# How to calculate equilibrium concentrations

## Elements, school book

58 3 THE CHEMICAL REACTION Calculation of equilibrium concentrations In the course of the reaction the concentration of the starting materials decreases and the concentration of the end products increases until the equilibrium concentrations are reached in each case. The decrease and increase of the substances can, however, be related with the help of the reaction equation. First you consider the concentrations at the beginning of the reaction and then the concentrations in equilibrium. A + BD + E at the beginning: c 0 (A) c 0 (B) 0 0 in equilibrium: c 0 (A) - xc 0 (B) - xxx If the values ​​determined for the equilibrium are inserted into the law of mass action, the following applies : c 0 (A) - x = cg (A), c 0 (B) - x = cg (B) and x = cg (D) = cg (E) and the result is: Are the equilibrium constant and the initial concentrations known , x and subsequently the equilibrium concentrations can be determined. In the case of stoichiometrically more complicated reactions, similar considerations apply, taking into account the stoichiometric factors. However, the calculation becomes much more difficult because exponents> 2 can occur, which makes it necessary to solve higher equations. Examples: a) The equilibrium constant for the formation of hydrogen iodide from the elements is at 448 ° C → K = 50.54. The initial concentration of the substances is 0.1 mol / L in each case. The equilibrium concentrations of all substances involved must be calculated. H 2 + I 2 2 HI at the beginning: 0.1 0.1 0 in equilibrium: 0.1 - x 0.1 - x 2x Solving the quadratic equation gives the value 0.078 for x (the second value is chemically meaningless, because x would be greater than 0.1). This gives the equilibrium concentrations: c (I 2) = c (H 2) = 0.022 mol / L and c (HI) = 0.156 mol / L The formation of hydrogen iodide is a typical equilibrium reaction. At the end of the reaction, the starting materials and end products are present in detectable quantities. b) The equilibrium constant for the formation of hydrogen chloride from the elements is K = 2.75 • 10 33. The initial concentrations of H 2 and Cl 2 are, for example, 0.1 mol / L. The exact calculation does not bring any advantages. The equilibrium constant is so large that one can speak of a complete reaction. It is a very good approximation that this reaction resulted in HCl with c g = 0.2 mol / L. Before every calculation, it is therefore useful to examine the equilibrium constant for its chemical significance. With very large and very small equilibrium constants, one very often comes to chemically correct and meaningful results through qualitative considerations and simple calculations. Initial state equilibrium c 0 (I 2) = 9 c 0 (H 2) = 9 cg (I 2) = 2 cg (HI) = 14 cg (H 2) = 2 K = 50.54 Initial state equilibrium c 0 (Cl 2 ) = 9 c 0 (H 2) = 9 cg (Cl 2) ~ 0 cg (HCl) = 18 cg (H 2) ~ 0 K = 2.75 • 10 33 Fig. 58.2: Establishing the hydrogen chloride equilibrium (example b) Fig. 58.1: Setting the hydrogen iodide equilibrium (example a) K = cg (D) • cg (E) cg (A) • cg (B) = x 2 (c 0 (A) - x) • (c 0 (B) - x) K = 50.54 = (2x) 2 (0.1-x) 2 For testing purposes only - property of the publisher öbv