# Analysis Of The Half Life Of A Substance

2322 words - 9 pages

The rate of a reaction would be the change of concentration of a reactant divided by the time (Green & Damji 161). The rate law is an expression deduced to show the relation of rate to the concentrations of the reactants in a chemical reaction. The rate law equals the rate constant, multiplied by the concentration of the reactants raised to their respective reaction orders (Green & Damji 170). The rate law of the equation given above is:

k is the rate constant (given in M/sec or sec-1 or M-1sec-1)
A is first reactant and [A] is the concentration of the first reactant (given in M)
m is the order with respect to A

* Any reactant in brackets refers to the concentration of the particular reactant

The rate constant is a variable that is defined using a set of characteristics (Green & Damji 170):

• It is dependent on temperature and the availability of a catalyst (a substance that increases rate)
• It is measurable through experimentation
• It is specific to each chemical reaction
• It does not change throughout a reaction

Reaction order is defined as the relationship between the concentrations of reactants and the rate of the reaction or simply as the power to which the reactants’ concentrations are raised (Green & Damji 170). The power raised is the coefficient to the left of the reactant, as seen in the rate law above. The overall reaction order refers to the sum of all the powers (Green & Damji 170). For example if the reaction order of [A] was 2 and the reaction order of [B] was 1, the reaction order would be a third reaction order. Three reaction orders will be discussed in this exploration:

• Zero reaction order (when [A] would be raised to the power of 0)
• First reaction order (when [A] would be raised to the power of 1)
• Second reaction order (when [A] would be raised to the power of 2)

The order of a reaction has an overall effect on the reaction’s rate. The relationships are explained in the Table 1 and Graph 1.

The half-life of a substance (expressed as ) is the time it takes for half of the dosage to diminish (Rouse). Calculating half-life is essential in the field of pharmaceutics, as it determines the time it takes for a substance to exit the body (Rouse). Half-life is usually calculated for drugs and substances such as caffeine, Adderall, etc. Yet, half-life calculations are also done for populations and radioactivity (Rouse).

It is a common misconception that half-life is an exponential decay with a rate of one half. When in reality, the output of half-life is an exponential decay with a rate of one half (Tobin 210). From previous knowledge from pre-calculus, an exponential function has the following form (Tobin 210):

• a is the initial amount
• b is the rate
• x is number of half-lives
• y is the output

For example, if the half-life of a population of 100 people is 2 years then after two years the remaining population would be 50 people. The second and third half-life outputs (after 4...

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