# Why is the minus sign (-) not allowed in reaction equations?

Recently in my chemistry class, the teacher told us that while writing "half equations" (such as a sodium atom losing one electron to form a sodium ion) we were not to use a simple minus sign. We were only allowed to use a plus sign. For example, this would not be allowed:

$$\ce{Na - e- -> Na+}$$

The "correct" way of writing it would be:

$$\ce{Na -> Na+ + e-}$$

My question is: Is this conventional, or somehow only related to my school? Could any example of a chemical equation utilising the minus sign please be given for clarification?

Don't get too caught up in notational rigidity. You're "allowed" to use any notation you want, if it gets you to the correct answer. If you really want, go ahead and use $\ce{Na\ - \ e^{-} -> Na+}$, or go all out and use $\ce{-Na^{+}\ - \ e^{-} -> - Na}$. However, as Richard Feynman discovered while learning trigonometry, if you start using too much obscure/uncommon/personal notation, you get into trouble showing others your work, which makes doing science hard. Standardizing notation is just a way to save time and headaches later on.

The most basic chemical equations actually carry very little chemical information, to the point that it's easy to write reactions which are chemically outrageous. One of their most fundamental purposes is simply to establish atom conservation (which is why so much time is spent on teaching how to "balance" reactions). Thus, chemical equations are always equivalent to a system of linear equations, which is why you can treat them like such and add/subtract molecules to both sides, multiply by a number, add two different reactions together, etc. Using negative stoichiometric coefficients would thus be a very trivial extension of this behaviour, and the equation would remain completely valid.

Let's look at an example. Take the intermolecular dehydration of ethanol to produce diethyl ether:

$$\ce{2 C2H5OH -> C2H5OC2H5 + H2O}$$

The equation is just as valid if you subtract a water molecule from each side:

$$\ce{2 C2H5OH\ -\ H2O -> C2H5OC2H5}$$

Not many people would write the above equation. However, we do have another type of standardized notation which is often used, and which involves a negative stoichiometric coefficient. Using this notation, the equation is written as:

$$\ce{2 C2H5OH ->[\ce{- H2O}] C2H5OC2H5}$$

The water molecule has a legitimate negative stoichiometric coefficient of -1, and again the equation is exactly as valid as all of the ones above. Why is it that negative stoichiometric coefficients are rarely written in the reactants or products, but common when written atop the reaction arrow? I have no idea, but ultimately it makes no difference. That's just how notation happened to become standardized, and if everyone understands it, that's fine.

• Thanks ! Just one more question: is it standard (or at least common) to use the last form of equation with other things as well? For the sake of example, (using the Sodium equation once again) can I write" Na--> Na+ "(with minus electron written on top of the arrow)? Will that be accepted? – Bob Ting Dec 13 '15 at 14:15
• Putting things other than water on top of the arrow is very common. It is done occasionally for electrons, e.g. see this and this. However, if your teacher said not to use negative stoichiometric coefficients, then you probably shouldn't test their resolve. It's good that you questioned the requirement and have learned more in the process, but there's no need to give your teacher a hard time about it. – Nicolau Saker Neto Dec 13 '15 at 20:48
• You can talk about negative stoichiometric coefficients with your teacher if you want, but don't try to be a rebel for the sake of it and go brazenly filling out your tests with them! – Nicolau Saker Neto Dec 13 '15 at 20:50
• Well, that bounty went exceptionally well. May I encourage you to include your comments into the answer, that would be really neat. I'll assign the bounty when I have time to pick for a new target. – Martin - マーチン Dec 20 '15 at 10:45
• @Martin Sorry for the extremely delayed response, but thank you for the exposure. To be honest I feel like my answer wasn't worthy of so much positive attention! I'd rather not bump the question to the top again just to add the comments (hopefully SE visitors always check the comments), but I'll think about it. – Nicolau Saker Neto Dec 29 '15 at 22:33

It's not a matter of what's conventional and what isn't. In real life, nothing can be subtracted or erased as is done in arithmetic. The law of conservation of mass, energy, etc applies. Thus when a Sodium Atom is Reduced to a Na+ Ion You cannot Right Na - e- = Na+ because the electron isn't disappearing, it's being ionically shared with another element via electrostatic forces of attraction.