Question #27e4d

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Question #27e4d

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Answer 1 · 2016-06-10T08:47:08

This is actually hard to do completely without actual data.

INITIAL GUESS

My initial ordering would be based on charge (smallest to largest):

${Al}^{3 +}$ $"Al"^(3+)$
${Mg}^{2 +}$ $"Mg"^(2+)$
${Na}^{+}$ $"Na"^(+)$
$Ne$ $"Ne"$
$F^{-}$ $"F"^(-)$
$O^{2 -}$ $"O"^(2-)$
$O^{3 -}$ $"O"^(3-)$

since a larger positive charge gives a larger effective nuclear charge relative to an element on the same period with a smaller positive charge, and thus a smaller ionic radius.

But we are looking way across the periodic table, and the period trend and group trend overlap.

PERIOD/GROUP TREND CONFLICTS

Recall that the atomic radius resets to be bigger due to the addition of a new quantum level $n$ $n$ , so $Ne$ $"Ne"$ is smaller than ${Na}^{0}$ $"Na"^(0)$ . However, that doesn't tell us everything we need to know.

How much smaller does $Mg$ $"Mg"$ get upon two ionizations, and $Na$ $"Na"$ get after one ionization? That's what I don't know. We can still say that $r_{{Na}^{+}}^{+} > r_{{Mg}^{2 +}}^{2 +}$ $r_("Na"^(+)) > r_("Mg"^(2+))$ , but...

The actual radii are:

$53 pm$ $"53 pm"$ (ionic radius)
$72 pm$ $"72 pm"$ (ionic radius)
$102 pm$ $"102 pm"$ (ionic radius)
$69 pm$ $"69 pm"$ (covalent radius)
$133 pm$ $"133 pm"$ (ionic radius)
$140 pm$ $"140 pm"$ (ionic radius)
$> 140 pm$ $>"140 pm"$ (ionic radius)

respectively, for the species listed at the top.

So I would have misplaced $Ne$ $"Ne"$ . Apparently, ${Mg}^{2 +}$ $"Mg"^(2+)$ is very slightly larger than $Ne$ $"Ne"$ , by virtue of its added quantum level.

(And I could also be wrong if the atomic radii I referenced were poorly calculated or poorly determined as well, because $3 pm$ $"3 pm"$ is not a large margin of error.)

The "real" order, at least based on the data I referenced, would be (from smallest to largest):

${Al}^{3 +}$ $"Al"^(3+)$ , $r_{ionic} = 53 pm$ $r_"ionic" = "53 pm"$
$Ne$ $"Ne"$ , $r_{covalent} = 69 pm$ $r_"covalent" = "69 pm"$
${Mg}^{2 +}$ $"Mg"^(2+)$ , $r_{ionic} = 72 pm$ $r_"ionic" = "72 pm"$
${Na}^{+}$ $"Na"^(+)$ , $r_{ionic} = 102 pm$ $r_"ionic" = "102 pm"$
$F^{-}$ $"F"^(-)$ , $r_{ionic} = 133 pm$ $r_"ionic" = "133 pm"$
$O^{2 -}$ $"O"^(2-)$ , $r_{ionic} = 140 pm$ $r_"ionic" = "140 pm"$
$O^{3 -}$ $"O"^(3-)$ , $r_{ionic} > 140 pm$ $r_"ionic" > "140 pm"$

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