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# 2015 AP Chemistry free response 5a: Finding order of reaction

Finding the order of reaction based on graphs of absorbance, ln(absorbance) and 1/(absorbance) vs. time for kinetics of bleaching food coloring. An alternative method of solving 2015 AP Chemistry free response 5a.

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• why should the graph be linear? • So the reaction is first order which means it will follow first order kinetic equations like the integrated rate law that they gave: ln([A]t) - ln([A]0) = -kt. You can rearrange the equation into: ln([A]t) = -kt + ln([A]0), which fits the slope-intercept equation y = mx + b where y is ln([A]t), x is t, m (the slope) is -k, and b (the y-intercept) is ln([A]0). Now if you graph the ln([A]t) as the y coordinate versus t as the x coordinate and they form a straight line, then the reaction is first order. And what's more you could find the rate constant k from the slope and initial concentration of A from the y-intercept.

So looking at the graphs they gave, graph 1 has [A] vs. t which follows the integrated rate of a 0th order reaction. But since the curve is not linear we can say that the data does not fit the 0th order model and that the reaction is not 0th order.

Graph 2 has ln[A] vs. t which follows the integrated rate law of a first order reaction as I've shown. Now since the data here is a nice and linear we can say that it fits much better using a first order model and that the reaction is first order.

Graph 3 has 1/[A] vs. t which would be following the integrated rate law of a second order reaction. And since it's not linear, it is similar to the 0th order model as to why it doesn't work.

It's pretty common to see if you're able to fit data onto a straight line in chemistry because it's a clear way to visualize if your model is predicting how the data should behave. I'm unsure as to why they didn't just solve it by looking at whether the graphs were linear or not, it's a much faster way to solve these problems especially in a test setting.

Hope that helps.