 Looking back at our rate concentration graph, you can see that we could do something very similar with rates. The rate is analogous to the volume of the shape, and the concentration, the reactant concentration, is analogous to the length of the width. By varying the concentration we can distinguish between different dependencies on concentration. The rate might be directly proportional to the concentration, or it could be proportional to the square of the concentration, or it might not depend on it at all. And we can turn that proportionality into a proper equation by determining the constant k, which is called the rate constant. So let's take this reaction as a starting point. Ammonium ions and nitrite ions can react together in aqueous solution to give nitrogen gas and water. In order to determine the rate law for this reaction a chemist would do a series of experiments varying the concentration of the ammonium and the nitrite separately and measuring the rate of the reaction just as we varied the length and the width of the prism and measured its volume. And here's a question for you to think about. For this particular reaction what would be a suitable experimental method of measuring the rate? Now in a second I'm going to ask you to pause the video and look at this data. Using the same process that we used for the prism, see what you can get out of the data. What's the rate proportional to? Can you write the full expression? Can you even figure out a constant that converts the expression into a proper equation? Okay, pause the video now and see what you can get out of it. Alright, so let's go through the data. Comparing experiments one and two you can see that the ammonium concentration was doubled while the nitrite was held constant and the effect on the rate was to double. If you look at experiments two and four you can see that the ammonium concentration triples and the rate triples. Although notice that the rate value appears to not quite triple. This could either be the effect of rounding off the data or it could just indicate normal variance or scatter in experimental data which almost never perfect. Nevertheless the data is good enough to say confidently that the rate is proportional to ammonium, the concentration of ammonium. Next let's have a look at the nitrite ion. In experiments five and six the ammonium is held constant and the nitrite is doubled and again the rate doubles. Looking at the rest of the data you can find that the rate also is proportional to, directly proportional to the nitrite concentration. Now knowing these two things we can say that the rate must be proportional to the product of these two concentrations. And going further we can say that to convert this expression into an equation we need to multiply the concentrations by a proportionality constant, that's the rate constant that will give us the actual value of the rate. So how do we find out the value of the rate constant? Well we've got our rate law here, rate equals k times the concentration of ammonium times the concentration of nitrite. So we can rearrange that equation to make k the subject. So that would give us k equals the rate over the concentration of ammonium times the concentration of nitrite. And we have values for those three variables. We've got the rate, we've got the ammonium and we've got nitrite. So we can just plug those in and that will give us a value for k. So here I've dropped all the data from the table into an Excel file. Here's my eight experiments, the ammonium concentrations, the nitrite concentrations and the observed initial rate. And I can put in an equation for the rate constant. We're saying that it equals the rate divided by the concentration of the two reactants like that. And that gives us a value for the rate constant of 0.000270. So 2.7 times 10 to the minus 4. And if I bring this down to all the other experiments, you can see that we get very similar values all the way down. Now you would expect a certain amount of variance. You can see they're all exactly the same because these are genuine experiments. So you're going to expect a certain amount of experimental scatter. But if we take the average of all those rate constant values, then that gives us a plausible value for the true rate constant. So that's giving us 2.68 times 10 to the minus 4. So to summarize what we've got for this particular reaction, the rate is proportional to both the concentration of ammonium and that of nitrite. The rate is therefore proportional to the concentration of ammonium multiplied by the concentration of nitrite. Now to turn this expression into a proper equation, there has to be a constant that we multiply the concentrations by to give us the actual numerical value of the rate. So we rewrite the expression like this as a rate equation or a rate law. The constant that converts the expression to an equation is called the rate constant and it's unique to a reaction at a particular temperature. It will change if the temperature changes because as we know temperature affects the rate of reaction. But we're going to go into that later. The rate law now shows the relationship between the reaction rate and the concentrations of the reactants. I should note here that it's also possible for gas phase reactants to use pressures instead of concentrations.