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Bonding Between Atoms [4] Bonding between Atoms [4] ¾ Free atom: equilibrium at attractive and repulsive electrostatic forces between nucleus and electrosphere. • nucleus: protons (+) and neutrons • electrosphere: electrons (-) • electrical charge: 1.60 x 10-19 C • mass of proton: 1.67 x 10-24 g • mass of electron: 9.11 x 10-28 g Carbon atom Z=6 M=12.01 g/mol R=70 pm 1> Bonding between Atoms ¾ Interatomic bonds: forces that hold atoms together which act like little springs, linking one atom to the next in the solid state. ¾ Interatomic Forces: ¾ attractive forces (Fa) ¾ repulsive forces (Fr) ¾ The Coulomb's law: http://matterandinteractions.org/index.html q : Charge of object 1 q1 ⋅q2 1 F = K ⋅ q : Charge of object 2 e 2 2 r r: Distance between the two objects 9 2 -2 Ke = 8.9875 x 10 N.m .C (Coulomb Constant) F: Force between the two objects. F > 0 implies a repulsive interaction, while F < 0 means an attractive interaction. 2> Bonding between Atoms ¾ Consider two isolated atoms: – When the atoms are at large inter-atomic separation distance, the atoms do not exert any force on each other. – When the distance is decreased, an attractive force FA starts to act pulling atoms closer. – FA increases as the atoms gets closer. – But as the atoms get closer a repulsive force FR begin to act. – The net force FN between the two atoms is given by: FN = FA + FR –At some inter-atomic distance ro, FR exactly equals FA and FN becomes Zero FN = 0 = FA + FR –ro is called the equilibrium inter-atomic separation distance at which atoms enter into bonding 3> Bonding between Atoms ¾ equilibrium spacing: A B F = − F = A r p R r q where A, B, p, q are constants; q > p • When FA + FR = 0, equilibrium exists. • The centers of the atoms/ions will remain separated by the equilibrium spacing xo. 4> Bonding between Atoms ¾ Force-Energy Relationship: dV F = − dr “Force is the negative gradient of potential energy” ¾ Energy calculation: r r V = F (r)dr + F (r)dr N ∫ A ∫ R ∞ ∞ ¾ Equilibrium is reached by minimizing VN 5> Bonding between Atoms ¾ The energy of the crystal is lower than that of the free atoms by an amount equal to the energy required to pull the crystal apart into a set of free atoms. This is called the binding (cohesive) energy of the crystal. ¾ Examples: – NaCl is more stable than a collection of free Na and Cl. – Ge crystal is more stable than a collection of free Ge. Cl Na NaCl 6> Bonding between Atoms ¾ Energy in Ball-Spring atomic bonding: The spring’s force is given by F = - k.x (k: spring constant), therefore the potential energy is given by: 1 V = −k r ⋅dr →V = ⋅k ⋅r 2 ∫ 2 ¾ Is this an appropriate potential to use to describe interatomic interactions under all conditions? ANSWER: No! Consider what happens to V as interatomic separation r →∞. This doesn’t make sense… bonding energy V should go to ZERO. 7> Energy Bonding between Atoms ¾ Lennard-Jones potential (1924): mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules. 12 6 ⎡⎛σ ⎞ ⎛σ ⎞ ⎤ V = 4ε ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎣⎢⎝ r ⎠ ⎝ r ⎠ ⎦⎥ Repulsive Attractive interaction interaction where ε is the depth of the potential well, σ is the finite distance at which the inter-particle potential is zero and r is the distance between the particles. http://en.wikipedia.org/wiki/Lennard-Jones_potential 8> Lennard-Jones potential ¾ This typical curve has a minimum at equilibrium V(R) distance R0 ¾ R > R0 : – the potential Repulsive increases gradually, approaching 0 as 0 R R Æ ∞ 0 R – the force is attractive Attractive ¾ R < R : 0 R – the potential r increases very rapidly, approaching ∞ at small separation. – the force is repulsive 9> Potential Energy vs. Internuclear Distance ¾ Animation of 2 hydrogen atoms: Dr. Kumar (2013) https://www.youtube.com/watch?v=Wl5QHeS2UXE 10> Bonding Forces and Energies When FA + FR = 0, equilibrium exists. The centers of the atoms will remain separated by the equilibrium spacing ro. This spacing also corresponds to the minimum of the potential energy curve. The bonding energy that would be required to separate two atoms to an infinite separation is Eo 11> Physical Properties vs. Bonding Forces ¾ Melting Temperature, Tm ¾ Elastic modulus, E Energy (r) E = slope of the F-r curve at ro. E ~ curvature of E-r curve at ro. ro Energy r unstretched length smaller Tm ro r larger Tm smaller Elastic Modulus Tm is larger if Eo is larger. • At room temperature, solids formed larger Elastic Modulus for large bonding energies, whereas for small energies the gaseous state is favored, liquids prevail when E is larger if Eo is larger. energies are of intermediate magnitude. 12> Physical Properties vs. Bonding Forces ¾ Coefficient of thermal expansion, α length, Lo Δ unheated, T1 L ΔL = α (T2-T1) Lo heated, T2 Energy ¾ α ~ symmetry at ro. ro r α is larger if Eo is smaller. larger α smaller α 13> Physical Properties vs. Bonding Forces Metal (Z) melting temperature Young’s modulus 0C GPa Pb (82) 327 14 Zn (30) 420 43 Mg (12) 649 45 Al (13) 660 71 Ag (47) 962 76 Au (79) 1064 82 Cu (29) 1085 124 Ni (28) 1455 214 Fe (26) 1538 196 Cr (24) 1863 289 Mo (42) 2623 324 W(74) 3422 411 14> Types of Atomic & Molecular Bonds ¾ Primary Atomic Bonds (strong) – Ionic Bonds – Covalent Bonds – Metallic Bonds ¾ Secondary Atomic & Molecular Bonds (weak) – Permanent Dipole Bonds – Fluctuating Dipole Bonds 15> Types of Atomic & Molecular Bonds 16> Ionic Bonding ¾Large inter-atomic forces are created by the “coulombic” effect produced by positively and negatively charged ions. ¾Ionic bonds are “non-directional”. ¾The “cation” has a + charge and the “anion” has the - charge. ¾The cation is much smaller than the anion. ¾ Properties: generally large bonding energies (600-1500 kJ/mol) and thus high melting temperatures, hard, brittle, and electrically and thermally isolative. 17> Ionic Bonding ¾ Chemistry: What is an Ionic Bond? https://www.youtube.com/watch?v=dqW7H7c7M4A 18> Ionic Bonding Ionic bond: metal + nonmetal donates accepts electrons electrons Dissimilar electronegativities ex: MgO Mg 1s2 2s2 2p6 3s2 O1s2 2s2 2p4 Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6 19> Ionic Bonding Periodic Table - electronegativities Give up electrons Acquire electrons Ionic compounds: NaCl, MgO, CaF2, CsCl, e.g. 20> Sodium Chlorine (NaCl) ¾ Notice that when sodium loses its one valence electron it gets smaller in size, while chlorine grows larger when it gains an additional valence electron. After the reaction takes place, the charged Na+ and Cl- ions are held together by electrostatic forces, thus forming an ionic bond. 21> Some characteristics of ionic compounds Property Explanation The melting and boiling points of ionic Melting point compounds are high because a large amount of and boiling point thermal energy is required to separate the ions which are bound by strong electrical forces. Solid ionic compounds do not conduct electricity when a potential is applied because there are Electrical no mobile charged particles. conductivity No free electrons causes the ions to be firmly bound and cannot carry charge by moving. Most ionic compounds are hard; the surfaces of their crystals are not easily scratches. This is Hardness because the ions are bound strongly to the lattice and aren't easily displaced. Most ionic compounds are brittle; a crystal will shatter if we try to distort it. This happens Brittleness because distortion cause ions of like charges to come close together then sharply repel. 22> Covalent Bonding ¾ Large inter-atomic forces are created by the sharing of electrons to form directional bonds. ¾ Covalent bonding takes place between atoms with small differences in electronegativity which are close to each other in periodic table (between non-metals and non- metals). ¾ The covalent bonding is formed by sharing of outer shell electrons (i.e., s and p electrons) between atoms rather than by electron transfer. ¾ This bonding can be attained if the two atoms each share one of the other’s electrons. So the noble gas stable electron configuration can be attained. ¾ Number of covalent bonds for a particular molecule is determined by the number of valence electrons. ¾ Rarely are compounds purely ionic or covalent but are a percentage of both. 23> Covalent Bonding ¾ Chemistry: What is a Covalent Bond? https://www.youtube.com/watch?v=ZxWmyZmwXtA 24> Covalent Bonding Pure element - silicon (Si): © Learning™ / Thomson Publishing Brooks/Cole 2003 Si (Z=14): 1s22s22p63s23p2 Covalent bonding requires that electrons be shared between atoms in such a way that each atom has its outer sp orbital filled. In silicon, with a valence of four, four covalent bonds must be formed. 25> Covalent Bonding © Learning™ / Thomson Publishing Brooks/Cole 2003 Silicon (Si): Covalent bonds are directional. In silicon, a tetrahedral structure is formed, with angles of 109.5° required between each covalent bond 26> Covalent Bonding Dissimilar compound - methane (CH4): 27> Some Properties of Covalent Bonding Property Explanation Very high melting points because each atom is bound by strong covalent bonds. Many covalent Melting point bonds must be broken if the solid is to be melted and boiling point and a large amount of thermal energy is required for this. Electrical Poor conductors because electrons are held either conductivity on the atoms or within covalent bonds. They cannot move through the lattice. They are hard because the atoms are strongly Hardness bound in the lattice, and are not easily displaced. Covalent network substances are brittle. If sufficient force is applied to a crystal, covalent bond are Brittleness broken as the lattice is distorted.
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