Chemical Equilibrium and Gibbs's Energy

This simulation illustrates the time evolution of a reversible chemical reaction, from a given set of initial reactants concentration until chemical equilibrium is reached. The concentrations are plotted against time and the respective numerical values are periodically displayed at the data Table. As chemical equilibrium is attained, the concentrations become constant, the reaction quotient (Q) equalizes the equilibrium constant and Gibbs's energy change (G/RT) approaches zero.

Model

In general, a chemical reaction does not occur in a unique step from the reactants to the products, but by a sequence of intermediate elementary steps, being the slowest one what determines the gobal rate reaction.

Suppose, the reversible global reaction at a fixed temperature and pressure:

A ⇄ C

that proceeds according to the mechanism:

A ⇄ B with k_ab the rate constant of A → B and k_ba the rate constant of B → A

B ⇄ C with k_bc the rate constant of B → C and k_cb the rate constant of C → B

where B is an intermediate species. The 1st order elementary and unimolecular reaction steps obey the following system of coupled rate equations:

d[A] / dt = k_ba [B] - k_ab[A]

d[B] / dt = - k_ba [B] - k_bc [B] + k_ab [A] + k_cb [C]

d[C] / dt = k_bc [B] - k_cb [C]

where [ ]'s are the concentrations of the chemical species.

Given a set of intial concentrations, the differential equations can be numerically solved to work out the concentrations along the time. From them, the reaction quotient and the Gibb's energy can be estimated.

When the dynamic chemical equilibrium is achieved both the forward and back reactions are taking place simultaneously at the same rate, so the concentrations become constant. This does not mean, of course, that the reactions have stop, but that the concentrations of each chemical species disappearing and forming, at any instant of time, are equal.

References:

- "Numerical integration of rate equations on a microcomputer", G. Ercolani and P. Mencarelli, Education in Chemistry, November 1986, p.p. 176-178.

- "Chemistry", R. Chang and K. A. Goldsby, 11th edition, McGraw Hill, New York, 2012.

Author: Fernando M.S. Silva Fernandes
University of Lisboa, Portugal

Email: fsilva@fc.ul.pt