Reversible Reactions and the Concept of Dynamic Equilibrium

A reversible reaction can proceed in both directions, and chemical equilibrium is the state in which the forward and reverse reaction rates are equal, so that the concentrations of reactants and products stay constant even though both reactions continue. In brief: in A ⇌ B with k_f = 0.20 min⁻¹ and k_r = 0.10 min⁻¹, the system reaches equilibrium when 0.20[A] = 0.10[B], that is [B]/[A] = 2.

Not every reaction goes to completion. In many cases, the products can react to re-form the reactants, and the system settles into a balance in which both are present. Equilibrium is a dynamic state, not a static one: nothing seems to change at the macroscopic level, while at the molecular level reactions continue in both directions at the same rate. This article explains reversibility and the features of equilibrium, follows a system as it approaches equilibrium in a data table and gives examples.

What is a reversible reaction?

A reversible reaction is written with a double arrow, ⇌. For example, when dinitrogen tetroxide (colorless) is heated in a sealed tube, it dissociates into nitrogen dioxide (brown): N₂O₄ ⇌ 2NO₂. The reverse reaction takes place when NO₂ molecules collide and combine. A reaction that goes completely in one direction, such as the burning of paper, is written with a single arrow. In principle all reactions are reversible, but for some the reverse reaction is negligible under the usual conditions.

What is dynamic equilibrium?

When the reactants are mixed in a closed container, the forward reaction starts at its highest rate, and the reverse reaction at zero because there are no products. As the reactants are used up, the forward rate falls, and as products accumulate, the reverse rate rises. At some point the two rates become equal:

rate_forward = rate_reverse

From this point on, the net change is zero and the concentrations remain constant. This is dynamic equilibrium. The same equilibrium composition is reached whether one starts with pure reactants, pure products or a mixture of the two, at the same temperature.

How does a system approach equilibrium?

The table follows the reaction A ⇌ B, starting with [A] = 1.00 M and no B, for k_f = 0.20 min⁻¹ and k_r = 0.10 min⁻¹. Both reactions are first order, so the rates are k_f[A] and k_r[B].

Approach to equilibrium for A ⇌ B
Time (min)	[A] (M)	[B] (M)	Forward rate (M/min)	Reverse rate (M/min)
0	1.000	0.000	0.200	0.000
2	0.699	0.301	0.140	0.030
5	0.482	0.518	0.096	0.052
10	0.367	0.633	0.073	0.063
20	0.335	0.665	0.067	0.067
Equilibrium	0.333	0.667	0.0667	0.0667

The forward rate falls and the reverse rate rises until they meet. At equilibrium [B]/[A] = 0.667 / 0.333 = 2.00, which equals k_f/k_r = 0.20 / 0.10. This ratio is the equilibrium constant.

Approach to equilibrium for A ⇌ B with k_f = 0.20 min⁻¹ and k_r = 0.10 min⁻¹, starting with 1.00 M A. [A] falls and [B] rises until both level off at 0.333 M and 0.667 M (dotted lines), where [B]/[A] = 2.00. After about 15 to 20 minutes the concentrations hardly change, although both reactions continue.

What are the features of equilibrium?

It requires a closed system: if a gas can escape or the products are removed, equilibrium cannot be reached.
It is dynamic: reactions continue in both directions at equal rates.
The macroscopic properties are constant: concentration, color, pressure and temperature do not change.
It can be approached from either side: the same composition results.
It depends on temperature: a change in temperature shifts the equilibrium.
The amounts are not equal: equilibrium means equal rates, not equal concentrations.

Examples of equilibrium systems

Examples of dynamic equilibria
System	Equilibrium	Type
Water in a closed bottle	H₂O(l) ⇌ H₂O(g)	Physical (phase)
Saturated salt solution	NaCl(s) ⇌ Na⁺(aq) + Cl⁻(aq)	Physical (solubility)
Brown gas in a sealed tube	N₂O₄(g) ⇌ 2NO₂(g)	Chemical
Ammonia manufacture	N₂ + 3H₂ ⇌ 2NH₃	Chemical
Vinegar in water	CH₃COOH ⇌ H⁺ + CH₃COO⁻	Acid–base
Carbonated drink	CO₂(g) ⇌ CO₂(aq)	Gas solubility

The position of equilibrium varies widely. For some reactions the mixture contains mainly products, and the reaction is said to “go to completion”; for others it contains mainly reactants, and little reaction seems to take place.

How do we know equilibrium is dynamic?

Experiments with isotopes show that nothing stops at equilibrium. If a saturated solution of lead(II) iodide in contact with solid is mixed with a trace of radioactive iodide ions, the radioactivity soon appears in the solid, although the amount of dissolved lead iodide does not change. This shows that dissolved ions continue to deposit on the solid, while the solid dissolves at the same rate. In a similar way, water labeled with ¹⁸O added to an equilibrium mixture of water and vapor soon appears in both phases.

How was equilibrium discovered?

The French chemist Claude Louis Berthollet noted in 1799, during Napoleon’s expedition to Egypt, that sodium carbonate formed at the edges of salt lakes, where a great excess of sodium chloride reacted with limestone. In the laboratory, sodium carbonate reacts with calcium chloride to give calcium carbonate and sodium chloride, so this was the reverse of the expected reaction, and he concluded that the direction of a reaction depends on the amounts of substances present. The quantitative law of mass action was formulated by Cato Guldberg and Peter Waage in 1864, and Max Bodenstein’s measurements on the hydrogen–iodine system in the 1890s confirmed it.

Which mistakes are common?

Believing that reactions stop at equilibrium: they continue at equal rates.
Thinking that concentrations are equal at equilibrium: the rates are equal, not the concentrations.
Forgetting the closed system: an open container allows products to escape.
Mixing up rate and extent: a fast reaction can have an unfavorable equilibrium.
Assuming that equilibrium needs a catalyst: a catalyst only gets there faster.