(d) Which salt, LiCl or NaCl, has the greater lattice enthalpy Justify your answer. In other words, treating the AgCl as 100% ionic underestimates its lattice enthalpy by quite a lot. based on occupied principal energy levels. Depending on where you get your data from, the theoretical value for lattice enthalpy for AgCl is anywhere from about 50 to 150 kJ mol -1 less than the value that comes from a Born-Haber cycle. A commonly quoted example of this is silver chloride, AgCl. Calculate the lattice energy of NaCl using the information given below.l The Born exponent is n8, the Madelung constant 1.748,08.85×1012 F/m, and the. The experimental and theoretical values do not agree.That means that for sodium chloride, the assumptions about the solid being ionic are fairly good. Sodium chloride is a case like this - the theoretical and experimental values agree to within a few percent. There is reasonable agreement between the experimental value (calculated from a Born-Haber cycle) and the theoretical value.There are several different equations, of various degrees of complication, for calculating lattice energy in this way. If you know how to do it, you can then fairly easily convert between the two. Calculations of this sort end up with values of lattice energy, and not lattice enthalpy. By doing physics-style calculations, it is possible to calculate a theoretical value for what you would expect the lattice energy to be. Let's also assume that the ions are point charges - in other words that the charge is concentrated at the center of the ion. Let's assume that a compound is fully ionic. Theoretical Estimates of Lattice Energies Once again, the cycle sorts out the sign of the lattice enthalpy. This time both routes would start from the elements in their standard states, and finish at the gaseous ions. You cannot use the original one, because that would go against the flow of the lattice enthalpy arrow. The bond between ions of opposite charge is strongest when the ions are small. The lattice energy of NaCl, for example, is 787.3 kJ/mol, which is only slightly less than the energy given off when natural gas burns. The lattice energies of ionic compounds are relatively large. It does, of course, mean that you have to find two new routes. Na + ( g) + Cl - ( g) NaCl ( s) Ho -787.3 kJ/mol. The only difference in the diagram is the direction the lattice enthalpy arrow is pointing. How would this be different if you had drawn a lattice dissociation enthalpy in your diagram? Your diagram would now look like this: So, from the cycle we get the calculations directly underneath it. The diagram is set up to provide two different routes between the thick lines. Now we can use Hess' Law and find two different routes around the diagram which we can equate. And finally, we have the positive and negative gaseous ions that we can convert into the solid sodium chloride using the lattice formation enthalpy.Remember that first electron affinities go from gaseous atoms to gaseous singly charged negative ions. The -349 is the first electron affinity of chlorine.Again, we have to produce gaseous atoms so that we can use the next stage in the cycle. The +122 is the atomization enthalpy of chlorine.Remember that first ionization energies go from gaseous atoms to gaseous singly charged positive ions. The +496 is the first ionization energy of sodium.We have to produce gaseous atoms so that we can use the next stage in the cycle. The +107 is the atomization enthalpy of sodium.The Born-Haber cycle now imagines this formation of sodium chloride as happening in a whole set of small changes, most of which we know the enthalpy changes for - except, of course, for the lattice enthalpy that we want to calculate. This can be thought of in terms of the lattice energy of NaCl \text. The arrow pointing down from this to the lower thick line represents the enthalpy change of formation of sodium chloride. In this case, the lattice energy definition isn't the change in energy when any two atoms form an ionic bond that is part of an ionic lattice, but instead: The energy required to fully dissociate a mole of an ionic lattice into its constituent ions in their gaseous state. Notice that we only need half a mole of chlorine gas in order to end up with 1 mole of NaCl. We are starting here with the elements sodium and chlorine in their standard states. If you wanted to draw it for lattice dissociation enthalpy, the red arrow would be reversed - pointing upwards.įocus to start with on the higher of the two thicker horizontal lines. You will see that I have arbitrarily decided to draw this for lattice formation enthalpy. The n values and the electronic configurations (e.c.\)Ĭonsider a Born-Haber cycle for sodium chloride, and then talk it through carefully afterwards. Where N is the Avogadro's number (6.022x10 -23), and n is a number related to the electronic configurations of the ions involved.
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