# What is charge density?

For example, Magnesium has a higher charge density compared to Sodium, therefore its metallic lattice is stronger and it has a higher melting point. Does that mean that Magnesium has more protons and a smaller atomic radius or is it about its charge (2+), that makes its lattice stronger?

What does charge density show?

• There are really two separate things here - "does having a higher ionic charge make magnesium's metallic bonding stronger", and "what is charge density". You might want to clarify exactly what your real question is. – Aesin Jan 12 '13 at 11:48

If it was about the number of protons in the nucleus, then Mercury would hardly be liquid at room temperature, would it?

Actually, it is about the density of free electrons, i.e. the density of the "electron gas" that makes up the metallic bonding. Obviously, this density has to be the negative of the ions' charge, so you might equivalently say it's about magnesium's (2+) charge, though that doesn't make much sense physically unless you also consider the conduction electrons, as the ions themselves of course repulse each other.

• So at my level it means the charge, like Magnesium's charge density is 2+ and sodium's in 1+. – Cyrus Jan 6 '13 at 13:28

# Charge density

Charge density is the density of charge around the ion. Silberberg (Chemistry: The Molecular Nature of Matter and Change. 4th ed. 2006) define it as:

"The ratio of the charge of an ion to its volume."

The factors playing into the strength of an ion's charge density are therefore the charge of the ion (e.g. 2+ for Mg, 1+ for Na) and the effective volume which that charge acts over - which is where the ionic radius comes in. (Note this is different to atomic radius.)

Charge density = charge/volume


As the magnesium ion and sodium ion both have the same electronic configuration i.e. that of neon (because Mg has lost 2 electrons and Na has lost 1 and they now both have 10 electrons in total) the charge of the electrons around the ions is the same. But - magnesium has one more proton in its nucleus. This means magnesium has a smaller radius (think more condensed due to the greater pull of the nucleus - see effective nuclear charge). $$Na^+$$ has an ionic radius of 102 pm and $$Mg^{2+}$$ has an ionic radius of 72 pm. (Also from Silberberg)

Since the volume is less and the charge is greater for magnesium, the charge density will be greater for magnesium than for sodium.

# Periodic trend

The periodic trend is that charge density will decrease going down the periodic table as the charge stays the same but the size increases. Going across (as for Mg and Na) the charge density increases going to the right as the charge increases and the size decreases.

# ...

What do you mean by "What does charge density show?"

In coordination compounds, charge density can be defined as the ratio of the charge to the radius of the metal ion. Charge density is directly proportional to the stability of Coordination Compounds. E.g The ionic radius of metals $\ce{Cu^2+}$ and $\ce{Cd^2+}$ are $\pu{69 pm}$ and $\pu{97 pm}$ respectively. Stability = $\frac{2}{69}$ and $\frac{2}{97}$ . The stability of $\ce{Cu^2+}$ > $\ce{Cd^2+}$.

• @Another.Chemist Thanks for your edits! For ions with multiple charges, you need to explicitly superscript the charge, or else mhchem will get confused: so, $\ce{O^2-}$ produces $\ce{O^2-}$ (oxide ion), but $\ce{O2-}$ (no caret ^) produces $\ce{O2-}$ (superoxide ion). – orthocresol Mar 19 '17 at 19:49