Carbon dating exercises

If two reactions have the same order, the faster reaction will have a shorter half-life, and the slower reaction will have a longer half-life.

The half-life of a first-order reaction under a given set of reaction conditions is a constant.

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An example is shown in Figure 8.16; radiocarbon dates from wood fragments in glacial sediments have been used to estimate the time of the last glacial advance along the Strait of Georgia.

Figure 8.16 Radiocarbon dates on wood fragments in glacial sediments in the Strait of Georgia [SE after Clague, J, 1976, Quadra Sand and its relation to late Wisconsin glaciation of southeast British Columbia, Can.

This becomes evident when we rearrange the integrated rate law for a first-order reaction (Equation 14.21) to produce the following equation: Figure \(\Page Index\): The Half-Life of a First-Order Reaction.

This plot shows the concentration of the reactant in a first-order reaction as a function of time and identifies a series of half-lives, intervals in which the reactant concentration decreases by a factor of 2.

It has a half-life of 1.3 billion years, meaning that over a period of 1.3 Ga one-half of the Figure 8.14 The decay of 40K over time.

Each half-life is 1.3 billion years, so after 3.9 billion years (three half-lives) 12.5% of the original 40K will remain.This is not true for zeroth- and second-order reactions.The half-life of a first-order reaction is independent of the concentration of the reactants.If we dated a number of individual grains in the sedimentary rock, we would likely get a range of different dates, all older than the age of the rock.It might be possible to date some chemical sedimentary rocks isotopically, but there are no useful isotopes that can be used on old chemical sedimentary rocks.Another approach to describing reaction rates is based on the time required for the concentration of a reactant to decrease to one-half its initial value.

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