Writing Chemical Equations for Reactions at Equilibrium Chemistry Tutorial

Key Concepts

• An arrow (→) is used in a balanced chemical equation to indicate that the chemical reaction is irreversible and goes to completion:

  reactants → products

• If a chemical reaction or physical change is reversible and reaches a state of dynamic equilibium, the equilibrium arrow (⇌) is used.

  reactants ⇌ products

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Chemical Equations for Irreversible Reactions

A chemical reaction or physical change is irreversible if :

• the reaction (reversible or irreversible) occurs in an open system and one or more reactants or products escapes from the system
• the reaction itself is irreversible (occurs in only direction)

Combustion reactions (burning in oxygen) is an irreversible chemical change.
Various carbon-containing substances are used as fuels because they release a lot of energy when they combust (burn).
Coal has been burnt in fireplaces to provide warmth. Coal (solid carbon) combusts by combining with oxygen from the air to produce a gaseous product, carbon dioxide.
The carbon dioxide gas escapes from the system by entering the atmosphere because this is an open system.
When we write a balanced chemical equation for this reaction we use the single direction arrow which points towards the products, →, as shown below

This chemical equation tells us that the coal (C(s)) will continue to react with oxygen gas (O₂(g)) until either there is no carbon left to react, or, there is no more oxygen left to react.
This chemical reaction goes to completion.
This chemical reaction is irreversible, it occurs in only one direction, because the carbon dioxide gas is not decomposing into coal and and oxygen gas at the same time as the coal is combining with oxygen to produce carbon dioxide.

You have probably added an acid like hydrochloric acid to a metal like magnesium in a test tube and watched bubbles of hydrogen gas form and rise up to the surface of the solution and escape into the atmosphere.
This is an open system (hydrogen gas is escaping to the atmosphere).
The reaction is irreversible because it goes in only one direction, that is, magnesium reacts with acid to produce a soluble salt and hydrogen gas, but, the hydrogen gas is not reacting with the soluble salt to reform the magnesium metal and acid.
For this reaction we use the single direction arrow pointing towards the products (reactants → products):

This chemical equation tells us that this reaction will go to completion, that is, the reactants will continue to produce products until either there is no more magnesium metal left to react, or, there is no more acid left to react.

Similaraly, if you add acid like hydrochloric acid to a carbonate like calcium carbonate (found in limestome and marble), you will produce a soluble salt (calcium chloride), carbon dioxide gas and liquid water. If you perform this experiment in an unstopppered test tube, this is an open system and the carbon dioxide gas will escape from the system and enter the atmosphere. The reaction is irreversible because it occurs in only one direction, acid reacts with carbonate to produce salt, carbon dioxide gas and water, BUT, the salt and carbon dioxide gas and water do not react together to reform the calcium carbonate and acid.
For this reaction we use the single direction arrow pointing towards the products (→) as shown below:

This chemical equation tells us that this reaction goes to completion, that is, the acid and carbonate continue to react to produce products until either there is no more carbonate left to react, or, there is no more acid left to react.

Very few chemical reactions are truly irreversible.
Chemical reactions and physical changes are generally reversible.
A chemical or physical change that is reversible and occurs in a closed system can reach a state of dynamic equilibrium ...

Chemical Equations for Systems at Equilibrium

A reversible chemical or physical change can reach a state of dynamic equilibrium if it is a closed system (matter cannot enter or leave the system).
At equilibrium, the system will contain some of each reactant and product.
At equilibrium, the concentration of each reactant is constant, and, the concentration of each product is constant.
When the system is in a state of dynamic equilibrium, the rate at which reactants react to produce products is equal to the rate at which products react to re-form reactants.

Physical changes in a closed system can achieve a state of dynamic equilibrium.
20 mL of liquid water in a 250 mL sealed volumetric flask is a closed system.
Liquid water will absorb energy to produce water vapor:

But, because this physical change is reversible, at the same time in the closed system, water vapor will be releasing energy to condense and produce liquid water (note the direction of the arrow, ←, in the chemical equation below):

Now, if we just combined those two reactions into one equation using the single direction arrows (→ and ←) as shown below:

we have a problem! If we write the equation in this way it tells us that ALL the liquid water evaporates to produce water vapor until no liquid is left and then ALL the water vapor condenses back into liquid water until no water vapor is present, then we we do it all over again, ad infinitum.
But this is NOT what happens at all.

In the sealed flask we have both liquid water AND water vapor present at the same time!
If we allow this closed system to come to dynamic equilibrium, then the rate at which the liquid water evaporates is the same as the rate at which the water vapor condenses.

We solve this problem by using a different kind of arrow, actually two half-arrows (or harpoons) pointing in opposite directions, ⇌, as shown below:

When we read this chemical equation we say that liquid water is producing water vapor at the same time (and at the same rate) as water vapor is producing liquid water.

Chemical reactions in which all the reactants and products are gases (an example of a homogeneous reaction mixture) will reach a state of dynamic equilibrium in a sealed vessel (a closed system).

For example, if we allow some colourless hydrogen gas to react with purple iodine gas in a sealed vessel, the purple colour fades a bit as colourless hydrogen iodide gas is produced, but the purple colour never disappears entirely because the system reaches a state of dynamic equilibrium in which hydrogen gas, iodine gas and hydrogen iodide gas are all present at the same time.
When this systen reaches a state of dynamic equilibrium, the rate at which hydrogen gas and iodine gas react to produce hydrogen iodide is the same rate at which hydrogen iodide gas is breaking apart (decomposing) to re-form hydrogen gas and iodine gas, so we use the equilibrium arrow (⇌) as shown below:

This reaction does not go to completion but achieves a balance where hydrogen, iodine and hydrogen iodide are all present at the same time and the concentration of hydrogen, iodine and hydrogen iodide is constant.

If we dissolve a salt, say blue copper sulfate, in water, the solution will turn blue was the copper sulfate breaks apart into ions which are completely surrounded by water molecules to produce an aqueous solution of copper sulfate.
If we add more copper sulfate to the water than the water is capable of dissolving, then we will have a blue solution but we will also have some solid blue copper sulfate on the bottom of the vessel.
This system is also a system that reaches dynamic equilibrium, because the rate at which the solid copper sulfate is dissoving in the water is the same as the rate at which copper ions and sulfate ions in the solution are coming together to re-form solid copper sulfate.
In this case we must use the equilibrium arrow in the balanced chemical equation:

Note that water is the solvent and does not appear in this equation as a reactant. We know that water is the solvent because we used (aq) to indicate the formation of an aqueous solution.
And a further note of caution ... we write this chemical equation as an equilibrium reaction even if it occurs in an open system (for example an unstoppered test tube) because we are assuming that the rate of evaporation of the solvent (water) is slow and will not be affecting the concentration of ions during the course of the experiment (or while we are observing it).
We make similar assumptions when we write chemical equations for precipitation reactions.
For example, if you mix colourless aqueous solutions of silver nitrate and sodium chloride in a test tube, we produce silver chloride, a white precipitate (a white solid), and an aqueous solution of soluble sodium chloride.
The reaction is reversible, and can achieve a state of dynamic equilibrium in a closed system in which the rate of formation of the silver chloride precipitate is the same as the rate at which the silver chloride breaks apart to re-form the silver ions and and chloride ions.
We use the equilibrium arrow (⇌) for this chemical reaction as shown below:

Even though the test tube represents an open system, the assumption is that the rate of evaporation of water is so slow that it will not affect the concentration of ions present in solution. This assumption is quite good as long as our observation of the experiment occurs over a short period of time (if we extend the same experiment over a long period of time we would need to put a rubber bung in the mouth of the test tube to make it a closed system).

Summary: When to Use Each Type of Arrow

Use the single direction arrow (→) if

• the chemical reaction goes to completion
• the chemical reaction is irreversible
• the chemical reaction occurs in an open vessel and cannot achieve a state of dynamic equilibrium

Use the equilibrium arrow (⇌) if the chemical reaction (or physical change) is reversible and

• occurs in a closed vessel so that it achieves a state of dynamic equilibrium
• occurs in an open system BUT reactants and products cannot effectively escape (and reactant or product molecules cannot effectively enter the system from the surroundings)

Note that reactions that involve one or more gases, as either reactants or products, MUST be reversible AND occur in a closed system in order to achieve a state of dynamic equilibrium.

Note that reactions that do NOT involve gases but are reversible are considered to reach a state of dynamic equilibrium even in an open system IF the concentration of reactants and products is effectively constant.

Problem Solving