Given the following values for steps in the formation of CaO(s) f...

Question

Given the following values for steps in the formation of CaO(s) from its elements, draw a Born–Haber cycle similar to that shown in Figure 6.7. Eea1 for O1g2 = -141 kJ/mol Eea2 for O1g2 = 745.1 kJ/mol Heat of sublimation for Ca1s2 = 178 kJ/mol Ei1 for Ca1g2 = 590 kJ/mol Ei1 for Ca1g2 = 1145 kJ/mol Bond dissociation energy for O21g2 = 498 kJ/mol Lattice energy for CaO1s2 = 3401 kJ/mol

Accepted Answer

welcome back everyone using knowledge of the formation of potassium chloride from its elements construct a born Haber cycle for K. C. O. We're going to begin by recalling the formula of are born Haber cycle which calculates the formation of our ionic compound solid which in this case is potassium chloride and that's going to begin by our heat of formation. So delta H. F. And recall that this is set equal to our entropy of sublimation which we should recall is our heat required to change one mole of a substance from solid to its gaseous form. Usually in standard conditions. This is done. We recall added to our bond association energy which describes energy required to break a bond. And this is A. D. Here. So this is B. D. E. For bond association energy. Then recall that this is then added to our first ionization energy. So we'll just have iii here which we recall is the amount of energy needed to remove an electron from a gaseous atom. And then recall that we would subtract from this our electron affinity represented by E. A. Which describes our gain of electrons to our atoms. Then added to our electron affinity. We have our lattice energy which is the energy released when one mole of a ionic solid or crystal is formed from its gaseous ions. So now that we have this born Haber cycle formula outlined, we're going to draw out our born Haber cycle. So we want to make a sort of diagram here and at the bottom of our diagram we're going to have our product which is our potassium chloride solid. Now as the prompt states, it's formed from its elements, so that would be its elements in their standard states. So we have first we have potassium which in its standard state is a solid based on its position and the periodic table. We see it's a group on a metal and then we have chlorine, which in its standard state is a di atomic gas, which is why we have this subscript of two and then our gas phase label. We need to make sure that this is balanced because we see on our product side we have just one mole of chlorine and here we have two moles. So we're going to need to place the coefficient of one half in front of chlorine gas. So what this is again describing is the formation of one mole of our solid compounds are ionic compound potassium chloride from its elements in their standard states. And this would be so we would need an arrow going from our elements in their standard states to our ionic compound. And again, as we stated earlier, this is our delta HF or entropy heat of formation. And according to our chart, the energy needed to make our product K C. L. So to make a bond between these two atoms is negative 436.5 killed jules per mole or our units. So next according to our born haber cycle formula, we have our entropy of sublimation. And so as we stated from our definition that describes the process of sublimating our atoms. So in this case we're going to sublimate our solid solid potassium to form from a solid into a gas. So we're going to form gaseous potassium and then we still have our one half mole of our chlorine gas. And because we're going from the previous step two, now this step above to form gaseous potassium, we need an upward arrow which describes again our entropy of sublimation. According to the chart. This value is equal to 89 kg joules per mole. So we're definitely going to need more room here for our born haber cycle. So we're going to actually move this all down so that we can keep our chart going. So this looks like enough room. And the next step of our born Haber cycle according to our formula that we outlined above is our bond association energy. So energy required to break a bond and the bond that we're breaking here is going to be the bond between our di atomic chlorine molecule. So the bond between the two chlorine atoms meaning our next step is going to be, we still have our potassium gas but now we have just one mole of chlorine gas no longer as a di atomic molecule. And to get to this point here from this point here we have our and let's actually make this line longer, our upward arrow which describes again our bond association energy. And according to our chart above the amount of energy needed to break this bond in our di atomic molecule of chlorine is 243 kg joules per mole. And this is not energy needed but rather energy released since we're breaking a bond. So apologies for that error. So this is a positive value to be clear. Let's make that We have our equal sign and our positive 243 kg per mole of energy released next. According to our born haber cycle, we now have our first ionization energy which we recall is our energy needed to remove a valence electron from an atom. And so here we're going to have our final point here or not our final point. But this uppermost point here of our chart where removing an electron from our gaseous potassium is now going to form potassium as a cat ion, recall Acadian means we remove that number of electrons. So we have a plus one charge because we removed one electron. It's still a gaseous ion. And this is then added to chlorine which we should recall does not form a caddy on but rather will form an an ion which we'll see when we go through our electron affinity. And so in this case for electron affinity we would see our atom gaining an electron with regard to chlorine. And so in that case because we're going from our electron affinity now recall that in our born haber cycle electron affinity is subtracted from the first ionization energy. So now we're going to have a downward arrow and this should be e capital A for electron affinity. And this will take us to the next point of our born Haber cycle where we now have again potassium cat ion but now chlorine has gained an electron and so we have chlorine with what we recognize as it's - and I in charge still with a gaseous label. And this makes sense to us because we see chlorine in group seven A. On the periodic table and we know Adam's in group seven A have a minus one an ion charge. And now this leads us to our last point of our born haber cycle which takes us all the way down to our ionic crystal, potassium chloride or ionic solid. And here we can see we're going from Our gaseous ions to form one mole of our ionic crystal. And this is going to be energy that is released which is why we have a downward arrow describing our lattice energy. And I just realized that we skipped one of our arrows here. We need to have our arrow going from our gaseous atoms of potassium that is neutral which goes through the first ionization energy where we remove an electron from it to form the potassium kati on here. So now we officially have our complete born haber cycle and we just need to finish filling in our values. So for the ionization energy we have from the chart above Energy required to remove that electron from potassium being joules per mole. Then our electron affinity which describes chlorine gaining an electron according to our chart, that amount of energy Is - joules per mole. And because chlorine is gaining an electron, it's technically forming a bond. And so that is why we have a negative amount of energy here we have a positive value for the ionization energy because we are removing an electron. So energy is being released. And then for our lattice energy according to the prompt we have a value of negative 717 kg joules per mole energy is being used to create a bond to form our one mole of our ionic solid potassium chloride from the gaseous ions. So energy is needed to form this bond And that's why we have a negative value for lattice energy. One last thing I'd like to note is that for our lattice energy this arrow can technically go in either direction. We can either have an upward arrow or we can, as we have written have a downward arrow, we would just have to change the value if we made our upward arrow because this value would now need to be positive 717 killed joules per mole. And it's okay to have an arrow in either direction because lattice energy can either describe the formation of one roll of our ionic crystal from its gaseous ions, or it can describe the energy released when we have our one mole of our ionic solid, breaking apart to form its gaseous ions, which would give us our upward arrow and a positive value. Other than that, this entire diagram that we've written out is our born haber cycle for the formation of potassium chloride from its elements in their standard states. And this is going to correspond to choice. Be in the multiple choice. I hope everything that I reviewed was clear. If you have any questions, please leave them down below and I'll see everyone in the next practice video.

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