Equations for chemical reactions

The pioneering work on this case was done by van Krevelen and Hofiijzer in 1948 based on the film model.30 They computed an approximate solution to the mass transfer chemical reaction equations for the case of cAh 0 and showed that the results could be represented with an accuracy of about 10% by the equation... 

Ion exchange differs from adsorption and chromatography in that one sorbate (a counterion) is exchanged for a solute ion, and the exchange is governed by a reversible, stoichiometric, chemical-reaction equation. For ion exchange, the law of mass action is applied to obtain an equilibrium ratio rather than to fit data to a sorption isotherm such as the Langmuir or Freundlich equation. 

Write the chemical reaction equation for the hydrolysis of the dipeptide glycylalanine into the constituent amino acids. 

Iron in the hemoglobin binds O. The chemical reaction equation for this binding is expressed as follows ... 

The chemistry is the same for both batteries. The positive electrode is made from lead oxide (Pb02), the negative electrode from lead (Pb), and the electrolyte from a concentrated sulfuric acid (H2SO4) aqueous solution. The chemical reaction equations for the lead-acid battery can be written as follows ... 

To isolate a system for study, the system is separated from the surroundings by a boundary or envelope that may either be real (e.g., a reactor vessel) or imaginary. Mass crossing the boundaiy and entering the system is part of the mass-in term. The equation may be used for any compound whose quantity does not change by chemical reaction or for any chemical element, regardless of whether it has participated in a chemical reaction. Furthermore, it may be written for one piece of equipment, several pieces of equipment, or around an entire process (i.e., a total material balance). 

It may be noted that, in the absence of a chemical reaction, equation 10.203 reduces to equation 10.146. For a steady-state process dCA/dt = 0, and for a first-order reaction n = l. Thus ... 

Thus, the conjugated anion represents an intermediate for the halide transfer from a complex anion to a Lewis acid. The quantum chemical reaction energies for the halide transfer AE(r can be calculated using the values of the interaction energies from Table 18 in the equation AEtr = AE(I) — AE(II). The results are presented in Table 20 and allow the following generalization ... 

In Eq. (13), r stands for the production (or consumption) of the species of interest due to a chemical reaction, while in Eq. (12) q represents the heat production, e.g., due to one of more chemical reactions. Equation (13) is often referred to as the Convection-Diffusion-Reaction (CDR) equation. 

It is sometimes stated as a rule of thumb that the rate of a chemical reaction doubles for a 10 K increase in T. Is this in accordance with the Arrhenius equation Determine the... 

Since most chemicals react while dissolved in a constant volume of solvent, the half-life of a chemical reaction equates to the time required for the concentration to halve. 

Here fif (T) is the Gibbs free energy per mole of an ideal gas at temperature T and standard pressure P°. Thus the condition of equilibrium for a gas phase system subject to a chemical reaction (Equation 4.36), whether at constant T and P or constant T and V, is given by... 

Most electrode reactions of interest to the organic electrochemist involve chemical reaction steps. These are often assumed to occur in a homogeneous solution, that is, not at the electrode surface itself. They are described by the usual chemical kinetic equations, for example, first- or second-order reactions and may be reversible (chemical reversibility) or irreversible. 

The ratio vJD can then be used to calculate a chemical reaction rate for a nonconservative solute, S. To do this, the one-dimensional advection-diffusion model is modified to include a chemical reaction term, J. This new equation is called the one-dimensional advection-diffusion-reaction model and has the following form ... 

The concentration A of molecules A is again taken constant and supposed so large that the reverse reactions may be neglected. Alternatively one may imagine that A is continually supplied and B is drained. The reaction scheme (1.1) therefore describes an open system, see VII.4. The chemical rate equation for the concentration of X is... 

I Sec also Chemical Reaction Rate.) For the qualitative effect temperature change, one may visualize the heat ol an equilibrium reaction as material, and an increase of temperature (hem intensity) as operating to increase the concentration of "heal material." thus shifting the equilibrium away from the side ol its increased concentration, and conversely. It is possible, knowing the heal of reaction. Q. on the assumption that the heat nf reaction is constant between two given (absolute) temperatures. 7j and T . to calculate the equilibrium constant A (at 73) when the equilibrium constant A tat 7j I and the gas constant, R (equals 2 calories per mole) are known, by the application of van l Holt s equation ... 

If, on the other hand, surface reaction determined the overall chemical rate, equation 3.68 (or 3.69 if an Eley-Rideal mechanism operates) would represent the rate. If it is assumed that a pseudo-equilibrium state is reached for each of the adsorption-desorption processes then, by a similar method to that already discussed for reactions where adsorption is rate determining, it can be shown that the rate of chemical reaction is (for a Langmuir-Hinshelwood mechanism) ... 

The enthalpy 7, besides a pair of variables determining the physical state of the material (e.g., p and S or p and v), also depends on the chemical variable n—the depth of occurrence of the irreversible chemical reaction which, for definiteness, we will equate with the concentration (dimensionless, g/g) of the final reaction product. It should be kept in mind that the reaction occurs, particularly at the beginning, irreversibly. 

By standard thermodynamics, a dimensionless equilibrium constant can be derived from this condition and, for a general reversible chemical reaction, Equation 3.7, we may write Equation 3.8 which defines the equilibrium condition ... 

The two steady-state heat-transfer coefficients, hr and hj, could be further described in terms of the physical properties of the system. The solution-to-wall coefficient for heat transfer, hT in Equation 8.8, is strongly dependent on the physical properties of the reaction mixture (heat capacity, density, viscosity and thermal conductivity) as well as on the fluid dynamics inside the reactor. Similarly, the wall-to-jacket coefficient for heat transfer, hj, depends on the properties and on the fluid dynamics of the chosen cooling liquid. Thus, U generally varies during measurements on a chemical reaction mainly for the following two reasons. 

Specificity of a concrete system accounts for the source of the appearance of a small parameter and for its type. For homogeneous reactions, a small parameter is usually a ratio of rate constants for various reactions some reactions are much faster than the others. For just such a small parameter Vasiliev et al. [25] distinguished a class of chemical kinetic equations for which the application of the quasi-stationarity principle is correct (they considered a closed system). 

Rate laws are determined by experimentation and cannot be inferred only by examining the overall chemical reaction equation (Sparks, 1986). Rate laws serve three primary purposes (1) they permit the prediction of the rate, given the composition of the mixture and the experimental value of the rate constant or coefficient (2) they enable one to propose a mechanism for the reaction and (3) they provide a means for classifying reactions into various orders. 

Extend Equations 4.1 through 4.2 with the term for a chemical reaction, Equation 4.6. Is the additional term consistent with the general structure of Equations 4.1 through 4.2 Where is the A for this term (Hint See the definition for A in Equation 4.4 and for the stoichiometric coefficient y in the nearby text.)... 

Generally, the gas-phase concentrations Nk are described by a set of master equations of chemical kinetic (equations for active masses at the source/sink of the kth substance in the chemical reactions Wk)... 

The Gibbs free energy of a dissolved species varies with the activity, a, and in the case of a gas, with the partial pressure, p. Consider the equation for the reaction isotherm (16) for the general chemical reaction Equation (9) ... 

Write the chemical-equilibrium equations for the three reactions, indicate how the equilib- constants are related, and show why Tom, Dick, and Harry all obtain the same result. 

Given mathematical expression, these laws lead to a network of equations from which a wide range of practical results and conclusions can be deduced. The universal applicability of this science is shown by the fact that it is employed alike by physicists, chemists, and engineers. The basic principles are always the same, but the applications differ. The chemical engineer must be able to cope with a wide variety of problems. Among the most important are the determination of heat and work requirements for physical and chemical processes, and the determination of equilibrium conditions for chemical reactions and for the transfer of chemical species between phases. 

Recall that in Section 10.3 we worked out a detailed theory for the equilibrium distribution for the reaction A + 11 C. Here the task is to determine the governing differential equation (chemical master equation) for the dynamics of the state probabilities in Equation (11.5). 

Here to illustrate the procedure for non-linear systems, we work out the chemical master equation for the Michaelis-Menten reaction of Equation (11.19). We let p(m, n, t) be the probability that m, S, and n ES molecules occur in the enzyme reaction system at time t. The probability p(m, n, t) satisfies the CME... 

To draw these diagrams, one needs the E[J values. These are listed in data books or may be determined by the standard potentials for each of the components of the reactions using Eq. 7.16. The dissolution and chemical reaction equations are then written for aU possible oxidation states with suitable values of x as a function of pH. Using dilferent values of (M +(aq))/ MO t), one can then calculate Ejj and plot the results vs. pH. 

FIGURE 81 The reaction container (10 mm i.d.) and the reaction equations for boron sulfides-assisted synthesis of matel polysulfides and sulfides xB(s) + yS(g) oBjSjtg) bBS2(g) + cS(g) m(metal oxide)(s) + t7B2S3(g) + bBS2(g) + cS(g) p(metal sulfide)(s) -qB203(v). The (s) stood for vitreous state. Reprinted with permission from Wu and Seo (2004). Copyright 2004 American Chemical Society. 

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