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