Coefficients in chemical equations

Recall that the coefficients in chemical equations represent numbers of molecules, not masses of molecules. However, in the laboratory or chemical plant, when a reaction is to be run, the amounts of substances needed cannot be determined by counting molecules directly. Counting is always done by weighing. In this section we will see how chemical equations can be used to deal with masses of reacting chemicals. 

All the laws you have learned so far involving gases can be applied to calculate the stoichiometry of reactions in which gases are reactants or products. Recall that the coefficients in chemical equations represent molar amounts of substances taking part in the reaction. For example, when butane gas burns, the reaction is represented by the following chemical equation. 

FIGURE 3.3 The difference between changing subscripts and changing coefficients in chemical equations. 

In Section 8.2, we illustrated dimensional problem solving for calculating the numbers of moles and the masses of reactants and products in chemical reactions. The coefficients in chemical equations and the molar masses of reactants and products provide the factors that must be combined to solve problems of this kind. Consider the equation for the reaction that occurs when copper(II) sulfide is heated in oxygen... 

Although this is considered a properly balanced equation, many chemists do not ordinarily use fractional coefficients in chemical equations. To convert the fractional coefficient into an integer value, one simply multiplies the entire balanced equation by the proper integer value to convert the fractional value into the smallest integer value. In this case, one would multiply the entire equation by a factor of 2 to produce the final balanced equation with all integer coefficients ... 

Chapter 8 describes how the coefficients in chemical equations can be used as conversion factors between moles of reactants and moles of products in a chemical reaction. These conversion factors could be used to determine, for example, the amount of product obtained in a chemical reaction based on a given amount of reactant or the amount of one reactant needed to completely react with a given amount of another reactant. The general solution map for these kinds of calculations is... 

You can apply the discoveries of Gay-Lussac and Avogadro to calculate the stoichiometry of reactions involving gases. For gaseous reactants or products, the coefficients in chemical equations not only indicate molar amounts and mole ratios but also reveal volume ratios, assuming conditions remain the same. For example, consider the reaction of carbon monoxide with oxygen to give carbon dioxide. 

In Section 4.2 we discussed how the coefficients in chemical equations are used as conversion factors between the amounts of reactants (in moles) and the amounts of products (in moles). In aqueous reactions, quantities of reactants and products are often specified... 

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

An alternative approach and perhaps more applicable to drug designers was taken by Verma and co-workers [109]. They estimated several PAM PA systems as a function of calculated logP and a number of what they call indicator variables ) . In the presence of specific chemical groups, such as -COOH, -SO2NH2, aromatic-OH and -N(CH3)2, these variables take the value of unity and their positive or negative coefficient in the equation describes whether their effect is favorable or detrimental to membrane permeability. 

Now there are four H atoms, two Na atoms, and two O atoms on each side and the equation conforms to the law of conservation of mass. The numbers multiplying entire chemical formulas in chemical equations (for example, the 2 multiplying HzO) are called the stoichiometric coefficients of the substances. A coefficient of 1 (as for H2) is not written explicidy. 

The atomic processes that are occurring (under conditions of equilibrium or non equilibrium) may be described by statistical mechanics. Since we are assuming gaseous- or liquid-phase reactions, collision theory applies. In other words, the molecules must collide for a reaction to occur. Hence, the rate of a reaction is proportional to the number of collisions per second. This number, in turn, is proportional to the concentrations of the species combining. Normally, chemical equations, like the one given above, are stoichiometric statements. The coefficients in the equation give the number of moles of reactants and products. However, if (and only if) the chemical equation is also valid in terms of what the molecules are doing, the reaction is said to be an elementary reaction. In this case we can write the rate laws for the forward and reverse reactions as Vf = kf[A]"[B]6 and vr = kr[C]c, respectively, where kj and kr are rate constants and the exponents are equal to the coefficients in the balanced chemical equation. The net reaction rate, r, for an elementary reaction represented by Eq. 2.32 is thus... 

As you learned in Chapter 4, the coefficients in front of compounds and elements in chemical equations tell you how many atoms and molecules participate in a reaction. A chemical equation can tell you much more, however. Consider, for example, the equation that describes the production of ammonia. Ammonia is an important industrial chemical. Several of its uses are shown in Figure 7.2 on the following page. 

It is usually unnecessary to correct for activity coefficients in chemical kinetics. However, when such a correction is deemed necessary, it is well to remember that it cannot be made by simply replacing the concentrations of the reactants by the respective activities in the rate equation, and the activity coefficient of the activated complex must also be considered. 

The 4x1 column vector in equation 7.1-4 is referred to as the stoichiometric number matrix because it gives the stoichiometric coefficients vin chemical equation 7.1-2. 

Sets of linear and/or nonlinear equations can be solved simultaneously using an appropriate computer code (see Table L.l) by one of the methods described in Appendix L. Equation-based flowsheeting codes pertaining to chemical engineering can be used for the same purpose. The latter have some advantages in that the physical property data needed for the coefficients in the equations are transparently transmitted from a data base at the proper time in the sequence of calculations. 

Each of the rate terms, k+ and k, in Eq. (9.16) is related to concentrations in a way that one would predict if the probability of reaction were dependent on the collision of randomly moving particles the rate is proportional to the product of the number of entities involved in the reaction. All other factors that determine the reaction rate (energy barriers, temperature dependence, the effect of other species in solution, catalysis, etc.) are represented in the rate constant, k, which has units necessary to balance the left- and right-hand sides of the rate expression. Because ion interaction effects that are accounted for by activity coefficients in chemical equilibrium calculations (Chapter 3) are all incorporated into the rate constant, concentrations and not activities are used on the right-hand side of the reaction rate equation. 

Balancing chemical equations by inspection is a trial-and-error approach. It requires a great deal of practice, but it is very important Remember that we use the smallest whole-number coefficients. Some chemical equations are difficult to balance by inspection or trial and error. In Chapter 11 we will learn methods for balancing complex equations. 

Conversions of moles of one substance to moles of any other in the balanced chemical equation is straightforward just remember that it is moles not mass that is related to the coefficients in the equation, ffowever, stoichiometry problems often give students more trouble than they should because the problems are often asked in terms of masses or other quantities that can be related to moles of reactant or product. These problems are multistep problems, but should not present too much difficulty because each individual step is straightforward. 

To calculate standard cell potentials from the half-cell potentials in Table 9-1, there are four principles that we must know (1) When we reverse the direction of the chemical reaction, we change the sign of the potential. (2) If we multiply the coefficients in the equation by some number, we do NOT change the potential. Potential is an intensive property, and does not depend on the quantity of reagents. (3) When we add chemical equations for half-cells, we add the corresponding potentials. (4) A positive potential for a complete cell reaction means that the reaction proceeds spontaneously in the direction of the equation, and a negative potential means that the reaction goes spontaneously in the opposite direction. 

An equilibrium-constant expression can be written only after a correct, balanced chemical equation that describes the equilibrium system has been developed. A balanced equation is essential because the coefficients in the equation become the exponents in the equilibrium-constant expression. 

The algebraic sum of the stoichiometric coefficients used in chemical equation (13.56) is —1 (see equation... 

Chemical reactions change only forms of existence of basis components in compliance with conditions of mass conservation law. Proportions, which equate moles of the components before and after reactions, are called stoichiometric coefficients or simply reaction coefficients. In reaction equations these coefficients are inserted before formulae of the compounds themselves. For instance, the silicon, when solved in water, forms orthosilicic acid, which with increase in pH loses oxygen. For this reason the entire reaction of dissolving SiO may be expressed by the equation... 

We have already reasoned that chemical reactions occur when reactants collide. Based on the kinetic-molecular theory, collisions between two particles should be rather common. Three-particle collisions are much less likely because they require that three randomly moving species arrive at the same place at the same time. And four-particle collisions are virtually unheard of However, when we look at the stoichiometric coefficients of chemical equations, they seem to imply that collisions can occur among many particles balanced equations often involve stoichiometric coefficients far greater than two or three. To understand reaction mechanisms, we need to distinguish between the overall stoichiometry of a reaction and the steps in the reaction mechanism. 

After oxygen, the most important member of group 6A is sulfur. Sulfur also exists in several allotropic forms, file most common and stable of which is the yellow solid wifii molecular formula S. This molecule consists of an eight-mem-bered ring of sulfur atoms, as shown in Figure 7.28 -4. Even though solid sulfur consists of Sg rings, we usually write it simply as S(s) in chemical equations to simplify the coefficients. 

A chemical reaction occurs when the atoms in substances rearrange and combine into new substances. We represent a reaction by a chemical equation, writing a chemical formula for each reactant and product. The coefficients in the equation indicate the relative numbers of reactant and product molecules or formula units. Once the reactants and products and their formulas have been determined by experiment, we determine the coefficients by balancing the numbers of each kind of atom on both sides of the equation. 

---