Account for the differences of ionization energies (kj/mol)?

Question

a) explain the difference between Ca and K in regard to
i) their first ionization energies
ii) their second ionization energies


K: 1st ionization energy =419 2nd: 3050
Ca: 1st ion. enery = 590 2nd: 1140

Answer 1

i)atoms of Ca and K have the same number of electron shells. this means that both atoms have similar screening effect of valence electrons by inner electron shells. but Ca has more protons than K (one, to be exact). therefore Ca's valence electrons are more strongly attracted to the nucleus. thus, more energy is required to remove it from the atom, hence Ca's higher 1st IE.

ii) Since K is a group I element, it has one valence electron only. to remove a second electron, the stable octet configuration must be disrupted. this involves a large amount of energy as compared to the 2nd IE of Ca, which does not involve a violation of the octet rule.

Answer 2

i) their first ionization energies
K: IE1 = 419, IE2 = 3050;
Ca: IE1 = 590, IE2 = 1140;
Even thought K and Ca have IE1 on the same energy level (row), IE1 for K is slightly smaller than that of Ca. This is because K has less protons, and therefore the larger element. This makes it easier to remove the first electron from K than from Ca.
This can also be shown through the Z-score (Zeffective)
Zeff = total electrons - shielding electrons.
the greater the Zeff, the greater the IE.
K Zeff = 19 - 18 = +1
Ca Zeff = 20 - 18 = +2
Ca Zeff > K Zeff, so this is another way to show why Ca has a greater IE1 that K.

ii) their second ionization energies
K: IE1 = 419, IE2 = 3050;
Ca: IE1 = 590, IE2 = 1140;
The differences of the two elements' IE2 can be explained both through their differences in energy level and their Zeff.
The second electron in K (which is now expressed as K-) is removed from a lower energy level (n=3) the second electron in Ca, wich is removed from the same E level as its first electron.
Due to K- being on a lower E level, K- has a much smaller radius, and the nucleus attracts the (complete) outer shell with a greater force. The trend for the radius is that it decreases from left to right and from bottom to top.
Again, this can also be shown through Zeff.
K- Zeff = 18 - 10 = +8; (10 is the amount of shielding)
Ca- Zeff = 19 - 18 = +1;
K Zeff >> Ca Zeff, and so the K IE2 >> Ca IE2.

Answer 3

First write the electron configuration for each atom.

K = 1s2, 2s2,2p6, 3s2, 3p6, 4s1

Ca = 1s2, 2s2, 2p6, 3s2, 3p6, 4s2

The first electron for each one is being removed from the 4th level, s orbital. No difference there. But, Ca has a "special case of stability" because its s orbital is full. This tends to produce unusually high ionization energies, therefore Ca's 1st i.e. is higher than K.

The second electron for K is coming from the 3p whereas Ca's second electron is still in the 4s. There are two reasons why K's 2nd i.e. is so much higher: the electron is a level closer to the nucleus (electromagnetic force depends on distance) and is coming from a filled level (special case of stability). Both of these will produce higher ionization energies.