Throughout this unit, I have emphasized the need to understand science at the atomic or molecular scale… where particles behave and interact in only the most basic and concrete ways. Understanding science on that scale is hard work, but I feel that it is worth it. Because in the long run, science at the atomic or molecular scale is simpler and more intuitive. Instead of treating science like a black box, impervious to analysis or synthesis, science should be a tool that we apply, integrate with other tools, and refine.

A chlorine atom has seven electrons in its outer valence shell. It needs one additional electron to achieve a stable electron configuration. When paired with a hydrogen atom, it can achieve that stable configuration by either sharing an electron with the hydrogen atom and forming a covalent bond, or taking an electron from the hydrogen atom and forming an ionic bond.

Because both of these configurations are stable, they exist in dynamic equilibrium. This means that covalently bonded HCl molecules can undergo a dissociation reaction and break into separate H+ and Cl- ions; and H+ and Cl- ions can undergo an association reaction and re-form HCl molecules.

The tendency of HCl molecules to dissociate and H+ and Cl- ions to associate depends on the relative stability of the two configurations, and the amount of activation energy required to move between them.

When dissolved in water and surrounded by polar water molecules, the dissociated state is actually more stable than the associated state, and it takes less energy and is much more likely for an HCl molecule to separate into H+ and Cl- ions than for a pair of H+ and Cl- ions to re-form an HCl molecule.

Substances that dissociate in water to form H+ ions are classified as acids. HCl is known as hydrochloric acid. The acidity of a solution is determined by the concentration of H+ ions in the solution. A solution with a higher concentration of H+ ions is more acidic than a solution with a lower concentration.

To model a hydrochloric acid and water solution, we need to model the dissociation reaction and the association reaction. The rate of dissociation (rated) should depend on two factors: the concentration of HCl molecules in the solution ([HCl]) and the probability that an individual HCl molecule will dissociate (probd). The higher the concentration, the more HCl molecules there are to dissociate. The higher the probability, the more likely an HCl molecule will dissociate.

Imagine that we have a solution with an HCl concentration of 0.1 mol/L. This means that there are 6.022 × 1022 molecules of HCl in one liter of solution… or 100 molecules in 1.66 × 10-20 mL. Zooming in on a 1.66 × 10-20 mL sample of solution, we can watch as the HCl molecules dissociate over time.

The probability that an individual HCl molecule will dissociate also depends on a number of factors. For example, the higher the temperature of the solution, the more energy each HCl molecule will have and the more likely an HCl molecule will have the activation energy to dissociate. I set up this simulation so that an HCl molecule has a 50% chance to dissociate every two seconds. This means that 50% (or 50) of the molecules in our sample will dissociate in the first two seconds, and 50% (or 25) of the remaining 50 molecules in our sample will dissociate in the next two seconds.

The rate of dissociation in our simulated 0.1 mol/L HCl solution starts out at 0.025 mol/L·s, but the rate drops as soon as the concentration of HCl molecules in the solution drops because the rate is directly proportional to the concentration.

In reality, HCl molecules dissociate at a much faster rate. Ideally, I would calibrate the simulation using experimental data from the real-world dissociation of hydrochloric acid. But since I do not have that data, I am going to have to estimate the probability that an individual HCl molecule will dissociate. This should not affect the equilibrium state of our simulated acid solution, but it will affect how quickly equilibrium is reached.

The rate of association (ratea) should also depend on two factors: the concentration of H+ and Cl- collisions in the solution ([collision]) and the probability that an individual collsion will result in the formation of an HCl molecule (proba).

I know from experimental data that an HCl molecule dissociating is 2,000,000 times more likely than a H+ and Cl- collision causing an association reaction. So while I do not know the actual values of probd and proba, I do know that:

The tricky part is figuring out the concentration of collisions between H+ and Cl- ions in the solution. The concentration of collisions should depend on the concentration of H+ and Cl- ions in the solution. The more concentrated the ions, the more collisions there are.

A dynamic equilibrium is reached when the rates of these two reactions are balanced and the concentrations of HCl molecules, H+ ions, and Cl- ions in the solution are constant over time.