Dynamic Equilibrium Example
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration shows a system with two states is in dynamic equilibrium when the average rate of change (here called the "flux") of the population from state A to state B is equal to that from state B to state A. For example, in a reversible chemical reaction, state A might represent the reactants and state B the products.[more]
You can set the probabilities to go from the red state to the blue or from the blue state to the red; they are represented by the widths of the flux arrows. The current number in each state is represented by the height of the flux arrows and additionally on a scrolling graph. Once equilibrium is obtained, the forward flux, given by the number of reds times the probability of changing to blue, is equal to the similarly defined reverse flux. Thus the arrows will be seen to be approximately equal in area.[less]
Contributed by: William Stewart (February 2013)
Open content licensed under CC BY-NC-SA
The Demonstration can be regarded as representing either a unimolecular process (e.g. a conformational change in a protein switch) or a schematic of a more general chemical reaction, in which case one can regard the red state as the reactants and the blue state as the products. Because the Demonstration is intended for instructional purposes, the positions of the entities have been fixed to make it easy to detect their change of state.
Snapshot 1: You can select either 50 or 500 total particles using the reset buttons. Use 50 to study the effects of transition probability on individual particles and use 500 for smoother graphs.
Snapshot 2: Set the "probability blue to red" to zero in order to simulate the simple case of exponential decay, half life, and so on.
Snapshot 3: After equilibrium is established, you can increase the ratio of red to blue and note the temporary increase in forward flux, until equilibrium is reestablished. This demonstrates Le Chatelier's principle.
"Dynamic Equilibrium Example"
Wolfram Demonstrations Project
Published: February 12 2013