Plot of reciprocal

Determination of VR/FA0 from plot of reciprocal rate versus fraction conversion. 

For a reaction of the type shown in (74) with hydroxide ion in excess, the expected variation of the time constant (t-1) for the first-order approach to equilibrium after a temperature perturbation is given by (75). Thus a plot of reciprocal relaxation time (t 1) against hydroxide ion concentration is... 

Figure 17.1, a plot of reciprocal rate, l/(—rA), versus /a illustrates the results expressed separately by equations 17.1-2 and 17.1-5. t/cAo for a CSTR is equivalent to the area A + B. For normal kinetics, in which the rate decreases with increasing /A, area A represents the integral in equation 17.1-2, that is, ttcAo in such a case, r > t. Conversely, for abnormal kinetics, as might be experienced for an autocatalytic reaction (Chapter 8), t > r, since area A + B + C represents tlcAo. 

Figure 13. Plot of reciprocal bimolecular clustering rate constant vs. reciprocal ion source pressure from which the transient Sn2 lifetime may be derived.

Figure 11. Mott-Schottky plots of reciprocal square of differential capacitance of n-type TiO electrode in 0.5M HfSO, vs, electrode potential. (O) In the dark (O) under illumination as in Figure 10. Intercept at C = oo gives the value of the flat-band potential (19).

Figure J. Reaction of CHzMn(CO)5 with triphenylphosphite in tetrahydrofuran. Plot of reciprocals.

Fig. 2. Plots of reciprocal energy transfer efficiency (y) against the concentration of benzene (B) and against reciprocal concentration of acetanilide (A) by the photo-rearrangement of acetanilide in cyclohexane, (o) 2-Aminoacetophenone ( ) 4-amino-acetophenone.

By using experimentally obtained data for 1 mM salicylic acid, a plot of reciprocal analytical signal versus reciprocal a, yielded a linear relationship for the pH range 1.65-3.01. This result supported the solvent extraction model. The corresponding estimate of capacity ratio and distribution coefficient using this treatment was 8.5. 

Total quantum yields in the absence of quencher for 2-pentanone and 2-hexanone are 0.20 and 0.25, respectively.326 Subtraction of the quantum yields for singlet reaction from the total quantum yields furnishes values of triplet quantum yields. Stern-Volmer plots of reciprocals of the triplet quantum yields versus piperylene concentration indicate that triplet 2-hexanone is five times as reactive as triplet 2-pentanone.273 Rough measurements have been made with methoxyacetone which suggest that at least 60% of its total photoelimination occurs from an unquenchable singlet state.273... 

The photoreactions of 3-ethoxyisoindolenone with 1,1-dimethoxyethene, tetra-methylethylene, and cts-2-butene in methylene chloride solvent were chosen for quantum yield studies50, s9 With 0.06 M 1,1-dimethoxyethene the quantum yield of cycloadduct formation is 0.72, and with 0.06 M tetramethylethylene the total quantum yield of adduct formation is 0.59. Over the concentration range 0.06—2.00 M, the quantum yields of product formation from addition to 1,1-dimethoxyethene and tetramethylethylene are inversely related to the olefin concentration. Plots of reciprocal of quantum yield of product formation vs. reciprocal of olefin concentration one non-linear however, plots of reciprocal of quantum yield vs. olefin concentration are linear with slopes and intercepts as shown in Table 5. For photoaddition of 3-ethoxyisoindolenone to tetramethylethylene and c/s-2-butene, the product ratios (56 57 58 and 59 60 61 62) are independent of olefin concentra-... 

Table 5. Slopes and intercepts of plots of reciprocal of quantum yield vs. olefin concentration...

The fact that plots of reciprocal of quantum yield of photoaddition vs. olefin concentration are linear with positive slope (Table 5) suggests that olefin quenches the singlet state and that all triplets formed are captured by olefin in the olefin concentration range examined in competition with unimolecular decay. Inefficiency... 

Fig. 2. Plots of reciprocal Michaelis Menten constant against copolymer composition in poly (IM-ac)...

An empirical method that is not related to a rigorous treatment of the convolution of a diffraction profile by size and strain is the Williamson-Hall analysis. This method is suitable for substances characterized by a large number of diffraction peaks and for highly defective samples for which analytical procedures bring upon problems with background definition. The method involves plotting of reciprocal breadth ((3 ) (FWHM) in units of the 20 scale versus the reciprocal positions (d ) of all peaks of a phase. The intercept yields the particle size and the slope the "apparent strain" 2r. The required quantities are defined as follows ... 

Figure 5 Plots of reciprocal capacitance against number of layers of polyimide 5a.

Plots of reciprocals of tiag as a function of 1.-DOPA concentration at different concentrations of lu-tyrosinase (102)... 

Fig. 3. Plot of reciprocal of rate of hydrogen production vs. pressure. (O) Cyclo-hexadiene ( ) hexatriene. Reprinted with permission from reference 44.

Figure 5-6 Plot of reciprocal concentration as a function of time.

Fig. 14.10 A plot of reciprocal luminescence lifetime (t" ) vs. mole fraction of H7O for DiO/HjO Tb(lll) solutions. Here we see a coordination number of 9 for Tbflll) in contrast to a coordination number of 8 shown in Fig. 14.9. Experiments like these sugge.st that perhaps the early lanthanides have coordination numbers of 10 while the later ones have coordination numbers of 9. In the presence of a quadridentate ligand, nitrilotriacetate (nta). four water molecules are lost and the number of coordinated water molecules drops to five. When ethylenediamineietraacetate (edta), a hexadentate ligand, is added, the number of water molecules drops to three. [From Horrocks, W. DeW. Sudnick, D. R. Acc. Cherri. Res. 1981. /4, 384-392. Reproduced with permission.)...

Figure 54. Plot of reciprocal of experimental measured capacity vs. reciprocal of calculated diffuse-layer capacity at constant charge zero, for different concentrations of solution Q > C2 > C3 > C4 > C5.

Fig. 6a. Plot of reciprocal of first ligand field transition 1/v in [Co(NH3)sX]54 against the reduced coupling constant XM-h in frans-[Pt(PEt3)2HX]. 1/v in units of kK-1.

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