Stoichiometric calculations for solutions

Notice from Example 4.7 that the procedures for doing stoichiometric calculations for solution reactions are very similar to those for other types of reactions. It is useful to think in terms of the following steps for reactions in solution. 

Because so many important reactions occur in solution, it is important to be able to do stoichiometric calculations for solution reactions. The principles needed to perform these calculations are similar to those developed in Chapter 9. It is helpful to think in terms of the following steps ... 

Stoichiometric calculations for redox reactions in water solution are carried out in much the same way as those for precipitation reactions (Example 4.5) or acid-base reactions (Example 4.7). 

We will introduce stoichiometric calculations for reactions in solution in Example 4.7. 

We know the amounts of pure substances by converting their masses into number of moles. But for dissolved substances, we need the concentration— the number of moles per volume of solution—to find the volume that contains a given number of moles. In this section, we first discuss molarity, the most common way to express concentration (Chapter 13 covers others). Then, we see how to dilute a concentrated solution and how to use stoichiometric calculations for reactions in solution. 

The emphasis is on writing and balancing chemical equations for these reactions. All of these reactions involve ions in solution. The corresponding equations are given a special name net ionic equations. They can be used to do stoichiometric calculations similar to those discussed in Chapter 3. 

Suppose we are titrating the triprotic acid H P04 with a solution of NaOH. The experimentally determined pH curve is shown in Fig. 11.13. Notice that there are three stoichiometric points (B, D, and F) and three buffer regions (A, C, and E). In pH calculations for these systems, we assume that, as we add the hydroxide solution, initially NaOH reacts completely with the acid to form the diprotic conjugate base... 

Solution Table 13.1 shows results calculated using Equation (13.4). The stoichiometric requirement for a binary polycondensation is very demanding. High-molecular-weight pol5Tner, say li > 100, requires a weighing accuracy that is difficult to achieve in a flow system. 

Numerous investigations have shown the existence of the heptamolybdate, [Mo7024]6 , and octamolybdate, [Mo8026]4, ions in aqueous solution. Potentiometric measurements with computer treatment of the data proved to be one of the best methods to obtain information about these equilibria. Stability constants are calculated for all species in a particular reaction model, which is supposed to give the best fit between calculated and experimental points. In the calculations the species are identified in terms of their stoichiometric coefficients as described by the following general equation for the various equilibria... 

A chemical formula tells the numbers and the kinds of atoms that make up a molecule of a compound. Because each atom is an entity with a characteristic mass, a formula also provides a means for computing the relative weights of each kind of atom in a compound. Calculations based on the numbers and masses of atoms in a compound, or the numbers and masses of molecules participating in a reaction, are designated stoichiometric calculations. These weight relationships are important because, although we may think of atoms and molecules in terms of their interactions as structural units, we often must deal with them in the lab in terms of their masses—with the analytical balance. In this chapter, we consider the Stoichiometry of chemical formulas. In following chapters, we look at the stoichiometric relations involved in reactions and in solutions. 

After we have developed an ionic equation for an electron-transfer reaction, we frequently need to show the molecules involved in the solutions—that is, the substances that are initially put into the solution, and those that are obtained from it after the reaction has occurred. We must have such molecular equations if stoichiometric calculations are to be made. 

The first of these theories applies the law of mass action to the equilibrium between unassociated molecules or ions and micelles, as illustrated by the following simplified calculation for the micellisation of non-ionic surfactants. If c is the stoichiometric concentration of the solution, x is the fraction of monomer units aggregated and m is the number of monomer units per micelle,... 

Molality and molarity are each very useful concentration units, but it is very unfortunate that they sound so similar, are abbreviated so similarly, and have such a subtle but crucial difference in their definitions. Because solutions in the laboratory are usually measured by volume, molarity is very convenient to employ for stoichiometric calculations. However, since molarity is defined as moles of solute per liter of solution, molarity depends on the temperature of the solution. Most things expand when heated, so molar concentration will decrease as the temperature increases. Molality, on the other hand, finds application in physical chemistry, where it is often necessary to consider the quantities of solute and solvent separately, rather than as a mixture. Also, mass does not depend on temperature, so molality is not temperature dependent. However, molality is much less convenient in analysis, because quantities of a solution measured out by volume or mass in the laboratory include both the solute and the solvent. If you need a certain amount of solute, you measure the amount of solution directly, not the amount of solvent. So, when doing stoichiometry, molality requires an additional calculation to take this into account. 

SOLUTION First, calculate the theoretical air from the feed rate of fuel and the stoichiometric equation for... 

Describe the procedure for preparing a solution of a certain molarity. Use molarity in stoichiometric calculations. 

In Figure 3, the stoichiometric difference between the calcium ion concentration in the rock runoff and the hydrogen ion concentration in the incident rain is plotted versus the rain pH. Lines are drawn for the two calculated stoichiometric differences for both open and closed systems. The representative points from the onsite experiment fall within these two limiting cases. These results illustrate that the onsite stoichiometry is dependent on the initial pH of the incident rainfall and on whether the reacting solution is open or closed to exchange of carbon dioxide in the atmosphere. 

Thermodynamic activities of ionic species in aqueous solutions with ionic strength (I) < 0.01 molal (m) commonly are calculated using the ion-pair model (3), which is valid also for solutions with I < 0.1 m. In dominantly NaCl solutions, the ion-pair model can be used for I < 3 m with appropriate adjustments to the activity coefficients (4). The specific ion interaction model ( may be more appropriate for solutions of high ionic strengths. The effect of pressure on the thermodynamic activities of single ions in this model can be estimated from the stoichiometric partial molal volume and compressibility data (]) However, a complete data set for all the ion-interaction parameters is not yet available for this model to be used in complex geochemical solutions. 

This reaction illustrates a very important general principle The hydroxide ion is such a strong base that for purposes of stoichiometric calculations it can be assumed to react completely with any weak acid that we will encounter. Of course, OH ions also react completely with the ions in solutions of strong acids. 

In this nonstoichiometric method, part of the solution is the set of values for the Lagrange multipliers In most situations these multipliers have little physical significance they merely serve to ensure conservation of atoms, so their values are a necessary but nonphysical by-product of the calculation. When the number of elements Mg is less than the number of species C, the C equations (10.4.35) could be combined to eliminate the nig multipliers X, so their values would not obtained explicitly. However, if such a combination is done, the result is equivalent to the stoichiometric expression for the equilibrium constant, and the computational advantages of the nonstoichiometric method are lost. 

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