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Chem FactsheetJanuary 2002 Number 29
Answering Questions On Born-Haber Cycles
To succeed in this topic you need to thoroughly understand how to write Born-Haber cycles (covered in Factsheet No. 28)
After working through this Factsheet you will know and understand:
• how to convert Born-Haber cycles into numerical answers given the relevant data;
• how the data given is used to test the understanding of definitions by candidates;
• the relationship between the marks for a question and the balance between writing the cycle and calculating an answer;
• the use of enthalpy level diagrams to test the understanding of candidates of definitions and Born-Haber cycles.
Questions on Enthalpy Level Diagrams 2. Calculating a numerical answer given all the other values and the diagram
There are two types of questions on these diagrams:
1. Identifying enthalpy changes
2. Calculating a numerical answer from given values on a diagram Ca2+(g) + O2−(g)
1. Identifying enthalpy changes X
Ca2+(g) + O(g)
Zn2+(g) + 2Br(g)
+250 KJ mol−1
c Zn2+(g) + Br2(g) b 2+
Ca (g) + ½O2(g)
d Zn+(g) + Br2(g) Zn2+(g) + 2Br−(g)
+1150 KJ mol−1 -3512 KJ mol−1
e Zn(g) + Br2(g) a Ca+(g) + ½O2(g)
f Zn(s) + Br2(g)
g +590 KJ mol−1
ZnBr(s)
Ca(g) + ½O2(g)
Example 1
+192 KJ mol−1
Question: Identify the stages a – g
Ca(s) + ½O2(g)
Method
For each arrow look to see what has changed. It is then a matter of -635 KJ mol−1
deciding which definition it matches and how many moles. CaO(s)
Answer: Question What is the value of X?
a = gaseous ions to ionic solid = L.E.
b = 2Br(g) → 2Br−(g) = 2 × 1st E.A. Method: Either convert to an enthalpy cycle:
c = Br2(g) → 2Br(g) = 2 × !H°at [½Br2]
d = Zn+(g) → Zn2+(g) = 2nd I.E. Identify each of: elements, compound and gaseous ions, then draw the
e = Zn(g) → Zn+(g) = 1st I.E. diagram:
f = Zn(s) → Zn(g) = !Hat°[Zn(s)] ∆Hf°
Elements Compound
g = elements → compound = !Hf° [ZnBr2(s)]
∆H1 L.E.
Gaseous ions
Example 2
Question: How are a – g linked by Hess’s Law? !H1 + L.E. = !Hf°
Method: Identify on the diagram: elements, compound and gaseous ions Identify the components in the diagram and put in the values.
∆Hf°
Elements Compound Answer -635 = + 192 + 590 + 1150 + 250 + X - 3512
-635 = X – 1330
∆H1 L.E. X = + 1330 – 635 = +695 kJ mol-1
gaseous ions
Or follow the diagram round, starting and finishing with the elements:
So: !H1 + L.E. = !Hf° 192 + 590 + 1150 + 250 + X + (-3512) − (-635) = 0
Answer: f + e + d + c + b + a = g Note: The direction of the arrow tells us whether to add or subtract. We are
going in the direction of the arrow for the -3512, so we add (-3512).
Or alternatively, "follow the diagram round" - starting and finishing with
the elements. If you go in the same direction as an arrow, you add the X − 695 = 0 so X = +695 kJmol-1
corresponding value; if in the opposite direction, subtract the value.
Finally, equate to zero: f + e + d + c + a − g = 0 For practice on this type of calculation, go to question 1.
1
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