In our earlier lessons on colligative properties, we talked about the importance of accounting for the number of moles of solute that are produced upon dissolution. We used the example of aluminum sulfate, where one mole of solute produces five moles of ions when it dissolves. We are now going to refine that understanding a bit. The main principle that we introduced still applies, but for quantitative accuracy we need to make a slight adjustment. The main idea is that ions, because of their opposite charges, can occasionally act as pairs rather than as individual ions. In this situation, when we are considering the effect of an ion pair on the surface of solvent or the interface with a semi-permeable membrane, that ion pair acts as a single entity rather than as a pair of entities. This means that when we look at an electrolyte, we could predict the multiplicative factor we need to apply based on the number of ions the compounds you separate into, but we may have to make an empirical measurement to determine how accurate that prediction is. This factor we multiply by, called the Vanthof factor, will always be equal to or smaller than the prediction, and the specific value will depend on how concentrated the solution is. Think about that for a moment. In dilute solutions, the ions on average will be quite far apart. As a result, they will only rarely exist in these ion pairs. But at high concentrations, the ions will, on average, be quite close to each other, and so will frequently exist as ion pairs. This means that at low concentrations, the predicted Vanthof factors will be extremely accurate, but at high concentrations, they will begin to deviate significantly. The end experiment always trumps theory. And so while it is wonderful to be able to make predictions for colligative properties, or frankly anything in science, understanding what the assumptions are that went into those predictions, and therefore why there are conditions where reality may differ from those predictions is what makes a person a scientist.