 So as we talk about electrolytic solutions, the stoichiometry of the electrolyte has a lot to do with the properties of the solution, in part because it affects the concentration of the solution, but also for other reasons as well. So for example, suppose we consider two solutions, one that's .01 molar in sodium chloride and one that's .01 molar in calcium chloride. In terms of just the concentration of the salt, they look like they're the same concentration. But of course that's misleading. This salt dissolves into one cation, one anion. So this generates a solution that's .02 molar in ions altogether, whereas the calcium chloride solution dissolves into one cation and two anions. So this will generate a solution that's a total concentration of .03 molar in ions. So already we can see the concentration of ions in the two solutions are different even though the nominal concentrations are the same. But we also know that these more strongly charged anions behave more non-ideally than the more weakly charged ions. So in fact, this solution is even stronger in ions than it appears to be if we consider those non-idealities as well. So for that reason, we need to consider a measure of the strength of the ions in these solutions that isn't just the concentration of ions. And that quantity called the ionic strength is defined as follows. We can add up the concentrations. So if I just stop here, this would be sort of what we've done here. .02 molar is the cation concentration plus the ion concentration. But instead what we're going to do is weight each of those concentrations by the charge on the ions themselves. So this Z sub i is the charge on the ion. So that might be plus 1 for sodium, minus 1 for chloride, plus 2 for calcium, and so on. So that's the ionic charge. This quantity is called the ionic strength, and it's going to turn out to be a very useful measure of the, essentially, as the name says, the strength of the ions, how strongly the ions are behaving in this solution in a way that goes beyond just what the concentration alone can capture it, allows the more strongly charged ions to contribute more strongly to the ionic strength than the weaker charged ions. This is how we define the ionic strength if we're using molarity as our concentration unit. It's just as common to use molality, and if we want to talk about the ionic strength when we measure the concentrations in terms of molality, we can do the same thing, but instead of summing up the molarity times the ionic charges, we sum up the molality times the ionic charges in the solution. So these are still the ion charges. This is still called an ionic strength. Unfortunately, usually we don't discriminate with a different variable between an ionic strength measured in molality or in molarity. We just rely on units in context to determine the difference between them, but this would be a molal ionic strength. This would be the definition of a molar ionic strength. Molality is perhaps more common because molalities, when I combine different solutions together, their masses and their moles sum together unlike volumes. So molality is a more convenient unit for talking about the sums of concentrations of multiple solutions. So let's see what I mean when I say this measure of ionic strength gives us a way to measure the strength of the ions in a solution that weights the more strongly charged ions more heavily. Let's go ahead and calculate the ionic strength of these two solutions that I've considered as an example. So for my first case, .01 molar sodium chloride, a one-to-one salt, just to be extra explicit about the stoichiometry and the concentrations. When I create a solution that's .01 molar in sodium chloride, that'll generate concentrations of .01 molar sodium ions and .01 molar for the chloride ions. These are the values we're going to need to know to calculate the molar ionic strength. So that molar ionic strength, I just need to sum up for all my ions, summing over sodium and chloride ions, concentrations. Oh, actually I've forgotten something very important. These definitions all involve a one-half in front of them. The ionic strength is one-half the sum of these concentrations times ionic strength. So I need a one-half times the sum of concentrations multiplied by ionic charges. So for sodium, concentration is .01 molar. The charge on a sodium is plus one, plus one, and that's squared. I do the same thing for chloride. The concentration of chloride is .01 molar, and I'm multiplying that by a charge of negative one, which gets squared. So .01 times one, .01 again times one. If I add those together, I get .02. So the ionic strength is one-half of .02, so that's .01 molar. So notice in this case, the ionic strength, .01 molar, is exactly the same as the concentration .01 molar of sodium chloride. That's intentional, that's by design. So for a one-to-one salt, the ionic strength is always going to be the same as the nominal concentration of the solution. You can think of this one-half here as accounting for the fact that I've got the cation and the anion added together. So it's removing that doubling of the concentration. Things work out a little bit differently for calcium chloride though. If I have a .01 molar solution of calcium chloride, so again, being explicit about the stoichiometry of .01 molar solution of calcium chloride, we'll generate a solution that's .01 molar in calcium and .02 molar in chloride. And again, these are the values we're going to need to use when I sum up concentrations times charges to get my ionic strength. So the ionic strength is one-half concentrations. So for calcium, the concentration is .01 charge. Charge on the calcium ion is plus two. So plus two quantity squared. I add to that the concentration of chloride ions, that concentration is .02 molar, multiplied by the charge on a chloride ion is negative one, and that quantity gets squared. So in this case, I have .01 times two squared, gives me .04, is the contribution from the cation, .02 times negative one squared is .02. So we can see that the cation is contributing more to the ionic strength than the anion is. There's twice as many of the anion, but the cation is more strongly charged. So numerically, .04 plus .02 is .06. When I have that, I get .03. So the ionic strength of this calcium chloride solution, nominally the same concentration as the sodium chloride solution, but the .01 molar calcium chloride solution has an ionic strength of .03 molar. So it's three times larger as an ionic strength than it was as a nominal concentration. And again, that's because the effect of the calcium ions in solution tends to be much stronger than the effect of the chloride ions. So we define this quantity ionic strength, which captures that. Turns out there's a good reason we use this weighting of ions ionic charge squared, as opposed to cubing it or some other power in that ionic charge, and that'll become more clear when we discuss the Debye-Huckel law in more detail. For now, we can just treat this as a definition of quantity of the ionic strength. For ions with charges greater than one, the ionic strength is always going to be larger than the nominal concentration, and as a way of describing how the effect of those strongly charged ions in solution. So it turns out this ionic strength is also going to be useful in allowing us to predict the activity of the ions in these solutions, and that's what we'll consider next.