 Oh, excuse me. I was working on my concentration. Actually, we're not going to be talking about that kind of concentration today. We're going to be talking about a different sort of concentration. So, let's talk. In science and engineering, we have common ways to measure the amount of something. And there are sort of three ways that we typically do that. We can do a unit count. We can count things by how many individual entities there are. For example, we might have 50 apples. Or we might have three dozen eggs. Or another example might be, oh, let's say 10 moles of oxygen. And again, remembering moles is something similar to a dozen, where it's a count of the number of molecules. Or, that's one way that we do things. We can also talk about the mass of something. And often mass slash weight, I'm going to put weight here, because often when we're doing our measurements near the surface of the earth, we can exchange mass and weight, even though they're not exactly the same thing. We can exchange them through some conversion factors. But our mass and our weight is another way to talk about the amount of something that we have. For example, perhaps we have 30 grams of salt. Or 750 milligrams of vitamin D. Might be in the pill that you took this morning, for example. Or one ton of bricks. Again, now I'm talking about a weight as opposed to a mass. So that's our second sort of idea or method of measuring amount. And our third one is generally using volume. And in volume, we're measuring the amount of space something takes up. For example, one gallon of iced tea, which apparently you can buy as part of a meal at Bojangles, for example. Or 10 acre inches of rainfall, which is the amount of space or the amount of volume that some rain would actually, an inch of rain over 10 acres would take up, for example. Or a more simple version that we might be familiar with, maybe we have a graduated cylinder, we measure 100 milliliters of water. Now it's sometimes useful to relate these measurements to each other. For example, we know the density is equal to mass over volume. For example, we know the density of water is one gram per milliliter. So that's one relationship. We can measure the molar mass. For example, the molar mass of carbon dioxide is 44.01 grams per mole, not milliliter per mole. So for one mole of carbon dioxide where we've counted them up, we actually determined the mass is 44.01 grams. So now we're relating our mass to our unit count. And you might also recognize maybe I have three apples per pound. For example, it might be the number of apples where we're counting the apples and we're fitting them into a weight. How much, how many apples you can get if you buy one pound of apples. So we're used to relating these different amount values to each other, but usually when they're referring to the same entity, to the same thing. In this case, the water or referring to the carbon dioxide or referring to the apples. Often, however, we're going to have mixtures of things that are two different substances or two different entities. For example, if you have water, water vapor mixed into air. If we have homogeneous mixtures and by homogeneous, I mean mixtures that are the same phase. In other words, both things are gaseous or both things are liquid or potentially even both things are solid. So long as we have mixtures that are the same, gas with gas or liquid with liquid, etc., then these are called solutions, mixtures of multiple substances. Typically, we'll have more than one thing, but there will be one particular substance that is in the majority. And the majority substance is called the solvent. And any minority substances, things that we have less of, are called solutes. So we're interested in the relationships between the different substances, the different amounts of different substances now. And those relationships, the relationship between different amounts of different substances, different substances, there's a term for that and that term is called concentration. And in general, the concentration is going to be the amount of solute divided by the amount of solution. It's a ratio between two amounts, some portion of the solution and the whole of the solution. In the same way that we had different ways of expressing amounts of one substance, we have different ways of expressing concentrations of the relative value of two different substances or one substance to the whole. By combining ratios of these two things. For example, we can have the count of my solute divided by the count of molecules in the entire solution. And notice we have a number of different possible combinations. The count over the mass, the count over the volume, and given the three combinations, we actually have nine possible combinations that we can put together here. Again, note that each of these things are relating one kind of substance, again the solute, to a larger mixture of substances, the entire solution that we're talking about here. So there are names for some of these. Some of these are very commonly used and there are names for them. For example, if we're counting molecules, this is usually termed the mole fraction. If we compare our molecule count instead to the mass of the overall system, this would be called the molality. And if we compare it to the volume, this is called the molarity. These are values commonly used in chemistry. The values here, this set of values here are often commonly used as well. Whereas the ones over here, generally, we don't count just some portion, count the overall, and then measure the mass of the volume of the smaller version. So these versions here are not used quite as frequently as the others. But the versions here where we're comparing mass to mass or volume to volume are very frequently used. And usually we will often compare mass to volume when we have something like water as the main solvent, because we know that water has that nice relationship of the density of 1 gram is equal to 1 milliliter. So often it's similar to a mass-mass comparison, but because we interchange the number 1 gram for 1 milliliter so easily, then mass over volume will often be used when the solvent is water. So when the measures are the same, for example, mass over mass or volume over volume, what we typically do is use something called parts per measurement. And you're already familiar with parts per because you've probably worked with percent. Percent is our fancy way of saying a certain number of parts per 100. For example, if I have three apples out of a total of 10 fruits, well, that's equal to 0.30 or 30%. Well, we can interpret that as being 30 apples per 100 total fruit. In the same way that percent is a fractional relationship that is multiplied by 100, so parts per 100, we also have some very typical values we use or abbreviations we use. Pt stands for parts per 1,000. This is also known as per meal, P-E-R-M-I-L-L-E, although that's less frequently used, at least in English. Ppm is parts per million, which means you might have 1 gram of a particular solute in 1 million grams of overall solution. And finally, Ppb stands for parts per billion. So this is again when we're talking about very, very small amounts relative to the overall solution in which they are contained. Note that for some applications, in some cases, the amount of, instead of it being the amount of solute over the total amount of solution, in some cases it may be simpler to simply measure the amount of solvent and replace that in the solution. Usually this is only done in applications where it's not going to be that important, where the variation is not going to be significant. For example, if you're talking about something that's two parts per billion, notice that that is very close to being equal to two parts per 999,999,998. In other words, those relationships are too close to be distinguished, so usually the measurement isn't, the detail isn't important. The other thing we want to notice here is that there are two ways we talked about of possibly measuring these. One of those was mass over mass, and the other one was volume compared to volume. Again, the distinction between these two things is important to notice, and usually in chemistry they will often use mass as weight over weight, because if you notice if we multiply the mass in both cases by the acceleration to the gravity, we get the same relationship, the same ratio. So often it will be called weight over weight, although it will be reported as grams over grams, or the measurements will often be done using masses. But in this case, if you have something like this and you're comparing weight to weight, that is different than if you compare volume to volume. Usually weight over weight is better if you're working with something like gases, because gases will often expand or contract with temperature, or pressure, or other relationships sort of, basically the volume is liable to change. So usually we want some consistency by measuring things in terms of weight. However, with liquids, you're often going to be much easier to simply measure things using a volume. So often we'll use volume over volume terms. Again, it can be important to report which way you're reporting your concentration, but as the densities are relatively close to each other, the density of whatever your solute is, if that's pretty close to the overall density of your solution, then the distinction is again unimportant. Particularly, if you have values in the parts per million or parts per billion, then the overall density is going to be very close to the density without whatever your contaminant is in this particular case. So, multiple ways of considering this idea of concentration, but again, the idea here is that your concentration values are going to be a ratio of two values. How much or an amount of solute over an amount of total solution.