This section will demonstrate the practical aspect of using equilibrium concepts to perform calculations using equilibrium constants. These types of computations are essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
Review: Stoichiometry in Reactions
Many of the useful equilibrium calculations that will be demonstrated here require terms representing changes in reactant and product concentrations. These terms are derived from the stoichiometry of the reaction, as illustrated by decomposition of ammonia:
$$NH_3\;(g)⇌N_2\;(g)+3H_2\;(g)$$As shown earlier in this chapter, this equilibrium may be established within a sealed container that initially contains either NH3 only, or a mixture of any two of the three chemical species involved in the equilibrium. Regardless of its initial composition, a reaction mixture will show the same relationships between changes in the concentrations of the three species involved, as dictated by the reaction stoichiometry (see also the related content on expressing reaction rates in the chapter on kinetics). For example, if the nitrogen concentration increases by an amount x: $$Δ[N_2]=+x$$
Using stoichiometry, we know that the corresponding changes in the other species concentrations are:
$$Δ[H_2]=ΔN_2=+3x$$
$$Δ[NH_3]=-ΔN_2=-2x$$
where the negative sign indicates a decrease in concentration.
Determining Relative Changes in Concentration
Derive the missing terms representing concentration changes for each of the following reactions.
| (a) | $C_2H_2\;(g)$ | + | $2Br_2\;(g)$ | $\rightleftharpoons $ | $C_2H_2Br_4\;(g)$ | ||
| x | __?__ | __?__ | |||||
| (b) | $I_2\;(aq)$ | + | $I^-\;(aq)$ | $\rightleftharpoons $ | $I_3^-\;(aq)$ | ||
| __?__ | __?__ | x | |||||
| (c) | $C_3H_8\;(g)$ | + | $5O_2\;(g)$ | $\rightleftharpoons $ | $3CO_2\;(g)$ | + | $4H_2O\;(g)$ |
| x | __?__ | __?__ | __?__ | ||||
Solution
| (a) | $C_2H_2\;(g)$ | + | $2Br_2\;(g)$ | $\rightleftharpoons $ | $C_2H_2Br_4\;(g)$ | ||
| +x | +2x | -x | |||||
| (b) | $I_2\;(aq)$ | + | $I^-\;(aq)$ | $\rightleftharpoons $ | $I_3^-\;(aq)$ | ||
| -x | -x | +x | |||||
| (c) | $C_3H_8\;(g)$ | + | $5O_2\;(g)$ | $\rightleftharpoons $ | $3CO_2\;(g)$ | + | $4H_2O\;(g)$ |
| +x | +5x | -3x | -4x | ||||
Check Your Learning
Complete the changes in concentrations for each of the following reactions:
| (a) | $2SO_2\;(g)$ | + | $O_2\;(g)$ | $\rightleftharpoons $ | $2SO_3\;(g)$ | ||
| __?__ | +x | __?__ | |||||
| (b) | $C_4H_8\;(g)$ | $\rightleftharpoons $ | $2C_2H_4\;(g)$ | ||||
| __?__ | -2x | ||||||
| (c) | $4NH_3\;(g)$ | + | $7H_2O\;(g)$ | $\rightleftharpoons $ | $4NO_2\;(g)$ | + | $6H_2O\;(g)$ |
| -4x | __?__ | __?__ | __?__ | ||||
Solution
| (a) | $2SO_2\;(g)$ | + | $O_2\;(g)$ | $\rightleftharpoons $ | $2SO_3\;(g)$ | ||
| +2x | +x | -2x | |||||
| (b) | $C_4H_8\;(g)$ | $\rightleftharpoons $ | $2C_2H_4\;(g)$ | ||||
| +x | -2x | ||||||
| (c) | $4NH_3\;(g)$ | + | $7H_2O\;(g)$ | $\rightleftharpoons $ | $4NO_2\;(g)$ | + | $6H_2O\;(g)$ |
| -4x | -7x | 4x | 6x | ||||