Chemical equations balancing simple

J 3 Write and balance chemical equations for simple redox reactions (Self-Test K.4). 

Our first major task of this chapter is to learn to balance equations for chemical reactions. Balancing simple equations will be covered in this chapter equations for more complicated oxidation-reduction reactions will be considered in Chapter 16. 

If the source fingerprints, for each of n sources are known and the number of sources is less than or equal to the number of measured species (n < m), an estimate for the solution to the system of equations (3) can be obtained. If m > n, then the set of equations is overdetermined, and least-squares or linear programming techniques are used to solve for L. This is the basis of the chemical mass balance (CMB) method (20,21). If each source emits a particular species unique to it, then a very simple tracer technique can be used (5). Examples of commonly used tracers are lead and bromine from mobile sources, nickel from fuel oil, and sodium from sea salt. The condition that each source have a unique tracer species is not often met in practice. 

In all of these oxide phases it is possible that departures from the simple stoichiometric composition occur dirough variation of the charges of some of the cationic species. Furthermore, if a cation is raised to a higher oxidation state, by the addition of oxygen to tire lattice, a conesponding number of vacant cation sites must be formed to compensate tire structure. Thus in nickel oxide NiO, which at stoichiomen ic composition has only Ni + cations, oxidation leads to Ni + ion formation to counterbalance the addition of extra oxide ions. At the same time vacant sites must be added to the cation lattice to retain dre NaCl sUmcture. This balanced process can be described by a normal chemical equation thus... 

We need to be able to write balanced chemical equations to describe redox reactions. It might seem that this task ought to he simple. However, some redox reactions can be tricky to balance, and special techniques, which we describe in Sections 12.1 and 12.2, have been developed to simplify the procedure. 

If you know the reactants and products of a chemical reaction, you should be able to write an equation for the reaction and balance it. In writing the equation, first write down the correct formulas for all reactants and products. After they are written down, only then start to balance the equation. Do not balance the equation by changing the formulas of the substances involved. For simple equations, you should balance the equation by inspection. (Balancing oxidation-reduction equations will be presented in Chap. 13.) The following rules will help you to balance simple equations. 

A complex reacting system is defined as one that requires more than one chemical equation to express the stoichiometric constraints contained in element balances. In such a case, the number of species usually exceeds the number of elements by more than 1. Although in some cases a proper set of chemical equations can be written by inspection, it is useful to have a universal, systematic method of generating a set for a system of any complexity, including a simple system. Such a method also ensures the correct number of equations (R), determines the number (C) and a permissible set of components, and, for convenience for a very large number of species (to avoid the tedium of hand manipulation), can be programmed for use by a computer. 

Equation 1.5-1 used as a mass balance is normally applied to a chemical species. For a simple system (Section 1.4.4), only one equation is required, and it is a matter of convenience which substance is chosen. For a complex system, the maximum number of independent mass balance equations is equal to R, the number of chemical equations or noncomponent species. Here also it is largely a matter of convenience which species are chosen. Whether the system is simple or complex, there is usually only one energy balance. 

In this chapter, you learned how to balance simple chemical equations by inspection. Then you examined the mass/mole/particle relationships. A mole has 6.022 x 1023 particles (Avogadro s number) and the mass of a substance expressed in grams. We can interpret the coefficients in the balanced chemical equation as a mole relationship as well as a particle one. Using these relationships, we can determine how much reactant is needed and how much product can be formed—the stoichiometry of the reaction. The limiting reactant is the one that is consumed completely it determines the amount of product formed. The percent yield gives an indication of the efficiency of the reaction. Mass data allows us to determine the percentage of each element in a compound and the empirical and molecular formulas. 

We have seen how analytical calculations in titrimetric analysis involve stoichiometry (Sections 4.5 and 4.6). We know that a balanced chemical equation is needed for basic stoichiometry. With redox reactions, balancing equations by inspection can be quite challenging, if not impossible. Thus, several special schemes have been derived for balancing redox equations. The ion-electron method for balancing redox equations takes into account the electrons that are transferred, since these must also be balanced. That is, the electrons given up must be equal to the electrons taken on. A review of the ion-electron method of balancing equations will therefore present a simple means of balancing redox equations. 

However, if reaction is not of a simple stoichiometry but involves different number of moles of reactants or products, the rate should be divided by corresponding stoichiometric coefficient in the balanced chemical equation for normalizing it and making it comparable. For example, for a general reaction aA + bB — cC + dD... 

Sigma (a) bonds Sigma bonds have the orbital overlap on a line drawn between the two nuclei, simple cubic unit cell The simple cubic unit cell has particles located at the corners of a simple cube, single displacement (replacement) reactions Single displacement reactions are reactions in which atoms of an element replace the atoms of another element in a compound, solid A solid is a state of matter that has both a definite shape and a definite volume, solubility product constant (/ p) The solubility product constant is the equilibrium constant associated with sparingly soluble salts and is the product of the ionic concentrations, each one raised to the power of the coefficient in the balanced chemical equation, solute The solute is the component of the solution that is there in smallest amount, solution A solution is defined as a homogeneous mixture composed of solvent and one or more solutes. 

One must immediately be aware of the limitations of the law of mass action. Almost every chemical reaction is in actual fact an extremely complicated process, and the familiar balanced chemical equation (which shows the molar relationships between the original reactants and the final products) gives no clue at all to the many intricate sequences of simple intermediate steps that are followed in going from "reactants" to "products." Always bear in mind the following points. 

The basic principles discussed at the beginning of Chapter 17 (in connection with the construction of simple electrochemical cells) are exactly the ones used to write and balance chemical equations for electron-transfer reactions. These principles also enable you to predict whether or not a given electron-transfer reaction will actually take place. 

For our present purposes, we use the term reaction mechanism to mean a set of simple or elementary chemical reactions which, when combined, are sufficient to explain (i) the products and stoichiometry of the overall chemical reaction, (ii) any intermediates observed during the progress of the reaction and (iii) the kinetics of the process. Each of these elementary steps, at least in solution, is invariably unimolecular or bimolecular and, in isolation, will necessarilybe kinetically first or second order. In contrast, the kinetic order of each reaction component (i.e. the exponent of each concentration term in the rate equation) in the observed chemical reaction does not necessarily coincide with its stoichiometric coefficient in the overall balanced chemical equation. 

An early objective in a mechanistic investigation is to establish the rate law (see Chapter 3) which is an algebraic equation describing the instantaneous dependence of the rate on concentrations of compounds or other properties proportional to concentrations (e.g. partial pressures). Rate laws cannot be rehably deduced from the stoichiometry of the overall balanced chemical equation-they have to be determined experimentally. The functional dependence of rates on concentrations maybe simple or complicated, and concentrations may be of reactants, products or even materials not appearing in the overall chemical equation, as in the case of catalysis (see Chapters 11 and 12) [3-7]. 

The observant reader will notice that some of the equations in this book are not balanced. Although unbalanced chemical equations can be distracting, there are times when trying to balance them is even more distracting. Chemical equations involving polymers certainly can be balanced, but doing so often leads to confusion. For example, consider this simple reaction from Chapter 2 indicating the formation of nylon-6 ... 

Most reactions do not occur in the simple fashion that we describe in a balanced chemical equation. Chemical equations show the reactants and products of the reaction but do nothing to describe how the former converts to the latter. A method that is used to show the intermediate processes that occur during a reaction is a reaction mechanism. A reaction mechanism lists the proposed changes that take place to the reactants as the product(s) are being formed. Usually this consists of two or three chemical reactions, referred to as elementary reactions or elementary steps, shown one on top of the other. For example, in the reaction of nitrogen dioxide and carbon monoxide, the balanced chemical equation looks like this ... 

If you are in doubt about writing simple chemical formula or how to balance an equation, see formula and balancing chemical equations in the Glossary. If you are uncertain of any symbol for an element then refer to the lists in the Appendies. 

Balance simple chemical equations (Section 2.4, Problems 31 and 32). 

Depending on the nature of the class, the instructor may wish to spend more time with the basics, such as the mass balance concept, chemical equilibria, and simple transport scenarios more advanced material, such as transient well dynamics, superposition, temperature dependencies, activity coefficients, redox energetics, and Monod kinetics, can be skipped. Similarly, by omitting Chapter 4, an instructor can use the text for a water-only course. In the case of a more advanced class, the instructor is encouraged to expand on the material suggested additions include more rigorous derivation of the transport equations, discussions of chemical reaction mechanisms, introduction of quantitative models for atmospheric chemical transformations, use of computer software for more complex groundwater transport simulations, and inclusion of case studies and additional exercises. References are provided... 

Students often prefer to perform simple calculations, like the direct titration of citric acid, using absolute molarities of titrant instead of deriving the equivalent and making use of factors. The procedure adopted is to convert the volume of titrant required to a number of moles and, from the balanced chemical equation, relate this to the number of moles of reactant used in the assay. This number is then converted into a weight and the... 

Learning to balance simple chemical equations (Section 4.2)... 

This introductory chapter describes the simple ideas of atoms and molecules, types of chemical formula and their molecular weight for students who have not studied chemistry before. Chemical equations and balanced chemical equations are introduced through the reactions used in an introductory practical laboratory course. The concepts of molarity and molar solutions are introduced through solving volumetric problems, to enable the student to start a laboratory course in practical Inorganic Chemistry. 

As we mentioned earlier, an overall balanced chemical equation does not tell us much about how a reaction actually takes place. In many cases, it merely represents the sum of several elementary steps, or elementary reactions, a series of simple reactions that represent the progress of the overall reaction at the molecular level. The term for the sequence of elementary steps that leads to product formation is reaction mechanism. The reaction mechanism is comparable to the route of travel followed during a trip the overall chemical equation specifies only the origin and destination. 

It is very important to recognize in this example that there is no simple link between the stoichiometry of the reaction and the form of the experimental rate equation. Trying to equate the partial orders of reaction for S20 and I to their balancing coefficients in the chemical equation would be similar to trying to relate apples to pears. It cannot he overemphasized that partial orders of reaction can be determined only from experimental measurements of the kinetics of a process. In the case of SiOs" turns out by coincidence, and no more than this, that the partial order has the same value as the balancing coefficient. For I , the partial order and the balancing coefficient (equal to 3) are very different. 

In many simple chemical equations, such as Equation 20.2, balancing the electrons is handled automatically in the sense that we can balance the equation without explicitly considering the transfer of electrons. Many redox equations are more complex than Equation 20.2, however, and caimot be balanced easily without taking into account the number of electrons lost and gained. In this section we examine the method of halfreactions, a systematic procedure for balancing redox equations. 

In the next section, we collect several models that we use repeatedly later on. We begin by introducing some concepts from chemical kinetics in this section. This is intended to be a very simple review of a few facts needed to discuss rate equation for chemical reactions. Consider the following (abstract) balanced chemical equation ... 

If V depends on the concentration of some species that does not appear in the balanced chemical equation, then that species is called a catalyst if v increases as the concentration of that species increases. If an increase in the concentration of that species leads to a decrease of the reaction velocity v, it is called an inhibitor. If V depends on one or more products, then the reaction is called autocatalytic if the product increases the reaction velocity. If the product decreases the reaction velocity, the reaction is called self-inhibiting. Rate laws are determined experimentally from kinetic data. Such a rate law is called an empirical rate law. Rate laws are often, but not always, found to depend on simple powers of the concentrations ... 

---