Hey everyone, so in this set of videos we're going to take a look at the idea of thermal dependency. Now, first of all, we're going to say that calibration is the process of measuring the actual quantity of mass, volume, and other chemical measurements that relate to what we observe on an analytical scale. Remember, analytical chemistry itself is the chemistry of precision and accuracy. We want to be as accurate and precise as possible and make sure we minimize any outside factors. A way of doing this is by calibrating our instruments. Now, in general, when taking the measurement of a solution you must take into account any type of thermal expansion that occurs with solutions and instrumentation. To do this, we use a correction for thermal expansion, where cᴛ here represents the concentration of our solution, dᴛ represents the density of our solution, here c represents our new concentration of our solution, and d here represents our new density of our solution.

If we take a look here at this chart, we have temperatures ranging from 10 degrees Celsius all the way to 30 degrees Celsius, and with it, we have the density of water. Now remember, we're accustomed to seeing density as being 1, but that's only true at a specific temperature, pressure, and ideal conditions. Most of the time, density is a value that's less than 1 and here we're seeing the varying forms of density with water. Here we have the volume of 1 gram of water at these different temperatures, so for example, at 10 degrees Celsius, we have a density here and at that temperature, this is the volume that we have. What this number is telling me, it's telling me that at 10 degrees Celsius we deliver 1.0014 milliliters of water for every 1 gram of water. But again, remember, analytical chemistry is the chemistry of accuracy and precision, so we have to correct the basic glassware. And what we do here is we're going to correct it to 20 degrees Celsius. So here this is where the glassware is calibrated at 20 degrees Celsius, and by doing that we get a more accurate read on the volume involved. It now becomes 1.0015 milliliters.

When we're looking at this table, we can also make some observations from it, and we can come up with some ideas. And what we can see here is that as we go from 10 degrees Celsius to 30 degrees Celsius, we can see that the temperature is increasing. As the temperature is increasing, what effect does that have on our density? Well, if you're looking, you could see that our density as we go from 10 degrees Celsius to 30 degrees Celsius, it's decreasing. Now, why would that happen? So think about it, density equals mass over volume. And you learned in general chemistry that temperature and volume are connected to one another. If we're increasing our temperature this is going to cause our volume to increase. Our mass is staying constant, but our volume is increasing as the temperature goes up. What overall effect does this have on our density? Well, the numerator is staying the same but the denominator is increasing. This causes density to decrease. Okay. So that's the connection we need to see here. This is one of the consequences of thermal expansion. It can affect our density by affecting our volume. So now that we've looked at this table and talked about the idea of thermal expansion and the accuracy and precision involved, click on to the next video, and let's continue with our discussion of thermal expansion.