# Why can you "cancel out" chemical species from a chemical equation that appear on both sides of a chemical equation?

Why is it acceptable in chemistry to "cancel out" chemical species from a chemical equation that appear on both sides of a chemical equation (as reactants and as products)?

On the one hand, it makes sense, since you could argue that if a set amount of a chemical species was used up (reactant) and the exact same amount of the same chemical species was also produced (product), it would seem as if the species was chemically inert and you could "ignore it" from the chemical reaction.

However, on the other hand, you could also argue that the reaction, might not happen if that said chemical species (that appears both as a reactant and a product in the equation) wasn't there.

For example, (this is from an application of Hess's Law exercise), the following reaction:

$$\ce{2CO2_(g) + H_2 O(l) + 2C(s) +\frac{5}{2} O_2 (g) +H_2(g) -> C_2 H_2(g) + 2CO_2(g) + H_2O(l) +\frac{5}{2} O_2(g)} \tag{1}$$

can also be written as:

$$\ce{2C(s) +H_2(g) -> C_2H_2(g)} \tag{2}$$

However, reaction (2), as it is written might not be able to happen, since maybe the chemical species that have been cancelled out, might be needed for the reaction to take place?

• Reaction equations are fundamentally just mathematics, nothing but a system of linear equations written in a different way, purely to establish atom conservation. All the chemistry in reaction equations is tacked on after the fact. So with zero effort you can make mathematically consistent but chemically absurd reactions. Commented Feb 5 at 5:57
• Related, possibly (near) duplicate: Why can we add/substract/cross out chemical equations for Hess law? Commented Feb 5 at 11:42
• Does this answer your question? If a reactant appears on both sides of an elementary equation, can it be cancelled? Commented Feb 5 at 12:07
• What you're talking about in the second part of your question, has to do with mechanisms of reaction, and within that particular subject the equations are written as to reflect the actual compounds/molecules formed in the reaction, even temporarily Commented Feb 6 at 5:29
• @AlexVo I converted your answer into a comment. I agree with what you write but this needs to be expanded. Commented Feb 6 at 10:45

## 3 Answers

The nice thing about chemical equations is that they can be treated algebraically in many cases. You can add or subtract chemical equations. One can add something on both sides. For example in algebra, in 3+a+b = c+d+3, three cancels out leaving behind a+b=c+d. In the same way, if a chemical species is present on the left and the right, it simply would mean that particular entity did not participate in the chemical reaction and it can be cancelled.

On the other hand, there are chemical nuances regarding chemical equations as written. They do not contain all the information about the real reactions.

If we started with a mixture of carbon dioxide, water, carbon and hydrogen as suggested here, supplying heat would result in oxygen combining with hydrogen rather than carbon because of different reaction speeds. Hydrogen will combine with oxygen way to fast before carbon can begin to react.

2CO2(g) + H2O(l) + 2C(s) +5/2 O2 (g) +H2(g) ---> C2H2(g) + 2CO2(g) + H2O(l) +5/2 O2(g) ...(1)

In short, the context matters. When you are treating a system mathematically, chemical equations can behave like algebraic statements. However, when we are thinking in terms of actual chemical reactions, a written chemical equation may not describe the reality or actual products.

In hess's law, we are concerned with the overall energy changes happening due to the reaction that is final - initial and nothing in the intermediate steps. Species reappearing again on the product side do not change the overall energy as their contributions cancel out. Hence just to simplify and to shorten writing amount, we in a sense cancell them out. But this does not mean their presence is meaningless.

The Reactants that are also present on the product act like a catalyst. Or you can say that they actually are important for the reaction but don't involve the breaking and making of bonds. For example,

Photosynthesis can be written as:- 6CO2 + 6 H2O -----> C6H12O6 + 6O2

whereas what actually happens is:- 6CO2 + 12H2O -----> C6H12O6 + 6O2 + 12H2O

We remove the 6H2O in writing the equation. Although it's important for the reaction.

• I think you made a mistake writing out that second equation? Commented Feb 5 at 10:27
• Is that what really happens!! what about plants, chlorophyl, other functional compounds, sunlight etc. Commented Feb 5 at 22:09