Question

As far as I understand, the equation for a kinetic equilibrium is always the same, and is given by: K=concentration of productspconcentration of reactantsr Wherepandrare the stoichiometric coefficients. So, for elementary reactions, it is clear that the equilibrium constant is always the same (for the same temperatureT), notwithstanding the initial concentration. For example, for the reaction: A−⇀↽−2B If we assume dummy kinetic rates for forward and reverse reaction: rf=1·cA=[A] rr=3·c2B=3[B]2 Assuming the following:[A]0=10kmol/m3,[B]0=0kmol/m3,˙v=1m3/s. We know that the equilibrium is reached when the rate forward equals the reverse rate rf=rr [A]=3[B]2(1) And if we consider the mass balances: [A]=[A]0−[B]/2[B]=2([A]−[A]0) We can substitute these in the rate expression(1)and solve the equations for the roots: [A]0−[B]/2=3[B]2[B]=1.74,[A]=9.13 And the equilibrium constant is therefore: K=1.7429.13=0.33 And if we change the initial concentration, to something like double:[A]0=20kmol/m3, the result of the quadratic equation changes to: [B]=2.5,[A]=18.75 And the equilibrium constant remains the same: K=2.5218.75=0.33 So everything makes sense. But I understood that this behavior should continue even when the reactions are non-elementary. If we now have the same reaction, but the kinetics are given by: A−⇀↽−2B rf=1·[A]2 rr=3·[B]2 Now it changes. If we develop the mass balance in equilibrium: [A]2=3[B]2 ([A]0−[B]/2)2=3[B]2 For an initial concentration of[A]0=10: [A]20−[A]0[B]+[B]2/4=3[B]2 Solving the quadratic equation and mass balance: [B]=4.48,[A]=7.76 And the equilibrium constant: K=4.4827.76=2.58 And when we repeat the calculations for[A]0=20: [B]=8.96,[A]=15.52 And now the equilibrium constant is: K=8.96215.52=5.17 Why does this happen?

Answer 1

The equilibrium constant is calculated using the concentrations of the reactants and products at equilibrium. For elementary reactions, the constant remains constant regardless of initial concentrations. However, for non-elementary reactions, the equilibrium constant can vary with different initial concentrations.

Step-by-step explanation:

Equilibrium constants (K) are calculated using the concentrations of the reactants and products at equilibrium. The equilibrium constant expression is a ratio of the mathematical product of the concentrations of the products to the mathematical product of the concentrations of the reactants, with each concentration raised to the power of its coefficient in the balanced chemical equation.

In elementary reactions, where the stoichiometric coefficients are the same for both forward and reverse reactions, the equilibrium constant remains constant regardless of the initial concentrations. However, for non-elementary reactions, where the stoichiometric coefficients differ, the equilibrium constant can change with different initial concentrations.

This behavior occurs because the equilibrium constant is determined by the ratio of reactant concentrations to product concentrations at equilibrium. When the stoichiometric coefficients are different, the concentrations of reactants and products can vary, leading to changes in the equilibrium constant.