TBR G. Chem: Section 8, Passage 3, Question 17

[circulus vitios]

How do the lattice energies of NaCl, LiF, and MgO compare to one another?
A. MgO > LiF > NaCl
B. MgO > NaCl > LiF
C. LiF > NaCl > MgO
D. NaCl > LiF > MgO

Equation for lattice energy is E = k ((Qcation)(Qanion))/r

where k is a constant, Q is charge, and r is the distance between ions in the lattice.

I said the answer is B. They say the answer is A.

MgO has the most energy since the charges are +/- 2. Li, Na, F, and Cl are both +/- 1.

Li and F ions are smaller than Na and Cl ions because they're a principal quantum number lower. Since Li and F ions smaller there would be more space between ions in the lattice and because the "r" term is in the denominator, this would make the overall lattice energy for LiF smaller. So MgO > NaCl > LiF.

The book just says "Because Li is smaller than Na and F is smaller than Cl (all ions), the second highest lattice energy is associated with LiF."

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[circulus vitios]

Ok I read the answers to two more questions involving this equation.

One question says "substituting a larger cation for a smaller cation increases the distance between ions...reducing the lattice energy." Another question says "the atomic radius of sodium cation is larger than the atomic radius of lithium cation....the lattice energy decreases when lithium is replaced by sodium."

Am I ******ed or are they switching between defining r as the distance between atomic radii and the size of the atomic radius?

 

[justhanging]

The distance between atomic radii and the size atomic radius of two ions are related, that is why they are using both definition interchangeably. The larger the atomic radius of both ions the larger the distance between atomic radii and the less the lattice energy. Your getting this concept backwards since you think that smaller atomic radius produces more space but instead when the of the atomic radius is small the ions get closer together and distance between atomic radii decreases.

 

[MT Headed]

Since Li and F ions smaller there would be more space between ions in the lattice

And therin lies the conceptual problem.

It is a useful approximation in genchem that the atoms and ions more or less touch each other. Therefore the bond length "r", which is the distance between the nuclei of the atoms, is just the radius of one atom plus the radius of the other atom.

If Li and F are smaller, there would be less space between the ions in the lattice.