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Batch add initials

Here's an example where the mass balances were developed in a previous screencast, and what I want to show here is a way to solve these equations, two differential equations, an initial value equation, using POLYMATH. Now this is not a complicated problem. We could probably just solve it without using numerical methods, but it's easier on a simple problem to see how to use the software, and then more complicated problems means more equations, but the same approach. So I'm going to write down the equations that were developed in the previous screencast first. I'm going to pause and do that. So here's the equations, and we assume constant density. This may not be a great assumption - we're making a polymer from these monomers, but as a first approximation we're going to do that. So that means we can take the volume out. The volume times the concentration is the number of moles, and so for both of these equations we factor out the volume. We have derivatives in terms of concentration and volume on both sides of the equations cancel, the result is that they're independent of volume. In a bigger reactor, we still have the same behavior and the same time to reach a certain conversion. So now we're going to put these equations into POLYMATH, and also of course putting in the value for the rate constant, and then calculating the concentration after 10 hours. So here's the POLYMATH program, and under programs, what I want is the differential equation solver, and then I can enter differential equations like so, so I'm going to enter one of them just to show you. Concentration of styrene, I'm going to differentiate with respect to time, my initial concentration of styrene, 0.78, and then the differential equation is minus k multiplied by the concentration of S and the concentration of B. So that enters the differential equation and initial conditions. I'll do the same thing for the other differential equation, so I'm going to pause and enter the other one. So I've entered the other differential equation. I've also made the fonts bigger to make it a little bit easier to see. To finish and be able to solve it, we have to enter a value for k, which is 0.036, and then we have to tell the program when to start integrating and when to stop, so initial, we enter the initial value of time equals zero, and the final value is 10 hours, since that's the time we're interested in determining concentrations. Now if you notice this purple arrow up here lights up, meaning we have all the information, so if I hit this, it gives me a report and we can see that the final concentration of B is 1.92 and the final concentration of S is 0.32 approximately. It also lists the differential equations and explicit equations. Alternatively, I could select graph, and hit this and now it shows the graph, where the concentration of B is on the top and the concentration of S is on the bottom, and we can format this and make it look nicer, but the general behavior is what we're interested in. So we can solve fairly quickly ordinary differential equations, and solve a number of them simultaneously using POLYMATH, and they can certainly be more complicated differential equations than shown here.