Calculated Quantities

If we perform a calculation such as 19.24 x 56.32, our calculator displays the result as 1083.5968. As we saw earlier, the number of digits displayed is an indication of the precision of a number. We may suspect that the calculator is giving us more digits than are justified. How then, do we decide how many digits to quote  

Such calculations are best considered by writing the example by hand in the form we may have first used to do such operations. For example, 

Consequently, the summation in that column is really 3 plus an undefined number, which itself is undefined. The result of this should thus be written as a blank. If we do this, the problem doesn t arise elsewhere and so the result of the summation should be written as 19.6. 

In practice, we apply this rule by remembering that for sums and differences the answer should be quoted to the same number of decimal places as that in the least well defined piece of data. For example, 

Also we need to round as appropriate, by considering one digit further than given in the answer. So, for example, (3.69 - 2.1) gives 1.59, which we then round to 1.6 to give the appropriate level of precision. 

---

The nitrogen adsorption isotherm is determined for a finely divided, nonporous solid. It is found that at = 0.5, P/P is 0.05 at 77 K, gnd P/F is 0.2 at 90 K. Calculate the isosteric heat of adsorption, and AS and AC for adsorption at 77 K. Write the statement of the process to which your calculated quantities correspond. Explain whether the state of the adsorbed N2 appears to be more nearly gaslike or liquidlike. The normal boiling point of N2 is 77 K, and its heat of vaporization is 1.35 kcal/mol. 

By addition of slaked lime, in calculated quantity for the par ticular degree of hardness (Clark s method) ... 

Sulphuric acid. Ordinary concentrated acid, sp. gr. 1-84, is a constant boiling point mixture, b.p. 338°/760 mm., and contains 98 per cent. H2SO4. The 100 per cent, acid may be prepared by the addition of the calculated quantity of oleum it is also available commercially. 

Let us suppose it is desired to calculate the theoretical yield of ethyl maleate when 33 g. of silver maleate, suspended m dry ether, are treated with the calculated quantity of ethyl iodide (31-2 g.). 

Mix together 1 0 g. of pure p-naphthol and the theoretical quantity of 50 per cent, potassium hydroxide solution, add 0-5 g. of the halide, followed by sufficient rectified spirit to produce a clear solution. For alkyl chlorides, the addition of a little potassium iodide is recommended. Heat the mixture under reflux for 15 minutes, and dissolve any potassium halide by the addition of a few drops of water. The p-naphthyl ether usually crystallises out on cooling if it does not, dilute the solution with 10 per cent, sodium hydroxide solution untU precipitation occurs. Dissolve the p-naphthyl ether in the minimum volume of hot alcohol and add the calculated quantity of picric acid dissolved in hot alcohol. The picrate separates out on cooling. Recrystallise it from rectified spirit. 

Excess of keten over the calculated quantity does not increase the yield it leads to more acetic anhydride being collected in the low boiling point fraction. 

The method is generally applicable when other modes of esterification are either slow, inefficient, or likely to cause isomerisation it is, however, time-consuming and expensive. Small quantities of acid impurities are sometimes produced, hence it is advisable to wash the ester with saturated sodium bicarbonate solution. The silver salt can usually be prepared by dissolving the acid in the calculated quantity of standard ammonium hydroxide solution and... 

From the acid chloride. By the interaction of the acid chloride (prepared from the acid and thionyl chloride) and the calculated quantity of the alcohol at 0°, for example ... 

Preparation of silver maleate. Dissolve 65 g. of pure maleic acid (Section 111,143) in the calculated quantity of carefully standardised 3-5N aqueous ammonia solution in a 1-htre beaker and add, whilst stirring mechanically, a solution of 204 g. of silver nitrate in 200 ml. of water. Filter oflf the precipitated silver maleate at the pump, wash it with distilled water, and press well with the back of a large flat glass stopper. Dry in an electric oven at 50-60° to constant weight. The yield of the dry silver salt is 150 g. Store in a vacuum desiccator in the dark. 

N-Nitrosodiethylamine. Add 36-5 g. (51-5 ml.) of diethylamine slowly to the calculated quantity of carefully standardised 5A-hydra chloric acid cooled in ice (1). Introduce the solution of the hydi ochloride into a solution of 39 g. of sodium nitrite (assumed to be of 90 per cent, purity) in 45 ml. of water contained in a 250 ml. distilling flask. Distil the mixture rapidly to dryness. Separate the yellow upper layer of the nitrosamine from the distillate saturate the aqueous layer with soUd potassium carbonate and remove the nitroso compound which separates and add it to the main product. Dry over anhydrous potassium carbonate and distil. Collect the diethylnitrosamine at 172-173-5°, The yield is 41 g. 

This substance is conveniently obtained by treating p-bromoacetophenone (Section IV, 138) with the calculated quantity of bromine dissolved in glacial acetic acid ... 

Fluorescein is obtained by condensing phthahc anhydride (1 mol) with resorcinol (2 mols) in the presence of anhydrous zinc chloride. The tetra-bromo derivative, readily prepared by the addition of the calculated quantity of bromine, is eosin. 

The difference of a factor of 2 between these values comes about because the conditions were chosen to give the same rates. Since a given micelle-swollen polymer particle is active only half of the time, it must produce chains which are twice as long to polymerize at the same rate as the bulk case. Reducing Rj by 1/4 produces the following effects on the calculated quantities ... 

Evaluate ASj for ideal solutions and for athermal solutions of polymers having n values of 50, 100, and 500 by solving Eqs. (8.28) and (8.38) at regular intervals of mole fraction. Compare these calculated quantities by preparing a suitable plot of the results. 

This is true in all cases, but is most evident in the first column of calculated quantities in Table 8.4. 

The spherical geometry assumed in the Stokes and Einstein derivations gives the highly symmetrical boundary conditions favored by theoreticians. For ellipsoids of revolution having an axial ratio a/b, friction factors have been derived by F. Perrin, and the coefficient of the first-order term in Eq. (9.9) has been derived by Simha. In both cases the calculated quantities increase as the axial ratio increases above unity. For spheres, a/b = 1. 

Some plants use a bleed-and-feed process where a calculated quantity is withdrawn to waste treat each day and replaced with an equivalent amount of fresh solution. Using cleaners that reject oils can be effective if proper equipment is available. Stripping racks and reject parts off-line helps extend the... 

Additional near-surface measurements may also be required to support calculated quantities such as the bulk Richardson number (a stability parameter) ... 

Hasegawa and Sato (1977) showed that, when the calculated amount of flash vaporization equals 36% or more, all released fuel contributes to the BLEVE and eventually to the fireball. For lower flash-vaporization ratios, part of the fuel forms the BLEVE, and the remainder forms a pool. It is assumed that, if flash vaporization is below 36%, three times the calculated quantity of the flash vaporization contributes to the BLEVE. 

The mechanical design drawings for equipment can be used to calculate quantities of material contained in major equipment items. Also include quantities in hold-up within the process area. 

Colourless liquid b. p. 213—214° (ordinary pressuie). To convert the anhydiide into citraconic acid tlae calculated quantity of water is added (i mol. acid i mol. water), and the mi-vture well stirred. The whole solidifies, on standing, to a mass of colourless crystals of citraconic acid, whicb arc dried on a porous plate m. p. 84—86°. 

One problem in molecular modelling calculations is that large powers of 10 tend to appear in all the calculated quantities. Thus, for example, molecules have... 

The rate of iodine formation depends on the degree of A"-substitu-tion. Compounds which are unsubstituted on both the iV-atoms (35) and those wdth a single A -substituent (43) liberate instantly the calculated quantity of iodine in the cold. However, the 1,2-disubstituted diaziridines (44) need brief heating with the acid iodine solution they then give 95-100% of the calculated iodine. " This effect of substitution is so well defined that it can be used for a proof of constitution. The diaziridino-triazolidincs (37) prepared from aldehydes, ammonia, and chloramine give complete iodine liberation only on heating. Thus the structure 57 which is isomeric with 37 can be eliminated. ... 

It can be prepared by digesting y3-naphthol-sodium with the calculated quantity of methyl iodide in methyl alcohol solution or by heating 1 part of y3-naphthol, 3 parts of methyl alcohol, and 1 part of hy ochloric acid in an autoclave to 150°. 

When the temperature of the plasma reaches about 5° to 8°C, the calculated quantity of calcium chloride solution is added in amount which is from 0.2 to 0.3% in excess of that needed to react with and precipitate the anticoagulant. The temperature of the plasma is allowed to rise to about 24°C. At 18° to 24°C strands of fibrin begin to appear and the... 

From air velocity, ft/min, calculate quantity and film coefficient considering fm efficiency. 

Determine the number of significant figures in a calculated quantity. 

The standard redox potential is 1.14 volts the formal potential is 1.06 volts in 1M hydrochloric acid solution. The colour change, however, occurs at about 1.12 volts, because the colour of the reduced form (deep red) is so much more intense than that of the oxidised form (pale blue). The indicator is of great value in the titration of iron(II) salts and other substances with cerium(IV) sulphate solutions. It is prepared by dissolving 1,10-phenanthroline hydrate (relative molecular mass= 198.1) in the calculated quantity of 0.02M acid-free iron(II) sulphate, and is therefore l,10-phenanthroline-iron(II) complex sulphate (known as ferroin). One drop is usually sufficient in a titration this is equivalent to less than 0.01 mL of 0.05 M oxidising agent, and hence the indicator blank is negligible at this or higher concentrations. 

Procedure. The solution should contain antimony(III) (0,1 -0.2 g). Add a slight excess over the calculated quantity of potassium sodium tartrate to avoid the formation of basic salts upon dilution. Dissolve approximately five times the theoretical quantity of pure pyrogallol in 100 mL of air-free water, add this all at once to the antimony solution, and dilute to 250 mL, After 30-60 seconds... 

---