The particular reaction that represents the oxidation of Mg metal would be the following:
Mg => Mg+2 + 2e-
This is the half reaction of the oxidation of the magnesium metal, another charged species would need to receive it to become reduced or gain the 2 electrons lost.
Calculate the ratio between the mass of this sample after and the initial mass:
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Let denote the number of half-lives in that (where might not necessarily be an integer.) The mass of the sample is supposed to become the previous quantity after each half-life. Therefore, if the initial mass of the sample is (for example,) the mass of the sample after half-lives would be . Regardless of the initial mass, the ratio between the mass of the sample after half-lives and the initial mass should be .
For this question:
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Take the natural logarithm of both sides of this equation to solve for :
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In other words, there are half-lives of this sample in . If the length of each half-life is constant, that length should be .