Law of atomic balance

An elementary requirement is the law of atomic balance the number of atoms should be the same on both sides of each of the reactions. Calculating the number of atoms of each kind on both sides of both of the reactions is equivalent to multiplying the matrices Z and y according to the rule of ordinary matrix multiplication and setting the product equal to zero ... 

The law of atomic balance means for the rth elementary reaction that... 

It is obvious that none of the elementary reactions obey the law of atomic balance. Still, the Oregonator model of the Belousov-Zhabotinskii reaction, of which (3.9) is a subset, has served well for a long period of time when carefully interpreted. 

The moral to be drawn from these examples is either that one has to abandon the law of atomic balance, or that the atomic structure of the chemical components should be disregarded. 

An atomic reaction is said to be complete if any of the conceivable elementary reactions fulfilling the law of atomic balance can be written as linear combinations of the elementary reactions of the given reaction. 

Show that an atomic reaction obeying the law of atomic balance is necessarily conservative as well. 

General Material Balances. According to the law of conservation of mass, the total mass of an isolated system is invariant, even in the presence of chemical reactions. Thus, an overall material balance refers to a mass balance performed on the entire material (or contents) of the system. Instead, if a mass balance is made on any component (chemical compound or atomic species) involved in the process, it is termed a component (or species) material balance. The general mass balance equation has the following form, and it can be applied on any material in any process. 

However, the equation built so far does not follow the law of conservation of matter. If the number of atoms on the left-hand side and the number of atoms on the right-hand side of the equation are added up, they do not balance. Take the hydrogen atoms, for example. On the left-hand side of the equation, there are three... 

Now there are four hydrogen atoms on the reactant side (two in sulfuric acid and one in each of the two molecules of potassium hydroxide) and four hydrogen atoms on the product side (two in each of the two molecules of water). All of the other atoms have equal numbers on each side as well. Now the equation conforms to the law of conservation of matter, and it is a balanced chemical equation. 

A chemical equation describes a chemical reaction in many ways as an empirical formula describes a chemical compound. The equation describes not only which substances react, but the relative number of moles of each undergoing reaction and the relative number of moles of each product formed. Note especially that it is the mole ratios in which the substances react, not how much is present, that the equation describes. In order to show the quantitative relationships, the equation must be balanced. That is, it must have the same number of atoms of each element used up and produced (except for special equations that describe nuclear reactions). The law of conservation of mass is thus obeyed, and also the "law of conservation of atoms. Coefficients are used before the formulas for elements and compounds to tell how many formula units of that substance are involved in the reaction. A coefficient does not imply any chemical bonding between units of the substance it is placed before. The number of atoms involved in each formula unit is multiplied by the coefficient to get the total number of atoms of each element involved. Later, when equations with individual ions are written (Chap. 9), the net charge on each side of the equation, as well as the numbers of atoms of each element, must be the same to have a balanced equation. The absence of a coefficient in a balanced equation implies a coefficient of 1. 

The Law of Conservation of Matter provides the basis for balancing a chemical equation. It states that matter is neither created nor destroyed during an ordinary chemical reaction. Therefore, a balanced chemical equation must always contain the same number of each kind of atom on both sides of the equation. 

The Law of Conservation of Mass states that the total mass remains unchanged. This means that the total mass of the atoms of each element represented in the reactants must appear as products. In order to indicate this, we must balance the reaction. When balancing chemical equations, it is important to realize that you cannot change the formulas of the reactants and products the only things you may change are the coefficients in front of the reactants and products. The coefficients indicate how many of each chemical species react or form. A balanced equation has the same number of each type of atom present on both sides of the equation and the coefficients are present in the lowest whole number ratio. For example, iron metal reacts with oxygen gas to form rust, iron(III) oxide. We may represent this reaction by the following balanced equation ... 

A balanced chemical equation provides many types of information. It shows which chemical species are the reactants and which species are the products. It may also indicate in which state of matter the reactants and products exist. Special conditions of temperature, catalysts, etc., may be placed over or under the reaction arrow. And, very importantly, the coefficients (the integers in front of the chemical species) indicate the number of each reactant that is used and the number of each product that is formed. These coefficients may stand for individual atoms/molecules or they may represent large numbers of them called moles (see the Stoichiometry chapter for a discussion of moles). The basic idea behind the balancing of equations is the Law of Conservation of Matter, which says that in ordinary chemical reactions matter is neither created nor destroyed. The number of each type of reactant atom has to equal the number of each type of product atom. This requires adjusting the reactant and product coefficients—balancing the equation. When finished, the coefficients should be in the lowest possible whole-number ratio. 

BALANCE. (1) Exact equality of the number of atoms of various elements entering into a chemical reaction and the number of atoms of those elements in tlie reaction products. For example, in the reaction NaOH + HC1 -j- NaCl + H2O. the atoms in tlie input side are H[2], Na[l], 0(1], and 0(1]. Each of these is also present in the products, though in different combination. The atoms of catalysts (when present) do not enter into reactions and therefore are not involved. The balance of chemical reactions follows the law of conservation of mass. 

The requirement that an equation be balanced is a direct consequence of the mass conservation law discussed in Section 2.1 All chemical equations must balance because atoms are neither created nor destroyed in chemical reactions. The numbers and kinds of atoms must be the same in the products as in the reactants. 

A chemical equation is a shorthand way for a chemist to show a chemical change. On the previous page, to show ion formation, chemical equations are used. In the equations, reactants are on the left and products are on the right. The arrow separating reactants and products means yields. A chemical equation is balanced so that reactant atoms and product atoms are the same and equal in number, conforming to the law of conservation of matter. In an ionic equation, charge is also balanced. 

The law of conservation of matter states that in a closed system when a chemical change occurs, there is no change in mass. This is because atoms are conserved in a chemical change so atoms must be balanced in a chemical equation. In a balanced equation, coefficients tell the number of reactant and product substances that react and are produced. Subscripts tell the number of atoms of each kind in these substances. When a coefficient is multiplied by a subscript in a substance formula, the number of atoms is determined. Since a mole is an amount of a substance, the coefficients in a chemical equation can stand for the number of moles that react and are produced. 

Students will write balanced chemical equations for the chemical changes observed and explain that an equation is balanced to reflect the conservation of atoms in a chemical change, as required in the law of conservation of matter. 

Nuclear transmutations are represented by nuclear equations. Nuclear equations show the change in the nucleus as well as the particle emitted during the decay process. Just like chemical equations, these equations must follow the Law of Conservation of Mass and the Law of Conservation of Charge. That is, they are balanced by equating the sum of mass numbers on both sides of a reaction equation and the sum of atomic numbers on both sides of a reaction equation. 

Stoichiometry is defined as the mass balance of chemical reactions as they relate to the law of definite proportions and conservation of mass. The Redfield ratio provides the most well-known example of stoichiometric distinction where the average atomic ratios of C, N, and P in phytoplankton are relatively consistent (106 16 1) in most marine species. 

A mixture of electrons, ions, and atoms forms a system similar to that which we considered in Chap. X, dealing with chemical equilibrium in gases. Equilibrium is determined, as it was there, by the mass action law. This law can be derived by balancing the rates of direct and inverse collisions, but it can also be derived from thermodynamics, and the equilibrium constant can be found from the heat of reaction and the chemical constants of the various particles concerned. The heats of reaction can be found from the various ionization potentials, quantities susceptible of independent measurement, and the chemical constants are determined essentially as in Chap. VIII. Thus there are no new principles involved in studying the equilibrium of atoms, electrons, and ions, and we shall merely give a qualitative discussion in this section, the statements being equivalent to mathematical results which can be established immediately from the methods of Chap. X. 

Balanced chemical equations obey the law of conservation of matter by placing equal numbers of atoms of each element on both sides of a chemical equation. 

A balanced chemical equation reflects the law of conservation of mass. This type of equation shows that there is the same number of each kind of atom on both sides of the equation. Some skeleton equations are, by coincidence, already balanced. For example, examine the reaction of carbon with oxygen to form carbon dioxide, shown in Figure 4.1. In the skeleton equation, one carbon atom and two oxygen atoms are on the left side of the equation, and one carbon atom and two oxygen atoms are on the right side of the equation. 

Balancing a chemical equation requires an understanding of the Law of Conservation of Mass, which says that mass cannot be created or destroyed. The amount of mass in the reactants will be the amount of mass in the products. The credit for this discovery is given to Antoine Lavoisier, who took very careful measurements of the quantities of chemicals and equipment that he used. Conservation of mass also holds true when balancing equations. The number of atoms of each element in the reactants will be equal to the number of atoms of each element in the products. A useful mnemonic device for conservation of mass is What goes in, must come out. ... 

Even better, we can write a balanced equation, which shows the relative numbers of atoms of each of the elements involved. The unbalanced equation just presented seems to indicate that an iodide ion has disappeared during the reaction and that a nitrate ion has appeared from nowhere. As written, that equation violates the law of conservation of mass. Thus, we must always write balanced equations for reactions. The word equation is related to the word equal an equation must have equal numbers of atoms of each element on each side. Such an equation is said to be balanced. 

You know that symbols represent elements, and formulas represent compounds. In the same way, equations are used to represent chemical reactions. A correctly written chemical equation shows the chemical formulas and relative amounts of all reactants and products. Constructing a chemical equation usually begins with writing a word equation. This word equation contains the names of the reactants and of the products separated by an arrow. The arrow means forms or produces. Then, the chemical formulas are substituted for the names. Finally, the equation is balanced so that it obeys the law of conservation of mass. The numbers of atoms of each element must be the same on both sides of the arrow. 

The same types of atoms appear in both the reactants and products. However, Table 3 shows that the number of each type of atom is not the same on both sides of the equation. To show that a reaction satisfies the law of conservation of mass, its equation must be balanced. 

---