First-Order Reactions

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First-order reactions are VERY common.  The most common example is radioactive decay, where half of the sample disappears every 5 minutes (for example) goes by.

The Rate Equation

First-order reactions mean the exponent on the reactant concentration is 1:

How Concentration Changes with Time

Just like with zero- and second-order reactions, you can integrate the rate equation to determine how the concentration of the reactant changes with time.  If you know a little calculus (antiderivatives) you'll be able to follow the integration that I've put on the right.  If you can't, just skip to the fourth line.

If the reaction is first-order, a graph of ln [A] vs. t will give a line!  Remember (from grade 9) how y=mx+b is the equation of a line?  Well here, y is ln [A], the ln of the reactant concentration.  x is t, the time elapsed.  m (the slope) is -k and b (the y-intercept, where t=0) is ln [A]o, the ln of the initial reactant concentration.