1.5 Chemical Equilibria

Effect of a Change in Concentration

If an equilibrium system is subjected to a change in the concentration of a reactant or product species, the rate of either the forward or the reverse reaction will change. As an example, consider the equilibrium reaction

$${\text{H}}_2(g)+{\text{I}}_2(g)\rightleftharpoons 2\text{HI}(g)K_c=50.0\text{at}400\text{°}\text{C}$$

The rate laws for the forward and reverse reactions are

$$\begin{array}{ccc}forward\hfill & {\text{H}}_2(g)+{\text{I}}_2(g)\to 2\text{HI}(g)\hfill & {\text{rate}}_f=k_f{[{\text{H}}_2]}^m{[{\text{I}}_2]}^n\hfill \\ reverse\hfill & 2\text{HI}(g)\to {\text{H}}_2(g)+{\text{I}}_2(g)\hfill & {\text{rate}}_r=k_r{[\text{HI}]}^x\hfill \end{array}$$

When this system is at equilibrium, the forward and reverse reaction rates are equal.

$${\text{rate}}_f={\text{rate}}_r$$ If the system is stressed by adding reactant, either H₂ or I₂, the resulting increase in concentration causes the rate of the forward reaction to increase, exceeding that of the reverse reaction:

$${\text{rate}}_f>{\text{rate}}_r$$

The system will experience a temporary net reaction in the forward direction to re-establish equilibrium (the equilibrium will shift right). This same shift will result if some product HI is removed from the system, which decreases the rate of the reverse reaction, again resulting in the same imbalance in rates.

The same logic can be used to explain the left shift that results from either removing reactant or adding product to an equilibrium system. These stresses both result in an increased rate for the reverse reaction

and a temporary net reaction in the reverse direction to re-establish equilibrium.

As an alternative to this kinetic interpretation, the effect of changes in concentration on equilibria can be rationalized in terms of reaction quotients. When the system is at equilibrium,

$$Q_c=\frac{{[\text{HI}]}^2}{[{\text{H}}_2][{\text{I}}_2]}=K_c$$

If reactant is added (increasing the denominator of the reaction quotient) or product is removed (decreasing the numerator), then Q_c < K_c and the equilibrium will shift right. Note that the three different ways of inducing this stress result in three different changes in the composition of the equilibrium mixture. If H₂ is added, the right shift will consume I₂ and produce HI as equilibrium is re-established, yielding a mixture with a greater concentrations of H₂ and HI and a lesser concentration of I₂ than was present before. If I₂ is added, the new equilibrium mixture will have greater concentrations of I₂ and HI and a lesser concentration of H₂. Finally, if HI is removed, the new equilibrium mixture will have greater concentrations of H₂ and I₂ and a lesser concentration of HI. Despite these differences in composition, the value of the equilibrium constant will be the same after the stress as it was before (per the law of mass action). The same logic may be applied for stresses involving removing reactants or adding product, in which case Q_c > K_c and the equilibrium will shift left.

Chemistry in Everyday Life

Equilibrium and Soft Drinks

The connection between chemistry and carbonated soft drinks goes back to 1767, when Joseph Priestley (1733–1804) developed a method of infusing water with carbon dioxide to make carbonated water. Priestly’s approach involved production of carbon dioxidey reacting oil of vitriol (sulfuric acid) with chalk (calcium carbonate).

The carbon dioxide was then dissolved in water, reacting to produce hydrogen carbonate, a weak acid that subsequently ionized to yield bicarbonate and hydrogen ions:

$$\begin{array}{cc}\text{dissolution}\hfill & {\text{CO}}_2(g)={\text{CO}}_2(aq)\hfill \\ \text{hydrolysis}\hfill & {\text{CO}}_2(aq)+{\text{H}}_2\text{O}(l)={\text{H}}_2{\text{CO}}_3(aq)\hfill \\ \text{ionization}\hfill & {\text{H}}_2{\text{CO}}_3(aq)={\text{HCO}}_3{}^{\text{−}}(aq)+{\text{H}}^{\text{+}}(aq)\hfill \end{array}$$These same equilibrium reactions are the basis of today’s soft-drink carbonation process. Beverages are exposed to a high pressure of gaseous carbon dioxide during the process to shift the first equilibrium above to the right, resulting in desirably high concentrations of dissolved carbon dioxide and, per similar shifts in the other two equilibria, its hydrolysis and ionization products. A bottle or can is then nearly filled with the carbonated beverage, leaving a relatively small volume of air in the container above the beverage surface (the headspace) before it is sealed. The pressure of carbon dioxide in the container headspace is very low immediately after sealing, but it rises as the dissolution equilibrium is re-established by shifting to the left. Since the volume of the beverage is significantly greater than the volume of the headspace, only a relatively small amount of dissolved carbon dioxide is lost to the headspace.

When a carbonated beverage container is opened, a hissing sound is heard as pressurized CO₂ escapes from the headspace. This causes the dissolution equilibrium to shift left, resulting in a decrease in the concentration of dissolved CO₂ and subsequent left-shifts of the hydrolysis and ionization equilibria. Fortunately for the consumer, the dissolution equilibrium is usually re-established slowly, and so the beverage may be enjoyed while its dissolved carbon dioxide concentration remains palatably high. Once the equilibria are re-established, the CO₂(aq) concentration will be significantly lowered, and the beverage acquires a characteristic taste referred to as “flat.”