Calculations Involving Other Quantities

The balanced equation expresses quantities in moles, but it is seldom possible to measure out quantities in moles directly. If the quantities given or required are expressed in other units, it is necessary to convert them to moles before using the factors of the balanced chemical equation. Conversion of mass to moles and vice versa was considered in Sec. 7.4. First we will use that knowledge to calculate the number of moles of reactant or product and use that value to calculate the numbers of moles of other reactants or products. 

EXAMPLE 10.5. How many moles of Na2S04 are produced by reaction of 124 g of NaOH with sufficient H2SO4  

the first step is to write the balanced chemical equation  

Since the mole ratio is given by the equation, we must convert 124 g of NaOH to moles  

The left two boxes of Fig. 10-2 illustrate the additional step required for this calculation. 

---

With the acceptance of the atomic view of the world - accompanied by the necessity to explain reactions in extremely dilute gases (where the continuum theory fails) - the kinetic gas theory was developed. Using this it is possible not only to derive the ideal gas law in another manner but also to calculate many other quantities involved with the kinetics of gases - such as collision rates, mean free path lengths, monolayer formation time. 

In cases where dynamic effects must be considered, the problem is typified by A and b matrices that are parametrized, say, by time or other quantities. One such example involves modeling corrosion effects where time, acidity, and material thickness and age might be relevant dynamical parameters. In most cases one calculates a sequence of static solutions at time steps t that are then pieced together to fit initial (and final) conditions. 

Finally, we remark that the problem of the calculation of molecular quantities directly comparable with the outcome of experiments in the liquid phase is not limited to the realm of the NLO processes. All experiments involving the interaction of light with molecules in condensed matter are plagued by this problem. The methodology reviewed here has been applied (with appropriate modifications) to various spectroscopies, IR [23], Raman [24], Surface Enhanced Raman Scattering (SERS) [25], vibrational circular dichroism (VCD) [26] and linear dichroism [27] with equal reliability, and other extensions will come. 

The business department established the production rate for the new system, and the plant context determined certain other quantities, such as the pressure and purity of the hydrogen feed stream. Given these, optimization of the reaction system was accomplished by iteratively solving the simulation equations to arrive at the lowest cost for the product butanol, which was calculated according to the scheme described in the last section. The optimization procedure utilized a non-linear optimum-seeking algorithm, and involved the manipulation and calculation of search variables, response variables, and constraints. 

The meaning of a chemical formula was discussed in Chapter 5, and we learned how to interpret formulas in terms of the numbers of atoms of each element per formula unit. In this chapter, we will learn how to calculate the number of grams of each element in any given quantity of a compound from its formula and to do other calculations involving formulas. Formula masses are presented in Section 7.1, and percent composition is considered in Section 7.2. Section 7.3 discusses the mole—the basic chemical quantity of any substance. Moles can be used to count atoms, molecules, or ions and to calculate the mass of any known number of formula units of a substance. Section 7.4 shows how to use relative mass data to determine empirical formulas, and the method is extended to molecular formulas in Section 7.5. 

Gutbezahl and Grunwald considered liquid-junction potentials between a solution of aqueous potassium chloride and solutions of acids in ethanol-water mixtures both theoretically and experimentally. They concluded that for mixtures containing up to 33% ethanol the liquid-junction potential should be 6 mV or less. For solvents containing higher percentages of alcohol, the liquid-junction potential increases rapidly—25 mV for 50%, 44 mV for 65%, and 75 mV for 80% ethanol. These numerical values should not be interpreted too literally, particularly as the composition approaches 100% ethanol. Calculated liquid-junction potentials contain an indeterminate term that involves all quantities other than those arising from unequal transfer activity coefficients (such as dipole orientation effects). 

Thermodynamic aspects of the insertion reactions have been considered, especially with regard to reactions (b), Y = O. The enthalpy change of the reaction is related to the disruption of the metal-carbon bond, the formation of the new metal-carbon bond, the formation of the new carbon-carbon bond, and the reduction of the CO bond order. From the estimated metal-carbon bond dissociation enthalpies (BDE) of reagent and product and from the energetics of the other quantities involved in the process, the AC of reaction (g) has been calculated to be negative for R = Me or Ph and positive for R = CF3. This is in agreement with the observation that the trifluoroacetyl derivative... 

In chemical work, it is important to be able to calculate how much raw material is needed to prepare a certain quantity of products. It is also useful to know if a certain reaction method can prepare more product from a given quantity of material than another reaction method. Analyzing material means finding out how much of each element is present. To do the measurements, parts of the material are often converted to compounds that are easy to separate, and then those compounds are measured. All these measurements involve stoichiometry, tlie science of measuring how much of one thing can be produced from certain amounts of others. Calculations involving stoichiometry are also used in studying the gas laws, solution chemistry, equilibrium, and other topics. 

The results of Fig. 1 permit the calculation, through material balances, of the amounts of CO and 0 adsorbed based on the various curves of Fig. 1. However, the calculations involve the subtraction from each other of several integrated quantities. The adsorbed quantities calculated in alternative ways were not in satisfactory agreement because of their being based on relatively small differences of various pairs of measured quantities. Rather than pursue the description of this process here, we turn to a different set of experiments, which have given satisfactory results. 

Figure 3.8 Summary of the mass-mole-number relationships in a chemical reaction. The amount of one substance in a reaotion is related to that of any other. Quantities are expressed in terms of grams, moles, or number of entities (atoms, molecules, or formula units). Start at any box in the diagram (known) and move to any other box (unknown) by using the information on the arrows as conversion factors. As an example, if you know the mass (in g) of A and want to know the number of molecules of B, the path involves three calculation steps ...

---