Solution Using Excel

To solve for the equilibrium in Eq. (4.14) using Excel, you put the equation in one cell, put a guess of x in another cell, and use Goal Seek or Solver to make the first cell zero by changing x. Since the total number of moles does not change, you can change Eq. (4.13) to one involving moles  

The calculations are conveniently done in a spreadsheet, and the final results are shown in Table 4.2. Let us see how to construct this spreadsheet. 

Step 1 Column B is the initial moles of each species. 

Step 2 Column C is computed according to the equation displayed in Column D. 

Step 3 Then the equilibrium equation, Eq. (4.15), is calculated in cell C9, according to the formula displayed in cell D9. 

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On page 235-241 is the explicit solution used in Excel format to make studies, or mathematical experiments, of any desired and possible nature. The same organization is used here as in previous Excel applications. Column A is the name of the variable, the same as in the FORTRAN program. Column B is the corresponding notation and Column C is the calculation scheme. This holds until line 24. From line 27 the intermediate calculation steps are in coded form. This agrees with the notation used toward the end of the FORTRAN listing. An exception is at the A, B, and C constants for the final quadratic equation. The expression for B was too long that we had to cut it in two. Therefore, after the expression for A, another forD is included that is then included in B. 

A titration requires a solution whose concentration is known. In Example the NaOH solution used as the titrant was known to be 0.1250 M. A titrant of known concentration is known as a standard solution, and the concentration of such a solution is determined by a standardization titration. In a standardization titration, the solution being titrated contains a known amount of acid or base. An excellent acid for standardization is potassium hydrogen phthalate, KHCg H4 O4. This substance, a carboxylic acid that contains one weakly acidic hydrogen atom per molecule, is easily obtained as a highly pure solid. A known number of moles can be weighed on an... 

The above model of settler flow behaviour, combined with entrainment backmixing was used by Aly (1972) to model the unsteady-state extraction of copper from aqueous solution, using Alamine 336 solvent. An identification procedure for the relevant flow parameters showed an excellent fit to the experimental data with very realistic entrainment backmixing factors, fL = fQ = 3.5 percent, the fraction of well-mixed flow in the settlers, (XX = ay = 5 percent and an overall mass transfer capacity coefficient, Ka = 25 s->. 

The spreadsheet used for this example was Microsoft Works. A copy of the solution using Microsoft Excel can be found on the Butterworth-Heinemann web site bh.com/compa-nions/0750641428. 

This is a transcendental equation, which is not easily solved by ordinary methods. Nowadays, however, computers make the solution of such equations by successive approximations easy. In this case, again using EXCEL , we find that the value of T that makes the left-hand side of equation (42-50) become zero, which thus gives the value corresponding to the transmittance corresponding to minimum relative error, is 0.32994, rather than the previously accepted value of 0.368... 

Notwithstanding the excellent analytical features inherent in molecular phosphorimetric measurements, their use has been impeded by the need for cumbersome cryogenic temperature techniques. The ability to stabilize the "triplet state" at room temperature by immobilization of the phosphor on a solid support [69,70] or in a liquid solution using an "ordered medium" [71] has opened new avenues for phosphorescence studies and analytical phosphorimetry. Room-temperature phosphorescence (RTF) has so far been used for the determination of trace amounts of many organic compounds of biochemical interest [69,72]. Retention of the phosphorescent species on a solid support housed in a flow-cell is an excellent way of "anchoring" it in order to avoid radiationless deactivation. A configuration such as that shown in Fig. 2.13.4 was used to implement a sensor based on this principle in order to determine aluminium in clinical samples (dialysis fluids and concen-... 

The absorbance of a mixture is the sum of absorbances of the individual components. At a minimum, you should be able to find the concentrations of two species in a mixture by writing and solving two simultaneous equations for absorbance at two wavelengths. This procedure is most accurate if the two absorption spectra have regions where they do not overlap very much. With a spreadsheet, you should be able to use matrix operations to solve n simultaneous Beer s law equations for n components in a solution, with measurements at n wavelengths. You should be able to use Excel SOLVER to decompose a spectrum into a sum of spectra of the components by minimizing the function (Aca c — Am)2. 

The dehalogenation of naphthyridines with hydrogen over palladium on calcium carbonate in a weakly basic alcoholic solution gives excellent yields (90-95%) of reduced compounds.38,45,134,137,138 This method for removal of halogens has been extensively used and generally surpasses the classic hydrazine-copper sulfate reduction method. 

Figures 11.15 and 11.16 compare the temperature and velocity profiles, respectively, for the steady-state, fully developed flow of the coupled flow-heat transfer pressure driven slit flow problem, using RFM and FDM. The agreement between the two solutions is excellent.

Borax pentahydrate (also known as Neobor ) is the most common form of sodium borate used in a variety of industries. Its advantages when compared with borax lie in the lower transportation, handling, and the storage cost of a more concentrated product. Borax pentahydrate readily effloresces upon heating. It starts to dehydrate at about 65°C, loses all water of hydration when heated above 320°C, and fuses when heated above 740°C. In water, it hydrolyzes to give a mildly alkaline solution with excellent buffering properties.7... 

C. Alginate "Snakes" This makes an excellent demonstration on an overhead projector. Fill a crystallizing dish or beaker to a depth of Vi to 3A inch with 2% Ca(N03)2 solution. Introduce a stream of 2% sodium alginate solution directly into the- Ca2+ solution using a pipet. You should be able to cause the formation of a long strand of gel (a snake ). For the most part, the properties of the strands should be the same as those of the beads that you explored above. To test the physical properties of your snakes, wash them in fresh water and let them dry. As they are drying, periodically test their strength and note their appearance. 

Nitric acid, UNO 3, and the nitrates are familiar enough so that little space need he devoted to them. It will be recalled that the acid is an excellent oxidizing agent when hot and concentrated, dissolving many metals and metallic sulfides, the latter with the formation of sulfur or sulfate. The reduction products of nitrate in acid solution are almost always the nitrogen(II) or nitrogen(IV) oxides, but nitrate can be reduced to ammonia in basic solutions, using active metals (such as zinc or aluminum). 

A test of the accuracy of these models is to compare the calculated vibrational frequencies against those measured in aqueous solutions. Using literature values for infrared (IR) and Raman spectra as well as our own UV-resonance Raman spectra (UVRR), the model and observed values are compiled in Table 5.1 and an example correlation is plotted in Figure 5.4. Excellent agreement between theory and experiment for these aqueous-phase species suggests that we are adequately representing these organic acids in solution. 

The first step involves hydrolysis, with concentrated sulfuric acid, of p-toluene-sulfonyl chloride, which is quite cheap. The resulting sulfonic acid is chlorinated smoothly in the position ortho to the —CHs group, the reaction being carried out in sulfuric acid solution using iron as a catalyst. Finally, the sulfo group is split out with steam, yielding the desired o-chlorotoluene in excellent yield. This process is less satisfactory for use in the laboratory, but gives the best results in industrial operations. 

Torii has reported the electrochemical oxyselenation-deselenation of alkenes to give allylically rearranged allyloxy products. A typical example is given below (equation 23).Benzyl- or acetyl-(S)-citronellol was mixed in acetonitrile/water solution with diphenyl diselenide (0.5 mol equiv.) and a catalytic amount of tetraethylammonium bromide, and was electrolyzed at room temperature in an undivided cell using platinum electrodes and a constant current density of 10 mA cm. The corresponding allylic alcohols were isolated in excellent yields. In methanolic solution, using a reduced amount of diphenyl diselenide (20 mol %), the methoxy compounds were obtained in slightly reduced yields. 

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