[A] × [B] / ([C] × [D]) = k2 / k1 = kequilibrium.
In this way the meaning of the fundamental law of chemical equilibrium may be developed from the consideration of the velocities of the reversible actions, such as are involved in all conditions of equilibrium, and the equilibrium constant represents the ratio of the velocity constants of the two opposite reactions. This conclusion has been fully verified by experiment, the equilibrium constant being, as a matter of fact, found equal to the ratio of the velocity constants.[172]
The relations, so far considered, have been those of the simplest type of reversible reaction. We may now discuss the modifications required for other types of reaction by the law of equilibrium.
When two molecules of any reacting component take part in a reaction—for instance, in A + 2 B ⇄ C + D—the concentration of this component is raised to the second power in the mathematical expression of the law of equilibrium; when three molecules of a component take part, its concentration is raised to the third power, etc.
For instance, hydrogen iodide is decomposed, reversibly, into hydrogen and iodine, according to 2 HI ⇄ H2 + I2. A condition of equilibrium is reached, at a given temperature when
[H2] × [I2] / [HI]2 = K.
At 440°, the results given in the following table were obtained by Bodenstein. The concentrations are expressed in moles per liter.[173] The constant is calcuated according to the equation just given. Analytical errors affect the value of the constant most in the first and last experiments, as a result of the very small concentrations of one component, I2 or H2. [p095]
| [H2] | [I2] | [HI] | K |
|---|---|---|---|
| 0.0268 | 0.000190 | 0.0177 | (0.016) |
| 0.00986 | 0.00203 | 0.0328 | 0.019 |
| 0.00308 | 0.00783 | 0.0337 | 0.021 |
| 0.00175 | 0.0114 | 0.0315 | 0.020 |
| 0.000653 | 0.0204 | 0.0236 | 0.024 |
| 0.000265 | 0.0242 | 0.0202 | (0.016) |
The mechanical significance of the raised powers of the concentrations of components, two or more molecules of which take part in a reaction as indicated, will be discussed further on, in connection with a case of equilibrium between an electrolyte and its ions (Chapter VI, p. [102]).