So now let's go to the short video lecture, in which we introduce the great Swedish chemist Svante Arrhenius, who quantified for us the important observation that chemical reactions happen more rapidly as we go to higher temperatures. And in fact, they happen more rapidly at an exponentially faster rate. That concept is one that we're going to see helpful in understanding solid state diffusion, but also in a number of other similar applications throughout the remainder of this course. And now we'll have a lesson on diffusion, the transport of atoms within a solid material. And to begin. Let's acknowledge a very important relationship, temperature relationship of chemical reaction rates, originally identified in that regard in the late 19th century. So, what this equation is telling us is at the rate at which chemical reactions occur, increase exponentially with temperature. We see temperature over here on the right side of the equation. It's important to appreciate that that temperature is in the denominator of this exponential term, but it is also in an exponential term that is negative. So if we think that through that means that ultimately as the temperature increases, The rate will increase also, and we'll see very specific examples shortly. We call this the Arrhenius equation, because we're indebted to Svante Arrhenius, a great Swedish chemist from the 19th century. One of the great scientists of the 19th century, he very appropriately won the second Nobel prize in chemistry for this work. In spite of the fact that he was a personal friend of Alfred Nobel, the benefactor for the Nobel prizes, he richly deserved this honor because again, this equation is of tremendous utility and understanding of the nature of chemical reactions in general across a wide temperature range. And very broadly gives us an expression that allows us to appreciate that exponential dependence on temperature for any thermally activated process and again, we'll see in this chapter that diffusion is an excellent example. And we begin to see how this somewhat complex looking small equation becomes elegantly simply if we simply take the logarithm of both sides of the previous form. So we have the logarithm of the rate is equal to the logarithm of that exponential term. And of course the natural logarithm of the base e, is the argument of that exponential and so that is -Q over RT. And the logarithm of a product is the sum of the logarithms, and so the right side of the equation becomes the logarithm of the pre-exponential constant, and the argument of the exponent. So Q over R now becomes the slope of a linear plot. This is basically y is equal to mx plus b, in the usual form, y is we think of y as mx plus b. We have our mx over here and our b over here. So we can look at a plot of this equation, this now nicely linear equation. So, we see as we look at a set of data points with a typical experimental scatter along a wide temperature range, that the best fit through that is a straight line slope. And again, that slope is the minus q over r. Also, because we're plotting this against 1 over temperature and the 0 on that scale is going to correspond to the hypothetical case of 1 over infinite temperature, then we can simply extend this experimental spot to the intercept and get the value then of the logarithm, natural logarithm of the pre-exponential constant. So we have the ability now to be very quantitative about monitoring the rate of chemical reactions.