THE CHANGE OF CONCENTRATION WITH TIME

Check A good way to check our rate law is to use the concentrations in experiment 2 or 3 and see if we can correctly calculate the rate. Using data from experiment 3, we have 

the rate law correctly reproduces the data, giving hoth the correct number and the correct units for the rate. 

The following data were measured for the reaction of nitric oxide with hydrogen  

The rate laws we have examined so far enable us to calculate the rate of a reaction from the rate constant and reactant concentrations. These rate laws can also be converted into equations that show the relationship between concentrations of reactants or products and time. The mathematics required to accomplish this conversion involves calculus. We do not expect you to be able to perform the calculus operations, but you should be able to use the resulting equations. We will apply this conversion to three of the simplest rate laws those that are first order overall, those that are second order overall, and those that are zero order overall. 

Z is described as being first order in [X] and third order 

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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. 

Estimate the change of concentrations with time for the following elementary reaction X + Y = 2Z... 

The rate of a chemical reaction is defined as the rate of change of the concentration of one of its components, either a reactant or a product. The experimental investigation of reaction rates therefore depends on being able to monitor the change of concentration with time. Classical procedures for reactions that take place in hours or minutes make use of a variety of techniques for determining concentration, such as spectroscopy and electrochemistry. Very fest reactions are studied spectroscopically. Spectroscopic procedures are available for monitoring reactions that are initiated by a rapid pulse of electromagnetic radiation and are over in a few femtoseconds (1 fe = 10 s). 

This paper is aimed at clarification of the change of concentration with time in the liquid phase before crystallization starts. To find optimum conditions for the commercial production of pure zeolites of the types A and faujasite, the reaction of fine-particle amorphous silica with sodium alu-minate solution was studied at 20°, 40°, and 75°C. The liquid phase separated by filtration nucleates the zeolite types Ay sodalite, phillipsite, and faujasite, depending on stirring time before liquid-solid separation. Quite similar conditions are observed in precipitated sodium aluminosilicate gels and mother liquor. 

If only the overall rate equation of a reaction is known, no information on the change of concentrations with time can be obtained. Therefore it is necessary to determine the mechanism of a reaction - that means the sequence of all the elementary partial steps. Then the rate law can be derived unambiguously in the following way ... 

Special devices - chromatographs - are installed at the exit to record the change of concentration with time as the mixture is passing by. The typical form of recordings (chromatograms) is depicted in Fig. 6.11. 

The diffusion coefficient of dissolved ions or neutral species such as oxygen in aqueous solution is on the order of 1 X 10 cm s h Under nonsteady state conditions diffusion is described by Pick s second law, which states that the change of concentration with time is equal to the difference of the diffusive fluxes in and out of a given volume element. 

In most solid-state systems, it is more convenient to investigate diffusion by determining the change of concentration with time (dc/dt). Tick s second law, derived from Equation 10.10, states that... 

THE CHANGE OF CONCENTRATION WITH TIME We learn that rate equations can be written to express how concentrations change with time and look at several examples of rate equations zero-order, first-order, and second-order reactions. 

The advantages of the application of polarography in reaction kinetics can be summarized as follows In the kinetic run the measurement of the changes of concentration with time can be carried out continuously. The dependence of current (or concentration respectively) on time can be automatically recorded, and the reaction mixture can be often placed directly in the polarographic cell. Also the presence of buffers and neutral salts (contrary to conductimetry), coloured materials, some solvents and even of complicated biological materials do not usually interfere. 

Pick s second law describes the change of concentration with time ... 

Once the absorption peaks of the transient species have been located, the changes of concentration with time can be determined much more accurately by flash kinetic spectropho-... 

A simple Sl-SECM model can be considered by the reductive interrogation of adsorbed species A. The surface is described by subdomain 2 of Figure 16.26a and the second-order interrogation reaction, with kinetic constant k, is described by Equation 16.16, while Equations 16.17 through 16.19 describe the change of concentrations with time ... 

Figure 6.6, due to Marrero and Mason [28], summarizes the techniques most frequently used for measuring ordinary molecular diffusivities. The figure is largely self-explanatory. The three unsteady state methods obtain results by measuring the change of concentration with time, as-do the two-bulb and capillary leak quasi-steady state methods. The steady state methods rely... 

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