX_6$) Molecules with six bonding pairs and no lone pairs have an **octahedral** geometry. All bond angles are **$90^\circ$**. **Example: Sulfur Hexafluoride ($SF_6$)** ### 3.5.6 Expanded Octet / Hypervalency The octet rule is primarily for second-row elements. Elements in the third period and beyond (e.g., P, S, Cl) have accessible *d* orbitals and can accommodate more than eight electrons in their valence shell. This phenomenon is known as having an **expanded octet** or being **hypervalent**. * Examples include $PCl_5$ (10 valence electrons around P) and $SF_6$ (12 valence electrons around S). ## Summary of Molecular Shapes | Total Electron Pairs | Bonding Pairs | Lone Pairs | A-X-E Notation | Molecular Geometry | Bond Angle(s) | Examples | | :---: | :---: | :---: | :---: | :--- | :---: | :--- | | 2 | 2 | 0 | $AX_2$ | Linear | $180^{\circ}$ | $BeCl_2, CO_2$ | | 3 | 3 | 0 | $AX_3$ | Trigonal Planar | $120^{\circ}$ | $BF_3, NO_3^-$ | | 3 | 2 | 1 | $AX_2E$ | Bent / V-shaped | $< 120^{\circ}$ | $SO_2, SnCl_2$ | | 4 | 4 | 0 | $AX_4$ | Tetrahedral | $109.5^{\circ}$ | $CH_4, SO_4^{2-}, NH_4^+$ | | 4 | 3 | 1 | $AX_3E$ | Trigonal Pyramidal | $\approx 107^{\circ}$ | $NH_3, PCl_3$ | | 4 | 2 | 2 | $AX_2E_2$ | Bent / V-shaped | $\approx 104.5^{\circ}$ | $H_2O, H_2S$ | | 5 | 5 | 0 | $AX_5$ | Trigonal Bipyramidal | $90^{\circ}, 120^{\circ}$ | $PCl_5, PF_5$ | | 6 | 6 | 0 | $AX_6$ | Octahedral | $90^{\circ}$ | $SF_6$ | ## Worked Examples ### 3.5.7 Working out the Shapes of Molecules 1. Sum the valence electrons from the central atom and all surrounding atoms. 2. Adjust for any ionic charge (add electrons for negative charge, subtract for positive charge). 3. Divide the total by 2 to get the number of electron pairs around the central atom. 4. Determine the number of bonding pairs (equal to the number of surrounding atoms). 5. Calculate the number of lone pairs: `(Total Pairs) - (Bonding Pairs)`. 6. Use the total number of electron pairs to find the electron geometry and the A-X-E notation to find the molecular geometry. | **Example 1: Predict the Geometry of $NH_3$** | **Example 2: Predict the Geometry of $NH_4^+$** | | :--- | :--- | | 1. **Valence Electrons:**
Nitrogen (N) = 5
3 Hydrogen (H) atoms = $3 \times 1 = 3$
**Total = 8 electrons** | 1. **Valence Electrons:**
Nitrogen (N) = 5
4 Hydrogen (H) atoms = $4 \times 1 = 4$
Charge = $+1$, so subtract 1 electron
**Total = $5+4-1=8$ electrons** | | 2. **Electron Pairs:**
$8 \div 2 = 4$ electron pairs
*Electron Geometry: Tetrahedral* | 2. **Electron Pairs:**
$8 \div 2 = 4$ electron pairs
*Electron Geometry: Tetrahedral* | | 3. **Bonding/Lone Pairs:**
Bonding Pairs = 3 (for 3 H atoms)
Lone Pairs = $4 - 3 = 1$ | 3. **Bonding/Lone Pairs:**
Bonding Pairs = 4 (for 4 H atoms)
Lone Pairs = $4 - 4 = 0$ | | 4. **Conclusion:**
The molecule has an $AX_3E$ arrangement.
**Molecular Geometry: Trigonal Pyramidal** | 4. **Conclusion:**
The molecule has an $AX_4$ arrangement.
**Molecular Geometry: Tetrahedral** | ## 3.5.8 Importance of VSEPR Theory in the Field of Drug Design VSEPR theory is crucial for medicinal chemists as it helps predict the 3D shape of molecules, which is fundamental to how drugs interact with biological targets. * **Molecular Shape and Enzymatic Reactions:** Enzymes are highly specific, recognizing and binding to substrates with complementary shapes. VSEPR helps predict the 3D structure of potential drug molecules, allowing chemists to design drugs that fit perfectly into an enzyme's active site. * **Enzyme-Substrate Interaction:** By understanding the geometry of a molecule like a neurotransmitter, drugs can be designed to mimic or block its action. For example, drugs targeting the enzyme *acetylcholinesterase* must have a specific shape to fit its active site. * **Drug Delivery Systems:** VSEPR influences the design of drug carriers like liposomes. The geometry of molecules forming the liposome affects its overall shape, stability, and ability to navigate biological barriers to deliver drugs effectively. * **Example - Cisplatin:** Cisplatin, $Pt(NH_3)_2Cl_2$, is a square planar complex used as an anticancer agent. Its specific shape allows it to bind to DNA, damaging it and inhibiting the synthesis of new DNA in cancer cells, ultimately leading to cell death. ## Possible Questions/Answers * **Q:** Predict the shapes of the following molecules: i) tetrachloromethane, $CCl_4$, ii) beryllium chloride, $BeCl_2$, iii) phosphorus(III) chloride, $PCl_3$. * **A:** * i) **$CCl_4$**: 4 bonding pairs, 0 lone pairs ($AX_4$). Shape is **tetrahedral**. * ii) **$BeCl_2$**: 2 bonding pairs, 0 lone pairs ($AX_2$). Shape is **linear**. * iii) **$PCl_3$**: 3 bonding pairs, 1 lone pair ($AX_3E$). Shape is **trigonal pyramidal**. * **Q:** Predict the shape of hydrogen sulfide, $H_2S$. * **A:** Sulfur (central atom) has 6 valence electrons. Each hydrogen contributes 1. Total = 8 electrons = 4 pairs. There are 2 bonding pairs (to H) and 2 lone pairs ($4-2=2$). The geometry is $AX_2E_2$, making the shape **bent** or **V-shaped**. * **Q:** What is the shape of sulfur hexafluoride, $SF_6$? * **A:** Sulfur has 6 valence electrons and is bonded to 6 fluorine atoms. This gives 6 bonding pairs and 0 lone pairs ($AX_6$). The shape is **octahedral**.