5.2.1 Answers Lattice Enthalpy 2012

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1 5.2.1 Answers Lattice Enthalpy 2012 Introduction In this topic we will construct a Born-Haber cycle (or lattice enthalpy cycle) which allows us to calculate numerical values for processes which occur in inorganic chemistry. The Born-Haber cycle is a more complicated version of the Hess cycle which was used in the AS F322 unit; in the Hess cycle there were 3 processes (arrows) whereas in a Born-Haber cycle there could be as many as 8 processes. We can calculate the lattice enthalpy, the enthalpy of formation or any one missing value if all the others are given. These values can consequently allow us to predict and compare different properties of ionic compounds. We first need to consider use of formulae for ionic compounds and some of the properties associated with these compounds. An ionic lattice consists of oppositely charged ions held together by strong electrostatic forces between them. Student Activity 1 1. Write the formulae for the following ionic compounds. Lithium fluoride Sodium oxide Magnesium chloride Barium oxide LiF Na2O MgCl2 BaO 2. Connect the property of an ionic lattice (compound) with the explanation. Property Soluble in water Conducts electricity when dissolved or molten High melting point Explanation The polar nature of water molecules allows bonding interactions between the charged ions and the water molecules. The ions can act as mobile charge carriers when they are not fixed within the lattice. There are strong electrostatic forces of attraction between the particles What is lattice enthalpy? Definition ΔH LE - the energy released when I mole of solid crystals are formed from the constituent ions in the gaseous state under standard conditions of 298K and 101 kpa. e.g Na + (g) + Cl - (g) NaCl (s) It is a measure of the strength of the ionic bond. Don t get this confused with the following process/equation. K (s) + ½ F 2 (g) KF(s) This represents the enthalpy of formation:- the enthalpy change when 1 mole of a compound is formed in its standard state from its constituent elements in their standard states, under standard conditions. If the lattice enthalpy for NaCl is 781 kjmol -1, then the energy needed to break down the lattice into its gaseous ions is the opposite, +781 kjmol -1. This is called the lattice dissociation enthalpy. 1

2 Student Activity 2 Write equations to represent the lattice enthalpies of: a) sodium oxide b) magnesium bromide c) Aluminium sulphide 2Na + (g) + O 2- (g) Na2O(s) Mg 2+ (g) + 2Br - (g) MgBr2(s) 2Al 3+ (g) + 3S 2- (g) Al2S3(s) Why do we need to draw a Born-Haber cycle? Gaseous ions cannot easily be obtained separately from the ions of opposite charge so an experiment to measure lattice enthalpy directly is impossible. We can, however, get a figure indirectly from an energy cycle. The cycle is simply a model to allow the determination of lattice enthalpy. The actual way in which ionic crystals are made is not known and if the compound in question is not perfectly ionic, the figure obtained will be inaccurate. The ionic compounds at A2 are normally: MX, MX 2, MO or M 2O (where M is the group 1 or group 2 metal ion and X is a halide). What are the processes which make up the Born Haber Cycle? During the formation of a lattice from its elements in their standard states, the following theoretical steps are imagined to take place. Atomisation of Metal ΔH atm This is the energy change when 1 mole of gaseous atoms are formed from the element in its standard state (metal lattice breaks into free gaseous atoms). M(s) M(g) Ionisation of Metal ΔH FIE ΔH FIE is the energy change when each atom in 1 mole of gaseous atoms loses 1 electron to become 1 mole of gaseous unipositive ions. We will deal with second ionisation energy ΔH SIE later. M(g) M + (g) Atomisation of Non-Metal ΔH atm Here free gaseous atoms of the non metal are formed. eg ½ X 2 X (g) Electron Affinity ΔH ea The energy change when 1 mole of atoms gain 1 mole of electrons in the gaseous state (can be first or second) eg. X(g) + e - X - (g) Formation of the lattice ΔH LE (gaseous ions combine to make solid lattice) X - (g) + M + (g) MX(s) 2

3 Student Activity 3 Complete the table by adding in the names of the processes and the standard symbols for these enthalpy changes. Energy change atomisation first ionisation energy lattice enthalpy formation electron affinity Definition The enthalpy change when 1 mole of gaseous atoms are formed from the element in its standard state The enthalpy change when each atom in 1 mole of gaseous atoms loses 1 electron to become 1 mole of gaseous unipositive ions The energy released when I mole of solid crystals are formed from the constituent ions in the gaseous state under standard conditions of 298K and 101 kpa The enthalpy change when 1 mole of a compound is formed in its standard state from its constituent elements in their standard states, under standard conditions. The enthalpy change when 1 mole of atoms gain 1 mole of electrons in the gaseous state Symbol ΔHatm ΔHFIE ΔHLE ΔHf ΔHea 3

4 Student Activity 4 (see supporting powerpoint for bigger cycle) Na + (g) + e - +Cl(g) Hea Hatm Na + (g) + Cl - (g) Na + (g) + e - +1/2Cl2(g) HLE HFIE Na(g) + 1/2Cl2(g) Hatm Na(s) + 1/2Cl2(g) Hf NaCl(s) 4

5 Student activity 5 (use supporting powerpoint to draw in answers) Add the standard symbols of the processes to this cycle (eg ΔHLE). Li + (g) + e - +Cl(g) Li + (g) + Cl - (g) Li + (g) + e - +1/2Cl2(g) Li(g) + 1/2Cl2(g) Li(s) + 1/2Cl2(g) LiCl(s) 5

6 Student activity 6 (use supporting powerpoint to draw in answers) Here are parts of different Born-Haber cycles. Add the missing species from the energy level (on the dotted line). Refer carefully back to the definitions of the processes- if two moles are involved in the change you must double the value up and show this clearly on the cycle. (a) Na + (g) + e - +Cl(g) Hatm... (b)... Hf MgCl2(s) (c) K + (g) + e - +Cl(g) Hea (d) 2Na + (g) + 2e - +1/2O2(g)... x HFIE... 6

7 Student activity 7 Drawing a cycle of type MX Complete the following cycle, in pencil, for potassium fluoride, without looking back at any of the preceding pages. 7

8 Student activity 8 Drawing a cycle of type MX2 Complete the following cycle, in pencil, for magnesium chloride. Remember to double up any relevant values and to start with the correct ions for the lattice enthalpy process. 8

9 Calculating the lattice enthalpy from the sodium chloride Born Haber cycle Na + (g) + e - +Cl(g) Step 4 Hea Step 3 Hatm Na + (g) Na + (g) + e - +1/2Cl2(g) Step 5 HLE Step 2 HFIE Na(g) + 1/2Cl2(g) Step 1 Hatm Na(s) + 1/2Cl2(g) Hf NaCl(s) Using Hess Law, you can see that the sum of steps 1-5 must be the same as ΔHf. Or if we know ΔHf and the values of steps 1,2,3 and 4, we can find the lattice enthalpy ΔHLE. It can also be used to find any of the other values as an unknown. ΔHf = Step 1 + Step 2 + Step 3 + Step 4 + Step 5 Or ΔHf = ΔHatm Na + ΔHFIE + ΔHatm Cl + ΔHea + ΔHLE ΔHLE = ΔHf (ΔHatm Na + ΔHFIE + ΔHatm Cl + ΔHea) 9

10 Student Activity 9 Calculating a value for ΔHLE (from an MX type cycle) 10

11 Student Activity 10 Calculating a value for ΔHf Using the tabulated values, calculate the enthalpy of formation for magnesium chloride. Label your diagram with the correct values for the processes. Show all working. Mg 2+ (g) + 2Cl(g)+2e- Mg 2+ (g) + Cl2(g)+2e- Mg 2+ (g) + 2Cl - (g) Mg + (g) + Cl2(g)+e- Mg(g) + Cl2(g) Mg(s) + Cl2(g) 11

12 Drawing a cycle which involves the oxide ion: MO or M2O type cycles In these cases it may be necessary to show the formation of the ions O - and O 2- as two separate processes. These are the first and second electron affinities respectively: ΔHea1 and ΔHea2. They can be represented by the two equations below. The first process is exothermic (arrow should be written going down the cycle) because it involves attraction, within a field, of the electron for the positive nucleus. It gives out energy. The second process is endothermic (arrow should be written going up the cycle) because it involves bringing together two negatively charged species which repel each other. Energy is required or taken in by the two particles in order to overcome the repulsion. Student activity 11 Complete the cycle for MgO Mg 2+ (g) + O(g) +2e- Mg 2+ (g) + 1/2O2(g) +2e- Mg + (g) + 1/2O2(g)+e- Mg(g) + 1/2O2(g) Mg(s) + 1/2O2(g) 12

13 Student Activity 12 Calculating a value for ΔHLE (from an MO type cycle) 13

14 Factors affecting the size of lattice enthalpies Here are the lattice enthalpies in kjmol -1 for some ionic lattices O 2- Cl - Br - I - Na Mg Al Ca Sr In examination questions comparing sizes of lattice enthalpy within two compounds, there are usually 3 marks :- charge comparison; size comparison; the explanation of how to the strength of attractive forces between the named cation and anion is affected by the first two factors. Remember - always compare the ions, not the atoms and there is no such thing as an ionic molecule. Student Activity 13 Explaining how different factors affect lattice enthalpy 1. What happens to the lattice enthalpy as the charge on an ion increases? 2. What happens to the lattice enthalpy as ionic size increases (for ions of the same charge)? 3. Explain which you would expect to have the most negative lattice enthalpy sodium chloride or lithium chloride? 14

15 3. Comparison of sodium chloride, sodium fluoride and magnesium fluoride You should have found that lattice enthalpy becomes more negative as the charge on the ion increases this means the lattice formed is stronger because more energy is given out when it is formed. Stronger forces within the lattice occur with ions of higher charge. (note that some ions, like Al 3+, with a high polarising ability in a compound with a large anion, have an even greater stability). Also important is the size...smaller ions form stronger lattices than bigger ions of the same charge. Student activity 14 A harder comparison question Explain why it is difficult to predict which of the compounds magnesium bromide and calcium chloride will have the highest lattice enthalpies. 15

16 Solubility and enthalpy of hydration Born Haber cycles can also be used to give some explanation of the solubilities of substances in water. Definition Enthalpy of hydration of an ion the energy change when 1 mole of gaseous ions are completely hydrated by water. X n+ (g) + aq X n+ (aq) Definition Enthalpy of solution- the energy change when 1 mole of a substance is dissolved in water. For example NaCl(s) Na+ (aq) + Cl- (aq) Student Activity 15 Draw diagrams to show how water molecules make interactions with cations and anions A typical enthalpy cycle diagram for a metal halide is: NaCl(s) ΔH1 Na+ (aq) + Cl- (aq) ΔH2 ΔH3 Na+ (g) + Cl- (g) ΔH1 = enthalpy of solution ΔH2 = lattice enthalpy -781 kjmol -1 ΔH3 = enthalpies of hydration of sodium ion and chloride ion -418 and -338 kjmol -1 So ΔH1 = - ΔH2 + ΔH3 ΔH1 = ( ) = +25 kjmol -1 16

17 We can use a Born Haber Cycle style diagram to illustrate the above process Use the information above to complete the cycle shown below Again, if we had other figures we could calculate other unknowns. A prediction of ΔH solution is not easy from data about the size and charge of the ions present. As an ion becomes smaller the lattice enthalpy becomes more negative and the hydration enthalpy becomes more negative. The relative decrease of these two is not easy to predict. Student Activity 16 (a) Draw the enthalpy cycle for the solubility of silver fluoride. 17

18 (b) Use the values below (kjmol -1 ) to calculate the enthalpy of solution of silver fluoride. ΔHhydration Ag ΔHhydration F ΔH LE AgF (c) Now draw the corresponding Born Haber Cycle for the solubility of silver fluoride. Note: useful to do a cycle such as MgCl2 18