Measuring the Rate of a Reaction

Nj and N2H+ are ions in the gas phase mass spectrometry for detection and estimation. 

This is a very low concentration species detection and estimation by laser induced fluorescence. 

Three of the species involve deuterium mass spectrometry is ideal, and can also be used for H20. 

Rates of reaction vary from those which seem to be instantaneous, e.g. reaction of H30+(aq) with OH (aq), to those which are so slow that they appear not to occur, e.g. conversion of diamond to graphite. Intermediate situations range from the slow oxidation of iron (rusting) to a typical laboratory experiment such as the bromination of an alkene. But in all cases the reactant concentration shows a smooth decrease with time, and the reaction rate describes how rapidly this decrease occurs. 

The reactant concentration remaining at various times is the fundamental quantity which requires measurement in any kinetic study. 

On the last page you saw that the rate of a reaction is found by measuring the amount of a reactant used up per unit of time or the amount of a product produced per unit of time. 

Take for example the reaction between magnesium and excess dilute hydrochloric add. Its equation is  

In this reaction, hydrogen is the easiest substance to measure. This is because it is the only gas in the reaction. It bubbles off and can be collected in a gas syringe, where its volume is measured. 

The magnesium is cleaned with sandpaper and put into one part of the flask. Dilute hydrochloric add is put into die other part. The flask is tipped up to let the two reactants mix, and the dock is started at the same time. Hydrogen begins to bubble off. It rises up the flask, and pushes its way into the gas syringe. The plunger is forced to move out  

Some reactions are so fast that their rates wouid be very difficult to measure—like this detonation of an old mine. 

---

Molecules are too small and much too numerous to follow on an individual basis. Therefore, a chemist interested in measuring the rate of a reaction monitors the concentration of a particular compound as a function of time. The concentrations of reactants, products, or both may be monitored. For example, Figure 15-6 shows some experimental data obtained from a series of concentration measurements on the decomposition of NO2 ... 

J2.2.2 Methods of Following the Course of a Reaction. A general direct method of measuring the rate of a reaction does not exist. One can only determine the amount of one or more product or reactant species present at a certain time in the system under observation. If the composition of the system is known at any one time, then it is sufficient to know the amount of any one species involved in the reaction as a function of time in order to be able to establish the complete system composition at any other time. This statement is true of any system whose reaction can be characterized by a single reaction progress variable ( or fA). In practice it is always wise where possible to analyze occasionally for one or more other species in order to provide a check for unexpected errors, losses of material, or the presence of side reactions. 

R. Kelley, Measure the rate of a reaction catalyzed by a single 1982... 

Different Ways of Expressing the Rate of Reaction There is usually more than one way to measure the rate of a reaction. We can study the decomposition of hydrogen iodide, for example, by measuring the rate at which either H2 or I2 is formed in the following reaction or the rate at which HI is consumed. 

Thermostats are commonly required for such purposes as controlling the temperature of a refractometer or keeping the temperature of the solution in a polarimeter tube or ultraviolet absorption cell constant. For these purposes, the fluid in the thermostat is usually circulated through the apparatus by a pump. A thermostat is also needed if one is to measure the rate of a reaction, since the rate is a function of temperature. 

The rate at which a reaction occurs is known as the reaction rate. This rate is typically determined by measuring the amount of one substance (either a reactant or product) over time. The reaction stoichiometry can then be used to determine the other substances that were not measured. The rate of a reaction is sometimes affected by the concentration of a reactant. The degree to which the reaction is affected depends on the rate law for the reaction. 

Stirring gases is inconvenient and inellicient at any scale. F >r the study of gas phase reactions catalyzed at the surface of a solid, the mechanical problem of setting up a gas-solid stirred-flow reactor is a difficult one. If, however, a recirculation pump for gases is available, a stirred-flow reactor can be built readily for measuring the rate of a reaction catalyzed by a solid. Show how. 

The choice of a given method for measuring the rate of a reaction is dictated by its half-life. Thus, the instrumentation required to monitor slow reactions is typically simpler than that needed for fast reactions. 

The process involved in measuring the rate of a reaction comprises the following stages ... 

It is possible to measure the rate of a reaction at various applied pressures and determine the variation of k with P. In recent years, such measurements have become increasingly widespread for a variety of inorganic reactions, and the interpretation of the pressure dependence adds a further tool to the arsenal of parameters available for mechanistic interpretations. The recommended units of pressure are megapascals, MPa, (1 atm = 0.1013 MPa = 1.013 bar). 

Another useful technique for measuring the rates of certain reactions involves measuring the quantum yield as a function of quencher concentration. A plot of the inverse of the quantum yield versus quencher concentration is then made Stern-Volmer plot). Because the quantum yield indicates the fraction of excited molecules that go on to product, it is a function of the rates of the processes that result in other fates for the excited molecule. These processes are described by the rate constants (quenching) and k (other nonproductive decay to ground state). 

There are obviously many reactions that are too fast to investigate by ordinary mixing techniques. Some important examples are proton transfers, enzymatic reactions, and noncovalent complex formation. Prior to the second half of the 20th century, these reactions were referred to as instantaneous because their kinetics could not be studied. It is now possible to measure the rates of such reactions. In Section 4.1 we will find that the fastest reactions have half-lives of the order 10 s, so the fast reaction regime encompasses a much wider range of rates than does the conventional study of kinetics. 

A consequence of the compensation effect is the presence of an isokinetic temperature. For a particular reaction, the logarithm of the rate of a reaction measured at different conditions versus 1/T should cross at the same (isokinetic) temperature. For conditions with varying n, this isokinetic temperature easily follows from Eq. (1.19) and is given by... 

It may be recalled that in homogeneous reactions all reacting materials are found within a single phase, be it gas, liquid or solid if the reaction is catalytic, then the catalyst must also be present within the phase. Thus, there are a number of means of defining the rate of a reaction the intensive measure based on unit volume of the reacting volume (V) is used practically exclusively for homogeneous systems. The rate of reaction of any component i is defined as... 

The study of polymerization kinetics allows us to understand how quickly a reaction progresses and the role of temperature on the rate of a reaction. It also provides tools for elucidating the mechanisms by which polymerization occurs. In addition, we are able to study the effect of catalysts on the rates of polymerization reactions, allowing us to develop new and better catalysts based on the measured performance. 

Most of the factors that affect the rate of a reaction are qualitative or semiquantitative, but the dependency of the rate on concentration (or pressure, which is a measure of concentration) may be... 

One of the first uses of ESR spectra to measure the rate of a chemical reaction was by Ward and Weissman in the early 1950s.1 They made use of a form of the Heisenberg uncertainty principle (eqn 5.1) to relate the lifetime of a spin state to the uncertainty in the energy of the state. 

One of the characteristics of acids and bases is that they catalyze certain reactions. Many years ago, J. N. Bronsted studied the relationship between acid strength as measured by the dissociation constant and the rate of a reaction that is catalyzed by the acid. The relationship that Bronsted recognized can be written as... 

Both ion and electron transfer reactions entail the transfer of charge through the interface, which can be measured as the electric current. If only one charge transfer reaction takes place in the system, its rate is directly proportional to the current density, i.e. the current per unit area. This makes it possible to measure the rates of electrochemical reactions with greater ease and precision than the rates of chemical reactions occurring in the bulk of a phase. On the other hand, electrochemical reactions are usually quite sensitive to the state of the electrode surface. Impurities have an unfortunate tendency to aggregate at the interface. Therefore electrochemical studies require extremely pure system components. 

Worked Example 8.2 yields a value for the rate constant k, but an alternative and usually more accurate way of obtaining k is to prepare a series of solutions, and to measure the rate of each reaction. A graph is then plotted of reaction rate (as y ) against concentration(s) of reactants (as V) to yield a linear graph of gradient equal to k. 

The rate of a reaction and its dependency on the concentrations of the reactants can be measured in several ways. A simple method involves the measurement of the rate at zero to low conversion at different concentrations of one of the substrates, keeping the concentration of other substrates constant. The latter can be done by using an excess of the other substrates (e.g. tenfold excess), which means that we can assume that the concentrations of the latter ones are constant under so-called pseudo-first-order conditions. Secondly we can monitor the reaction rate over a longer period of time taking into account the change in concentration for this one substrate. Alternatively, one can monitor the concentrations of all species and analyse the results numerically. 

If the rate of a reaction can be measured at a time for which the concentrations of the reactants are known, and if this determination can be repeated using different concentrations of reactants, it is clear that the rate law (1.2) can be deduced direetly. It is not often obtained in this manner, however, despite some distinet advantages inherent in the method. 

With the availability of perturbation techniques for measuring the rates of rapid reactions (Sec. 3.4), the subject of relaxation kinetics — rates of reaction near to chemical equilibrium — has become important in the study of chemical reactions.Briefly, a chemical system at equilibrium is perturbed, for example, by a change in the temperature of the solution. The rate at which the new equilibrium position is attained is a measure of the values of the rate constants linking the equilibrium (or equilibria in a multistep process) and is controlled by these values. 

In determining experimentally the rate of a reaction, it is imperative to define the reaction completely, with respect to the reaetants, the stoichiometry and even the products. This is preferably carried out before any detailed rate measurements are made, otherwise difficulties in understanding the rate data (particularly if these are eomplex) are likely to arise. 

The rate of a reaction is usually measured in terms of the change of concentration, with time, of one of the reactants or products, - d [reactant]/clt or +r/ [products]/r/t, and is usually expressed as moles per liter per second, or M s . We have already seen how this information might be used to derive the rate law and mechanism of the reaction. Now we are concerned, as kineticists, with measuring experimentally the concentration change as a function of the time that has elapsed since the initiation of the reaction. In principle, any property of the reactants or products that is related to its concentration can be used. A large number of properties have been tried. 

The polarographic technique can be used to measure the rates of rapid reactions. Because an internal process is examined the problem of mixing is avoided, as it is in the relaxation and other non-flow methods. The rate of diffusion of a species (which can be oxidized or reduced) to an electrode surface competes with the rate of a chemical reaction of that species, for example... 

The rate of a reaction in which a decrease in the concentration of substrate or reactant (or several reactants) is actually what is being measured. It is symbolized by v and may have a subscript for the species being measured (e.g., Va or Vgtp)- See Chemical Kinetics... 

---