Introduction

Imagine a beach populated with sunbathers and swimmers. As those basking in the sun get too hot and want to cool off, they head into the surf to swim. As the swimmers tire, they head to the beach to rest. If these two rates of transfer (sunbathers entering the water, swimmers leaving the water) are equal, the number of sunbathers and swimmers would be constant, or at equilibrium, although the identities of the people are constantly changing from sunbather to swimmer and back. An analogous situation occurs in chemical reactions. Reactions can occur in both directions simultaneously (reactants to products and products to reactants) and eventually reach a state of balance.

In this section, you will learn how to predict the position of the balance, the yield of a product of a reaction under specific conditions, how to change a reaction’s conditions to increase or reduce yield, and how to evaluate an equilibrium system’s reaction to disturbances.

Equilibrium

A chemical reaction is usually written in a way that suggests it proceeds in one direction, from left to right. But all chemical reactions are reversible and both the forward and reverse reaction occur to one degree or another depending on the reaction conditions. In a chemical equilibrium, the forward and reverse reactions occur at equal rates, and the concentrations of products and reactants remain constant, although not necessarily equal to each other. If we run a reaction in a closed system so that the products cannot escape, we often find the reaction does not yield 100% products. Instead, some reactants remain after the concentrations stop changing. At this point, when there is no further change in concentrations of reactants and products, we say the reaction is at equilibrium.

For example, when we place a sample of dinitrogen tetroxide (N₂O₄, a colorless gas) in a glass tube, it forms nitrogen dioxide (NO₂, a brown gas) by the reaction:

The color becomes darker as N₂O₄ is converted to NO₂. When the system reaches equilibrium, both N₂O₄ and NO₂ are present (Figure 1). On the left side of the figure, there is only colorless N₂O₄ in the system. But as the reaction progresses and equilibrium is achieved (moving from left to right), we can observe the formation of brown NO₂.

The formation of NO₂ from N₂O₄ is a reversible reaction, which is identified by the equilibrium arrow (⇌). In a reversible reaction, the reactants can combine to form products and the products can combine to form reactants. Thus, not only can N₂O₄ decompose to form NO₂, but the NO₂ produced can react to form N₂O₄. As soon as the forward reaction produces any NO₂, the reverse reaction begins and NO₂ starts to react to form N₂O₄. At equilibrium, the concentrations of N₂O₄ and NO₂ no longer change because the rate of NO₂ formation is exactly equal to the rate of NO₂ consumption, and the rate of formation of N₂O₄ is exactly equal to the rate of consumption of N₂O₄. Chemical equilibrium is a dynamic process: the numbers of reactant and product molecules remain constant, but there is a flux back and forth between them.

We can detect a state of equilibrium because the concentrations of reactants and products do not appear to change. However, it is important that we verify that the absence of change is due to equilibrium and not to a reaction rate that is so slow that changes in concentration are difficult to detect.

We use an equilibrium arrow when writing an equation for a reversible reaction. Such a reaction may or may not be at equilibrium. When we wish to speak about one particular component of a reversible reaction, we use a single arrow. For example, in the equilibrium shown in Figure 1, the rate of the forward reaction:

is equal to the rate of the reverse reaction:

Chemistry in Real Life: Equilibrium and Soft Drinks

The connection between chemistry and carbonated soft drinks goes back to 1767, when Joseph Priestley (1733–1804; mostly known today for his role in the discovery and identification of oxygen) discovered a method of infusing water with carbon dioxide to make carbonated water. In 1772, Priestly published a paper entitled “Impregnating Water with Fixed Air.” The paper describes dripping oil of vitriol (today we call this sulfuric acid, but what a great way to describe sulfuric acid: “oil of vitriol” literally means “liquid nastiness”) onto chalk (calcium carbonate). The resulting CO₂ falls into the container of water beneath the vessel in which the initial reaction takes place; agitation helps the gaseous CO₂ mix into the liquid water.

H₂SO₄(l)  +  CaCO₃(s)   →   CO₂(g)  +  H₂O(l)  +  CaSO₄(aq)

Carbon dioxide is slightly soluble in water. There is an equilibrium reaction that occurs as the carbon dioxide reacts with the water to form carbonic acid (H₂CO₃). Since carbonic acid is a weak acid, it can dissociate into protons (H⁺) and hydrogen carbonate ions (HCO₃^–).

CO₂(g)  +  H₂O(l)   ⇌   H₂CO₃(aq)   ⇌   HCO₃^–(aq)  +  H⁺(aq)

Today, CO₂ can be pressurized into soft drinks, establishing the equilibrium shown above under a higher pressure condition. Once you open the beverage container, however, a cascade of equilibrium shifts occurs. First, the CO₂ gas in the air space on top of the bottle escapes, causing the equilibrium between gas-phase CO₂ and dissolved or aqueous CO₂ to shift, lowering the concentration of CO₂ in the soft drink. Less CO₂ dissolved in the liquid leads to carbonic acid decomposing to dissolved CO₂ and H₂O. The lowered carbonic acid concentration causes a shift of the final equilibrium. The net result is that the CO₂ bubbles up out of the beverage, releasing the gas into the air (Figure 2), results in a soft drink with a much lowered CO₂ concentration, often referred to as “flat.”

Let us consider the evaporation of bromine as a second example of a system at equilibrium.

An equilibrium can be established for a physical change—like this liquid to gas transition—as well as for a chemical reaction. Figure 3 shows a sample of liquid bromine at equilibrium with bromine vapor in a closed container. When we pour liquid bromine into an empty bottle in which there is no bromine vapor, some liquid evaporates: the amount of liquid decreases and the amount of vapor increases. If we cap the bottle so no vapor escapes, the amount of liquid and vapor will eventually stop changing and an equilibrium between the liquid and the vapor will be established. If the bottle were not capped, the bromine vapor would escape and no equilibrium would be reached.

Le Châtelier’s Principle

If a system at equilibrium is subjected to a perturbation or stress (such as a change in concentration) the position of equilibrium changes. This process is described by Le Châtelier’s principle: When a chemical system at equilibrium is disturbed, it returns to equilibrium by counteracting the disturbance.

Effect of Change in Concentration on Equilibrium

A chemical system at equilibrium can be temporarily shifted out of equilibrium by adding or removing one or more of the reactants or products. The concentrations of both reactants and products then undergo additional changes to return the system to equilibrium.

Consider Figure 4, which shows the progression of an equilibrium after two applied stresses. Originally, the test tube contains a solution of [Fe(H₂O)₆]³⁺ in water (left picture). Next thiocyanate, SCN^–, is added to the test tube, which can react with [Fe(H₂O)₆]³⁺ to form a complex with iron, [Fe(SCN)(H₂O)₆]³⁺, resulting in an equilibrium between colorless SCN^–, orange [Fe(H₂O)₆]³⁺, and dark red [Fe(SCN)(H₂O)₆]³⁺ (middle photo):

[Fe(H₂O)₆]³⁺(aq)  +  SCN⁻(aq)   ⇌   [Fe(SCN)(H₂O)₆]²⁺(aq)

Then, silver ions, Ag⁺, are added to the test tube, which removes SCN^– precipitates as a white solid, AgSCN(s) (right photo). The stress on the system in Figure 4 is the reduction of the equilibrium concentration of SCN⁻. Le Châtelier’s principle leads us to predict that the concentration of SCN^– should increase, also increasing the concentration of [Fe(H₂O)₆]³⁺ and decreasing the concentration of [Fe(SCN)(H₂O)₆]³⁺ to restore an equilibrium relationship between all three.

Catalysts Do Not Affect Equilibrium

As we learned during our study of kinetics, a catalyst can speed up the rate of a reaction. Though this increase in reaction rate may cause a system to reach equilibrium more quickly (by speeding up the forward and reverse reactions), a catalyst has no effect on the equilibrium concentrations.

Chemistry in Real Life: Ammonia

The interplay of changes in concentration or pressure, temperature, and the lack of an influence of a catalyst on a chemical equilibrium is illustrated in the industrial synthesis of ammonia from nitrogen and hydrogen according to the equation

N₂(g)  +  3 H₂(g)   ⇌   2 NH₃(g)

A large quantity of ammonia is manufactured by this reaction. Each year, ammonia is among the top 10 chemicals, by mass, manufactured in the world. About 2 billion pounds are manufactured in the United States each year.

Ammonia plays a vital role in our global economy. It is used in the production of fertilizers and is, itself, an important fertilizer for the growth of corn, cotton, and other crops. Large quantities of ammonia are converted to nitric acid, which plays an important role in the production of fertilizers, explosives, plastics, dyes, and fibers, and in the steel industry.

It has long been known that nitrogen and hydrogen react to form ammonia. However, it became possible to manufacture ammonia in useful quantities by the reaction of nitrogen and hydrogen only in the early 20th century after the factors that influence its equilibrium were understood.

To be practical, an industrial process must give a large yield of product relatively quickly. One way to increase the yield of ammonia is to increase the pressure on the system in which N₂, H₂, and NH₃ are at equilibrium or are coming to equilibrium.

N₂(g)  +  3 H₂(g)   ⇌   2 NH₃(g)

The formation of additional amounts of ammonia reduces the total pressure exerted by the system and somewhat reduces the stress of the increased pressure.

Although increasing the pressure of a mixture of N₂, H₂, and NH₃ will increase the yield of ammonia, at low temperatures, the rate of formation of ammonia is slow. At room temperature, for example, the reaction is so slow that if we prepared a mixture of N₂ and H₂, no detectable amount of ammonia would form during our lifetime. The formation of ammonia from hydrogen and nitrogen is an exothermic process:

N₂(g)  +  3 H₂(g)   ⇌   2 NH₃(g)       ΔH = -92.2 kJ

Thus, increasing the temperature to increase the rate lowers the yield. If we lower the temperature to shift the equilibrium to favor the formation of more ammonia, equilibrium is reached more slowly because of the large decrease of reaction rate with decreasing temperature.

The decrease in the rate of formation caused by operating at lower temperatures can be regained by using a catalyst. The net effect of the catalyst on the reaction is to cause equilibrium to be reached more rapidly.

In the commercial production of ammonia, conditions of about 500 °C, 150–900 atm, and the presence of a catalyst are used to give the best compromise among rate, yield, and the cost of the equipment necessary to produce and contain high-pressure gases at high temperatures (Figure 5).

 

Chemistry in Real Life: Fritz Haber

In the early 20th century, German chemist Fritz Haber (Figure 6) developed a practical process for converting diatomic nitrogen, which cannot be used by plants as a nutrient, to ammonia, a form of nitrogen that is easiest for plants to absorb.

N₂(g)  +  3 H₂(g)   ⇌   2 NH₃(g)

The availability of nitrogen is a strong limiting factor to the growth of plants. Despite accounting for 78% of air, diatomic nitrogen (N₂) is nutritionally unavailable due the tremendous stability of the nitrogen-nitrogen triple bond. For plants to use atmospheric nitrogen, the nitrogen must be converted to a more bioavailable form (this conversion is called nitrogen fixation).

Haber was born in Breslau, Prussia (presently Wroclaw, Poland) in December 1868. He went on to study chemistry and, while at the University of Karlsruhe, he developed what would later be known as the Haber process: the catalytic formation of ammonia from hydrogen and atmospheric nitrogen under high temperatures and pressures. For this work, Haber was awarded the 1918 Nobel Prize in Chemistry for synthesis of ammonia from its elements. The Haber process was a boon to agriculture, as it allowed the production of fertilizers to no longer be dependent on mined feed stocks such as sodium nitrate. Currently, the annual production of synthetic nitrogen fertilizers exceeds 100 million tons and synthetic fertilizer production has increased the number of humans that arable land can support from 1.9 persons per hectare in 1908 to 4.3 in 2008.

In addition to his work in ammonia production, Haber is also remembered by history as one of the fathers of chemical warfare. During World War I, he played a major role in the development of poisonous gases used for trench warfare. Regarding his role in these developments, Haber said, “During peace time a scientist belongs to the World, but during war time he belongs to his country.”^[1] Haber defended the use of gas warfare against accusations that it was inhumane, saying that death was death, by whatever means it was inflicted. He stands as an example of the ethical dilemmas that face scientists in times of war and the double-edged nature of the sword of science.

Like Haber, the products made from ammonia can be multifaceted. In addition to their value for agriculture, nitrogen compounds can also be used to achieve destructive ends. Ammonium nitrate has also been used in explosives, including improvised explosive devices. Ammonium nitrate was one of the components of the bomb used in the attack on the Alfred P. Murrah Federal Building in downtown Oklahoma City on April 19, 1995.

Glossary

equilibrium
the point in a chemical reaction where the forward and reverse reactions occur at equal rates and the concentrations of products and reactants remain constant (although not necessarily equal)

Le Châtelier’s principle
when a chemical system at equilibrium is disturbed, it returns to equilibrium by counteracting the disturbance

reversible reaction
the reactants can combine to form products and the products can combine to form reactants, symbolized by equilibrium arrows, ⇌

stress
a perturbation applied to a system at equilibrium