Chemistry for medical professionals

Chemistry for medical professionals

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Half-life in 1st order reactions

The half-life can be calculated from the law of speed. Again we consider a simple reaction:


These reactions take place in the 1st order:


By changing (variable separation) one obtains:


The equation is now integrated, with the starting situation before the start of the reaction being chosen as the zero point. [A.]0 denotes the initial concentration of A at t = 0.


It follows:


This equation applies to the entire course of a first-order reaction. We now consider the half-life t½. After a half-life, the concentration of A has decreased by half: [A] = ½[A.]0. This is now plugged into the equation, [A.]0 can be shortened.


It applies ln(1/2)=-ln(2). By transformation we get an expression for the half-life:


The half-life is therefore independent of the concentration of the educt. This is characteristic of first-order reactions. Radioactive decay also obeys a rate law 1. This is used when determining the age, for example using the C14 method.

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