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Kinetic Methods. Rates. In order to use a reaction for analytical purposes, the reaction must have a rate slow enough to measure but fast enough to get it done in a reasonable time. There must be some way of monitoring the reaction’s progress. The rate law for the reaction must be known.
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Rates • In order to use a reaction for analytical purposes, the reaction must have a rate slow enough to measure but fast enough to get it done in a reasonable time. • There must be some way of monitoring the reaction’s progress. • The rate law for the reaction must be known. • Rate is defined so as to always be a positive quantity. Thus for Reactant → Product, Rate = -d(Reactant)/dt or +d(Product)/dt
Rate Laws • Reaction rates depend upon reactant concentrations in often complicated ways. • This is because reactions rarely proceed by one simple step but rather through several steps. • The dependence of rate on concentration really is a matter of what is involved in the slowest, or rate determining step. • If there are several reactants (A, B, etc.) we can write: Rate = k(A)a(B)b… where the sum a+b+… is referred to as the reaction order. • The reaction order must always be determined experi- mentally and may have little to do with the molecularity of the reaction, i.e., the balancing coefficients.
Some reaction orders • Zero order: Rate = k(reactant)0= constant This is often characteristic of heterogeneously catalyzed reactions. • First order: Rate = k(reactant)1 These reactions follow ln(At) = ln(A0) - kt if A is the reactant. Also, k = 0.693/t½, where t½ is the half-life of the reaction, the time required for half the reactant to disappear. • Second order: Rate = k(reactant)2or k(A)1(B)1. The first type follows 1/(At) = 1/(A0) + kt.
Pseudo-first-order Kinetics • It is sometimes possible to use such a great excess of one reactant that its concentration doesn’t change during the analysis and thus the rate depends on only the other reactant. Such conditions are called pseudo-first-order. • It may even be possible to adjust conditions so as to make the reaction pseudo-zero-order.
Analytical Methods • It is possible to use kinetic methods in many different ways (see diagram in text, p.626). • For example, one can measure the reactant concentration at some particular time and use the integrated rate law to calculate what the value was at t=0. This can sometimes be accomplished by stopping the reaction chemically to give time to measure (At). • An alternative is to measure the time required for some amount of reactant to disappear.
Radiochemical Methods • Isotopes of many elements are radioactive. Thus the presence of such isotopes makes for a sensitive way of detecting and quantifying them. • In substances where only very small amounts of radioactive isotope are present, it is possible to ‘activate’ the sample by bombarding with neutrons to produce more radioactivity and thus make the analysis easier. • Radioactive compounds can also be added to samples to enable one to see how effective certain transfer procedures are.
Radiation • Alpha particles, helium nuclei, 4He2+ • Beta particles, electrons • Gamma rays, high energy electromagnetic radiation, γ Radioactive decay follows first order kinetics. A = λN and Nt = N0e-λt where A is activity, λ is decay constant (in disintegrations per unit time), and N is the number of radioactive atoms. The decay constant is related to half-life by λ = 0.693/t½
Neutron Activation Analysis • An analysis method based on bombarding a sample with neutrons to make it radioactive and then measuring the disintegrations, generally as gamma radiation. • The sample is bombarded in a nuclear reactor or with a slow neutron instrument. It is allowed to ‘cool’ for a period to make it safe to handle and permit short-term interferences to decay to background. • The method is applicable to nearly all elements and is a nondestructive technique.
Neutron Activation Analysis • The rate of production of radioactive atoms depends on several parameters Rate = ΦσN where Φ is the neutron flux, σ is the reaction cross-section and N is the number of atoms originally present in the sample. • The initial radioactivity, A0, after radiation for some time, t, is given by A0 = ΦσN(1-e-λt) • Thus, if one can determine A0, and know the other parameters, one can calculate N, the number of atoms present in the sample.
Isotope Dilution Analysis • In this technique, a radioactive tracer is added to an analyte sample. • After the analyte has been treated to isolate it for final quantification, the radioactivity of the sample can be used to determine what fraction of the original analyte was lost in the analytical process, e.g. precipitation, filtration, or extraction.
Isotope Dilution Analysis • A mass, wT, of tracer with known activity, AT, is added to the unknown mass, wx, of analyte and the sample is made homogeneous. • If after the analysis it is found that wA grams of analyte were found, and one finds the activity of the isolated substance is AA, then following relationship will hold AA = AT [wA/(wx +wT)]
