A Key Skill: How to Calculate Formal Charge

by James

in Functional Groups, Nomenclature, Organic Chemistry 1, Where Electrons Are

Need to figure out if an atom is negative, positive, or neutral? Here’s the formula for figuring out the “formal charge” of an atom:

Formal charge = [# of valence electrons] – [electrons in lone pairs + 1/2 the number of bonding electrons]

This formula explicitly spells out the relationship between the number of bonding electrons and their relationship to how many are formally “owned” by the atom. However, since the “number of bonding electrons divided by 2″ term is also equal to the number of bonds surrounding the atom, here’s the shortcut formula:

Formal Charge = [# of valence electrons on atom] – [non-bonded electrons + number of bonds].

Let’s apply it to some examples. for example BH4 (top left corner).

  • The number of valence electrons for boron is 3.
  • The number of non-bonded electrons is zero.
  • The number of bonds around boron is 4.

So formal charge = 3 – (0 + 4)  = 3 – 4  = –1

The formal charge of B in BH4 is negative 1. 

Let’s apply it to :CH3 (one to the right from BH4)

  • The number of valence electrons for carbon is 4
  • The number of non-bonded electrons is two (it has a lone pair)
  • The number of bonds around carbon is 3.

So formal charge = 4 – (2 +3) = 4 – 5  = –1

The formal charge of C in :CH3 is negative 1. 

Same formal charge as BH4!

Let’s do one last example. Let’s do CH3 (with no lone pairs on carbon). It’s the orange one on the bottom row.

  • The number of valence electrons for carbon is 4
  • The number of non-bonded electrons is zero
  • The number of bonds around carbon is 3.

So formal charge = 4 – (0 +3) = 4 – 3 = +1

You can apply this formula to any atom you care to name.

Here is a chart for some simple molecules along the series B C N O . I hope beryllium and fluorine aren’t too offended that I skipped them, but they’re really not that interesting for the purposes of this table.

Note the interesting pattern in the geometries (highlighted in colour):  BH4(–), CH4, and NH4(+) all have the same geometries, as do CH3(–), NH3, and OH3(+).  Carbocation CH3(+) has the same electronic configuration (and geometry) as neutral borane, BH3. The familiar bent structure of water, H2O, is shared by the amide anion, NH2(–). These shared geometries are one of the interesting consequences of valence shell electron pair repulsion theory (VSEPR – pronounced “vesper“, just like “Favre” is pronounced “Farve”.)

The formal charge formula also works for double and triple bonds:

Here’s a question. Alkanes, alkenes, and alkynes are neutral, since there are four bonds and no unbonded electrons:  4 – [4+0] = 0.  For what other values of [bonds +  nonbonded electrons] will you also get a value of zero, and what might these structures look like? (You’ll meet some of these structures later in the course).

One final question – why do you think this is called “formal charge”?

Think about what the formal charge of BF4 would be. Negative charge on the boron. What’s the most electronegative element here? Fluoride, of course, with an electronegativity of  4.0, with boron clocking in at 2.0. Where do you think that negative charge really resides?

Well, it ain’t on boron. It’s actually spread out through the more electronegative fluoride ions, which become more electron-rich. So although the “formal” address of the negative charge is on boron, the electron density is actually spread out over the fluorides. In other words, in this case the formal charge bears no resemblance to reality.

Related Posts:

{ 26 comments… read them below or add one }

satyakam November 27, 2010 at 9:03 pm

sir
the sheet posted by u is really very excellent.i m teacher of chemistry in india for pre engineering test.if u send me complete flow chart of chemistry i will great full for u

Reply

Walt Sautter January 16, 2012 at 3:59 pm

nice, concise explanation

Reply

james January 16, 2012 at 11:02 pm

Thanks.

Reply

Samina January 19, 2012 at 2:36 pm

Very good explanation.I finally understood how to calculate the formal charge,was having some trouble with it.Thanks:)

Reply

james January 19, 2012 at 11:07 pm

Glad you found it helpful.

Reply

peter February 23, 2012 at 10:44 am

thank you for excellent explanation

Reply

james February 23, 2012 at 3:14 pm

Glad you found it useful Peter!

Reply

james March 5, 2012 at 12:16 pm

The answer to the question in the post above is “carbenes” – they have two substitutents, one pair of electrons, and an empty p orbital – so a total of four electrons “to itself”, making it neutral.

Reply

goshu abraham March 7, 2012 at 11:54 am

thank you for collaboration of formal charge

Reply

Bebtio March 22, 2012 at 2:23 am

Shouldn’t the formal charge of CH3 be -1? I was just wondering because in your example its +1 and in the chart its -1.

Reply

Unknown November 17, 2012 at 2:57 pm

In the question.. its mentioned that CH3 without any lone pairs.. which means the valence would be 4 but there will not be any (2electrons) lone pairs left.. Hence it will be (4-)-(0+3)= 1

Reply

james November 17, 2012 at 8:48 pm

Yes.

Reply

Dr Kamat November 3, 2013 at 7:43 am

In CH3 i think FC on C should be -1 as carbon valency is 4 it has already bonded with 3 hydrogen atom one electron is left free on carbon to get bond with or share with one electron H hence, number of non bonded electrons lone pair of electrons is considered as 2. 4-(2+3) = -1.
In your case if we take 0 than valency of c is not satisfied.

Reply

emerald July 22, 2012 at 9:02 am

Great!i can use this for my exam!thanks!

Reply

Manas patra June 17, 2013 at 2:10 pm

There are meny compounds which bears various structure among these which one is more stable or less energetic is it possible to predicu from the formal charge calculation?

Reply

Jeffery Seah September 24, 2013 at 8:29 am

If formal charges bear no resemblance to reality, what are their significance?

Reply

James Ashenhurst September 24, 2013 at 10:35 pm

I hope the post doesn’t get interpreted as “formal charges have no significance”. If it does I will have to change some of the wording.

What I mean to get across is that formal charges assigned to atoms do not *always* accurately depict electron density on that atom, and one has to be careful.

In other words, formal charge and electron density are two different things and they do not always overlap.

Formal charge is a book-keeping device, where we count electrons and assign a full charge to one or more of the atoms on a molecule or ion.
Electron density, on the other hand, is a measurement of where the electrons actually are (or aren’t) on a species, and those charges can be fractional or partial charges.

First of all, the charge itself is very real. The ions NH4+ , HO-, H3O+ and so on actually do bear a single charge. The thing to remember is that from a charge density perspective, that charge might be distributed over multiple atoms.
Take an ion like H3O+, for example. H3O *does* bear a charge of +1,

However, if one thinks about where the electrons are in H3O+, one realizes that oxygen is more electronegative than hydrogen, and is actually “taking’ electrons from each hydrogen. If you look at an electron density map of H3O+ , one will see that the positive charge is distributed on the three hydrogens, and the oxygen actually bears a slight negative charge. There’s a nice map here.

http://chemwiki.ucdavis.edu/Physical_Chemistry/Acids_and_Bases/Aqueous_Solutions/The_hydronium_Ion

When we calculate formal charge for H3O+, we assign a charge of +1 to oxygen. This is for book keeping reasons. As a book-keeping device, it would be a royal pain to deal with fractions of charges like this. So that’s why we calculate formal charge and use it.

Sometimes it does accurately depict electron density. For example, in the hydroxide ion, HO- , the negative charge is almost all on the oxygen.

If you have a firm grasp of electronegativity then it becomes less confusing.

Does that help?

Reply

Christian November 3, 2013 at 11:45 pm

Thank you very very more for the simple explanation! Unbelievably easy and saves so much time!!!!!!

Reply

Deborah February 16, 2014 at 8:35 pm

This works! I would take your class with organic chemistry if you are a professor. I am taking chemistry 2 now. Organic is next.
Thank you so much!

Reply

kaustubh March 8, 2014 at 8:15 am

you said that non bonded electrons in carbon is 2, but how ?
because i see it as only 1 because out of the 4 valence electrons in carbon, three are paired with hydrogen so it’s only 1 left

Reply

James March 9, 2014 at 7:56 pm

If the charge is -1, there must be an “extra” electron on carbon – this is why there’s a lone pair. If there was only one electron, it would be neutral.

Reply

BEY bee March 18, 2014 at 11:46 am

what does it means if we determine a molecule with zero charge
?

Reply

James April 15, 2014 at 10:43 am

It’s neutral!

Reply

mark beryllium April 14, 2014 at 7:17 am

I am beryllium and i got offended!!!!!!……..LOL Just kidding…….BTW, I found this article very useful.Thanks!!!!!!!!!!

Reply

PERCY KHOSA June 1, 2014 at 1:11 pm

AM REALLY LOST NOW
ON THAT EXAMPLE OF CH3
CARBON
# OF VALENCE ELECTRON=4
# OF BONDING=3
# OF UNSHARED=1

SO WHEN I CALCULATE

FORMAL CHARGE=(#OF VALENCE ELEC)+[(1/2#OF BOND)+(#OF UNSHARED)]
FORMAL CHARGE=4+[(1/2*3)+1]
=1.5

PLZ HELP IF AM MAKING MISTAKE

Reply

James June 26, 2014 at 5:22 pm

Should be 1/2 [# of bonding ELECTRONS] + # unshared.
This gives you 4 – [3 – 1]
= 0 for ch3 radical.

Reply

Leave a Comment