Reactions Chemical equations

We conclude that corrosion is a chemical reaction (equation 10.1) occurring by an electrochemical mechanism (equations 10.2) and (10.3), i.e. by a process involving electrical and chemical species. Figure 10.1 is a schematic representation of aqueous corrrosion occurring at a metal surface. 

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 ... 

After this iteration the desired model precision was achieved. Using the estimates of stoichiometric coefficients in chemical reaction equations, the following system is obtained ... 

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. 

C. Reactions and stoichiometry Provides the chemical reaction equations and stoichiometry. 

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... 

Fluorapatite can be prepared by heating a mixture of calcium pyrophosphate (Ca2P207) and Cap2 at 750°C [114,115]. POF3 gas is formed according to the following chemical reaction equation ... 

When you balance a chemical reaction equation, the primary concern is to obey the principle of conservation of mass The total mass of the reactants must equal the total mass of the products. (See Chapter 8 if you need to review this process.) In redox reactions, you must obey a second principle as well the conservation of charge. The total number of electrons lost must equal the total number of electrons gained. In other words, you can t just leave electrons lying around. The universe is finicky about that type of thing. 

By analogy with the first-order chemical reaction (equation 7.25) we know that ... 

Production of hydrogen by splitting water utilizing solar energy has long been a dream of researchers, and extensive studies have been carried out using semiconductor photocatalysts. The reaction is not easy despite its simple chemical reaction equation, which is expressed by... 

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 ... 

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.)... 

The product of a C x Ns matrix and a JVS x 1 matrix is a C x 1 matrix note that Ns disappears as one of the dimensions of the resultant matrix. The amounts of components in a reaction system are independent variables and consequently do not change during a chemical reaction. The amounts of species are dependent variables because their amounts do change during chemical reactions. Equation 5.1-27 shows that A is the transformation matrix that transforms amounts of species to amounts of components. The order of the columns in the A matrix is arbitrary, except that it is convenient to include all of the elements in the species on the left so that the canonical form can be obtained by row reduction. When the row-reduced form of A is used, the amounts of the components CO, H2, and CH4 can be calculated (see Problem 5.1). 

In writing chemical equations and biochemical equations it is important to be careful with names of reactants. Chemical reactions are written in terms of species. In chemical reaction equations, atoms of all elements and electric charges must balance. Biochemical reaction equations are written in terms of reactants, that is in terms of sums of species, H+ is not included as a reactant and electric charges are not shown or balanced. In biochemical reaction equations, atoms of all elements other than hydrogen must balance. The names of the reactants that must be used in making calculations with this data base are given later. 

On the basis of the principle of independency of the rates of elementary acts of chemical reactions, equations (2.5i)-(2.62) are assumed to be independent of each other. Therefore, the increases of layer thicknesses can explicitly be expressed from these equations as follows ... 

In chemistry, a transformation can be started in some way and will stop when all the possible changes in matter and energy have occurred within the system. The point before which any change in matter or energy has happened is called the initial state, the termination is the final state and the transition between the two is the reaction. The composition of the initial and final states is represented by the chemical reaction equation, which is an expression of the Law of the Conservation of Mass Matter can neither be created nor destroyed. As such the equation should balance electrically as well as chemically, unlike the shorthand biochemical equations seen in many textbooks. 

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) ... 

Solution processes are conveniently represented by physical-change equati analogous to chemical-reaction equations. Thus if 1 mole of LiCl is dissolVv 12 moles of H20, the process is represented as... 

Symbols connecting the reactants and products in a chemical reaction equation have the following meanings ... 

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. 

For an ideal-gas mixture with a constant average molecular weight, the term (dh/dYi)p p y. j i appearing in equation (55) is simply the (total) specific enthalpy of species i [that is, the quantity hi given in equation (1 -11)], and the dimensionless parameter Gi becomes Gi = hi/(Cp fT) thus the term Yj=x is a measure of the rate of liberation of heat by the chemical reaction. Equation (54) is a useful replacement for equation (45) in studies of the characteristic surfaces of the governing equations. 

See also Atomic number Atomic theory Chemical bond Chemical evolution Chemical reactions Equation, chemical Molecular geometry. 

This equation is the analytical expression of the second law of thermodynamics applied to chemical reactions. Equation (2) is equivalent to the general equation (1) as the quantities... 

One of the most important assumptions in MM kinetics is that the reaction in question wiU proceed in a three-dimensional vessel filled with a well-stirred fluid that obeys Pick s law for diffusion. This is rarely the case in a living cell, where many reactions are localized to membranes (two dimensions) or to small regions somewhere within the cell, creating an effectively one-dimensional environment with little or no diffusion. To circumvent this limitation, fractal kinetics have been developed which allow for the approximation of enzymatic reaction velocities in vivo [7]. Fractal kinetics can utilize MM-type kinetic constants to create a model of events in a spatially restricted environment. Briefly, as the dimensionality of a reaction is reduced from three dimensions to one, the kinetic order of a bimolec-ular reaction, for example, increases from 2 in a three-dimensional case, to 2.46 in a two-dimensional environment (e.g., membrane), to 3 in a one-dimensional channel, up to 50 for the case where fractal dimensions are less than 1. In simple terms, the kinetic order is the sum of all stoichiometric coefficients of the reactants in a balanced chemical reaction equation. Rearranging the familiar equation for MM kinetics... 

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... 

Using the data obtained, along with a balanced chemical reaction equation, calculate the concentration of calcium in parts per milhon for each trial. Report the mean and standard deviation. 

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. 

More complicated reactions can be easily treated by the methods outlined in the preceeding sections, that is (a) determine the coupled diffusion-chemical reaction equations, (b) linearize the equations in the concentration fluctuations, (c) solve the linearized rate equations by Fourier-Laplace transforms, (d) solve the dispersion equation... 

In Eq. (6.4.7) we saw that a fast chemical reaction would give rise to a broad angle-independent background. Angle-independence might then be surmised to imply the presence of chemical reactions. Equation (9.2.30), however, shows that the relaxation of the ionic atmosphere also leads to an angle-independent width. 

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