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Organic Chemistry

Introduction to Arrow-Pushing

A Crystal Clear Chemistry Tutorial

One of the main things to learn in introductory organic chemistry is how to properly do arrow-pushing (also called electron pushing) mechanisms. This article will review how it's done and give a few simple rules of thumb in the summary boxes.

Bonds and Arrows

Reactions follow a series of steps that begin from the starting material, go to some reaction intermediates (the "in between" chemicals), and end with the reaction products. Each step consists of some bond-breaking or bond-forming (a bond is a pair of electrons shared by two atoms). Often, a reaction step will consist of both a bond-breaking and bond-forming. When bonds break, the electrons move somewhere else (they don't just disappear), and this movement is depicted with arrows.

Arrows represent the movement of electrons (NOT atoms, which is a common mistake). A half-arrow (sometimes called a "hook" or "fishhook" arrow) represents a single electron (which is also known as a radical). A full-arrow (that is, a normal-looking arrow) represents an electron pair, and this will be the most common arrow that you draw. Usually, these arrows are drawn "curly" or "curved", so that they aren't confused with the "reaction arrows" that go from starting material to products. For example, in the below reaction between the hydrogen ion and a hydroxide ion to form water, the straight line is the reaction arrow that you've seen since general chemistry, and the curved arrow is an "electron-pushing" arrow. (This way of depicting the flow of electrons is sometimes called "curved arrow" or "curly arrow" notation).

The curved arrow from the oxygen to the hydrogen ion in (1) shows the formation of a bond between the oxygen and the hydrogen, which can be seen in the product diagram. You can see a common mistake students make is to draw the hydrogen ion "going to" the hydroxide ion. This is incorrect, since arrows shwo the movement of electrons, and the hydrogen ion has no electrons. In reaction (2) below, we can see a bond-breaking reaction step, in which a molecule of hydrogen chloride breaks up into a hydrogen ion and a chloride ion.

From now on, we will talk mostly about double-barbed full arrows (which we will simple call "arrows"), because those are the most common arrows. There will be a section at the end on half-arrows and reactions that involve single electrons.

Because they depict the flow of electrons, arrows always start from a lone electron pair or from a bond (these are the electrons that will move), and they always point to another atom (this is where the electrons move to). When the arrow starts at a lone electron pair, it depicts the formation of a bond between the atom which starts with the electron pair and the atom the arrow points to. When the arrow starts at a bonding electron pair, it depicts the breaking of that bond.

Arrows represent the movement of electrons when bonds form and break. A full arrow represents a pair of electrons. A half arrow represents one unpaired electron. Full arrows start at a lone electron pair or a bonding electron pair and point to another atom. If it starts at a bond, that bond is breaking. If it starts at an electron pair, a bond is forming with that electron pair.

Arrow-Pushing and Formal Charge

You may have learned how to calculate formal charge in general chemistry, and then promptly forgotten it, seeing as it was useless. Well, in organic chemistry, formal charges are used all the time! If you look at the reaction depicted above, you'll see that the hydrogen ion has a plus sign (in a circle, which is just for clarity), designating that it has a +1 formal charge, and the hydroxide ion has a minus sign on the oxygen (again, in a circle), showing that the oxygen atom has a -1 formal charge. The formal charge is a number that tells you the approximate balance of protons and electrons the atom has, overall. If the formal charge is negative, it means that the atom has more electrons than protons, and if the formal charge is positive, it means that the atom has more protons than electrons.

To calculate formal charge on an atom, count the number of protons in the nucleus of the atom. Subtract the number of non-valence electrons from that number of protons. Subtract an additional 2 from that number for each lone pair of electrons the atom has (that is, the non-bonding pairs of electrons). Subtract 1 for each bond the atom has to another atom. The number you get in the end is the formal charge.

For example, the oxygen atom in the hydroxide ion (OH^-) has 8 protons. There are 2 non-valence electrons (one pair in the 1s orbital), and so subtracting 8 - 2 = 6. There are 3 non-bonding electron pairs, and if we subtract 2 x 3 from 6, we get 6 - (2 x 3) = 0. Finally, oxygen has one bond to hydrogen, and so we subtract one more, giving 0 - 1 = -1. Thus, oxygen has a -1 formal charge.

From now on, we will call "formal charge" simply charge, and an atom with negative formal charge will be "negatively charged," positive formal charged atoms will be "positively charged."

A negatively charged atom will want to lose electrons, and positively charged atoms will want to gain electrons. In general, this means that negatively charged atoms will give their atoms to positively charged atoms. You can see in the reaction above, that the negatively charged oxygen forms a bond with the positively charged hydrogen ion (which is also called a proton), and this gives a neutrally charged product.

A full arrow always makes the atom it ends at more negative (by 1 electron), and it makes the atom it starts at more positive. If the arrow starts at a bond, then it makes the atom it doesn't end up on more positive.

Going back to the example reaction (it is shown again below), we see that an arrow points from the negatively charged oxygen atom's lone pair of electrons to the positively charged hydrogen ion. Because the arrow points from oxygen's electrons, oxygen becomes more positive (making it neutral), and since the arrow points towards hydrogen, it makes hydrogen more negative (making hydrogen neutral, too).

In the reaction where hydrogen chloride splits into a hydrogen ion and a chloride ion, the arrow starts at the bond between hydrogen and chlorine and ends on the chlorine atom. Thus, the electrons in the bond are transferred to chlorine, which becomes more negatively charged (resulting in a -1 overall charge), and hydrogen becomes more positively charged (resulting in a +1 overall charge).

The total formal charge of the system (the sum of all of the charges of the individual atoms that participate) does not change from before the reaction to after. When using the arrows, keep track of the creation and deletion of charges. Arrows show where electrons are going, so the place electrons are going TO gets more negatively charged, while the place electrons are coming FROM gets more positively charged. Electrons almost always move from negatively charged atoms to positively charged atoms.

» Page Two: The Octet Rule, Nucleophiles and Electrophiles, and Radical Reactions