What is a rate constant?

I mentioned earlier that reactions occur at different rates. An explosion from setting hydrogen on fire may last only a couple of seconds. The reactions involved in baking a cake might take a few minutes to a few hours. The chemistry that rusts your bike can take months or years. In our example above, the decay of carbon-14 takes thousands of years.

A rate constant tells you how fast a reaction goes. We might expect our explosion to have a very large rate constant, while carbon-14 might have a very small one. But how do we find out what this rate constant is?

A neat trick that scientists often use is to linearlize data. Remember that exponential decay from before? If we take the natural log of both sides with can get a new equation that looks like this:

If you look closely you should be able to see that plotting ln[C-14]t on the y-axis and t on the x-axis should give a straight line with an intercept of ln[C-14] at time 0 and a slope of k. That allows us to find our rate constant! But first let's program this linear data in python. Remember our data file is called carbondecay.csv

You should be getting a graph that looks like the one below. We will talk about how to calculate the rate constant from this graph in the next section.