Topic #2: The Chemical Alphabet Fall 2008 Dr. Susan Lait Sodium, Na Gallium, Ga CHEMISTRY 1000 METALS NONMETALS Topic #2: The Chemical Alphabet Fall 2008 Dr. Susan Lait METALLOIDS Forms of Carbon

Ionic Compounds Opposites attract. When a cation meets an anion, the electrostatic force of attraction pulls them together to make an ionic bond. The force each ion applies on the other can be calculated using Coulomb’s law: where e is permittivity (1/4pe = 8.988 × 109 N·m2·C-2 in a vacuum), Z is the charge of the ion (±1, ±2, etc.), e is the charge of an electron (1.602 × 10-19 C), and d is the internuclear distance. Note that a negative force is attractive and a positive force is repulsive. The energy of formation of an ionic bond can be calculated using a related formula: This formula calculates the energy of bond formation for one gaseous molecule. Note that a negative bond energy corresponds to a release of energy when the bond is formed!

Ionic Compounds Out of each pair below, which ions would you expect to have the more negative energy of bond formation? Why? K-Cl vs. K-Br Na-F vs. Mg-O Ionic compounds do not usually exist as gaseous molecules (except under high vacuum and/or high temperature). Under standard conditions, they exist as solid crystal lattices. This means that each cation is surrounded by multiple anions (and vice versa). This must be considered when calculating how much energy is released by adding an ion to the lattice (or how much energy is required to remove an ion).

Ionic Lattices (NaCl) The image below shows a crystal lattice corresponding to NaCl. Find a unit cell. Count the number of anions (green) and cations (silver) in a unit cell. When looking at the crystal lattices of ionic solids, we consider that the anions form a lattice (simple cubic, bcc, fcc, hcp, etc.) and the cations fill holes in the lattice. What kind of lattice is formed by the anions in this picture? Two types of “holes” can be found in a closest packed lattice: Octahedral holes are surrounded by six atoms. (# octahedral holes = # atoms in unit cell) Tetrahedral holes are surrounded by four atoms. (# tetrahedral holes = twice # atoms in unit cell) What kind of holes are the cations filling? Find an example of the other kind of hole in this picture.

Ionic Lattices (NaCl)

Ionic Lattices (CsCl) The image below shows a crystal lattice corresponding to CsCl. Find a unit cell. Count the number of anions (teal) and cations (gold) in a unit cell. What kind of lattice is formed by the anions in this picture? A third type of “hole” can be found in this lattice: Cubic holes are surrounded by eight atoms. (# cubic holes = # atoms in unit cell) The cations here are filling cubic holes. Note that this lattice is not body-centered cubic (bcc)! The lattice is named for the anions only! Image from http://www.chemistry.nmsu.edu/studntres/chem116/notes/crystals.html

Ionic Lattices (ZnS) ZnS can adopt two different structures: zinc blende (ccp for S2-) and wurtzite (hcp for S2-). Which picture corresponds to which structure for ZnS? What kind of holes are the cations filling? (hint: look at their co-ordination number – how many anions are they bonded to?) Note that the two structures are very similar at the level of one ion (which is bonded to ____ other ions in either structure). It is the larger symmetry that differs between the two structures.

Ionic Lattices (ZnS)

Ionic Lattices We’ve seen three different ionic compounds (NaCl, CsCl, ZnS) and the different crystal lattices they form: What makes an ionic compound adopt a particular lattice? (hint: consider what makes an ionic lattice stable)

Ionic Lattices ZnS NaCl CsCl Anion radius (r -) 184 pm 181 pm 181 pm Cation radius (r +) 75 pm 99 pm 169 pm Co-ordination # anions cations Anion lattice type Holes for cations

Ionic Lattices We can see that, the larger the cation (relative to the anion), the less densely the lattice can be packed: If r+/r – is between 0.225 and 0.414, we get a structure like ZnS If r+/r – is between 0.414 and 0.732, we get a structure like NaCl If r+/r – is above 0.732, we get a structure like CsCl Where do these numbers come from? Consider a CsCl structure in which the anions are exactly touching: What is r+/r – for this structure? The cation cannot be any smaller and support this structure. Why not?

Ionic Lattices Lattice enthalpy is a measure of how stable an ionic compound is in lattice form: The enthalpy of lattice formation will always be a negative number. The enthalpy of lattice decomposition will always be a positive number. It requires input of energy to break bonds! In a lattice, every ion is attracted to all ions of opposite charge and repelled by all ions with the same charge. Knowing the lattice structure, we could calculate the lattice enthalpy based on these attractions and repulsions; however, we will not be doing that in Chemistry 1000. Instead, we will calculate lattice enthalpy using a Born-Haber cycle as the math is much less complicated in this approach.

Ionic Lattices A Born-Haber cycle incorporates the enthalpy of each theoretical step of the process of making an ionic solid from neutral elements: Enthalpy to generate a single atom of gas (if necessary) Enthalpy of electronic attraction (to make the anion) Ionization energy (to make the cation) Enthalpy of lattice formation (to bring the ions together into a lattice) To construct a Born-Haber cycle, start by writing out a balanced equation for making 1 mole of ionic solid from neutral elements. e.g. Na(s) + ½ Cl2(g)  NaCl(s) Then, work through the steps to get to the necessary ions from the neutral elements. Finally, show the lattice formation step.

Ionic Lattices Na+(g) + Cl -(g) Na(g) Cl(g) Na(s) + ½ Cl2(g) NaCl(s) ΔLFH I1 ΔEAH Na(g) Cl(g) ΔsublH ½ ΔBDH Na(s) + ½ Cl2(g) NaCl(s) ΔfHo

Ionic Lattices Given the following data, calculate ΔLFH for NaCl(s) Enthalpy of sublimation of Na = +108 kJ/mol First ionization energy for Na = +496 kJ/mol Enthalpy of bond dissociation for Cl2(g) = +243 kJ/mol Enthalpy of electronic attraction for Cl = -349 kJ/mol Enthalpy of formation for NaCl = -411 kJ/mol

Ionic Lattices Enthalpy of lattice formation (ΔLFH) is important because it affects such properties as solubility, thermal stability and hydration: If the cation and anion have similar charge and size, they will pack closely, resulting in a large negative ΔLFH . As such, it takes a lot of energy to break up the lattice and the compound is not very soluble. Ionic compounds with mismatched ions tend to have less negative ΔLFH and be more soluble. Carbonates of alkaline earth metals decompose to the metal oxide and carbon dioxide: MgCO3 undergoes this reaction at 300 °C while CaCO3 requires heating to 840 °C. Because Mg2+ is smaller than Ca2+, it is a better match for the small spherical O2- than the larger nonspherical CO32- Compounds such as Mg(ClO4)2 and CuSO4 have small cations relative to their anions. As such, they can literally pull water out of the air (and are therefore useful as drying agents) to surround the small cation with the relatively small water molecules. This gives a hydrated solid: