Effect of dilution, 7,

From the relations 2.12 and 2.13, the pH value of a buffer will change with its dilution, because of changes in the ionic strength. Table 2.2 shows the magnitude of the effect of diluting an equimolar solution of a HA/A buffer (total molar concentration stated) with an equal volume of water. The quantity ApHv is defined as the increase in pH of a solution when it is diluted in this way. Dilution of acidic buffers increases the pH with bases there is a decrease. Conversely, the addition of an inert salt such as NaCl 

Greater effects are produced when higher ionic charges are involved. For example, for a HA /A buffer (such as KH2PO4, Na2HP04) dilution with an equal volume of water increases the pH by approximately three times the amount shown in Table 2.2. 

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Equations 13.31 and 13.32 are only valid if the radioactive element in the tracer has a half-life that is considerably longer than the time needed to conduct the analysis. If this is not the case, then the decrease in activity is due both to the effect of dilution and the natural decrease in the isotope s activity. Some common radioactive isotopes for use in isotope dilution are listed in Table 13.1. 

The concentration of the added spike is calculated by taking into account the effect of dilution. 

Since capillary tubing is involved in osmotic experiments, there are several points pertaining to this feature that should be noted. First, tubes that are carefully matched in diameter should be used so that no correction for surface tension effects need be considered. Next it should be appreciated that an equilibrium osmotic pressure can develop in a capillary tube with a minimum flow of solvent, and therefore the measured value of II applies to the solution as prepared. The pressure, of course, is independent of the cross-sectional area of the liquid column, but if too much solvent transfer were involved, then the effects of dilution would also have to be considered. Now let us examine the practical units that are used to express the concentration of solutions in these experiments. 

The optical activity of malic acid changes with dilution (8). The naturally occurring, levorotatory acid shows a most peculiar behavior in this respect a 34% solution at 20°C is optically inactive. Dilution results in increasing levo rotation, whereas more concentrated solutions show dextro rotation. The effects of dilution are explained by the postulation that an additional form, the epoxide (3), occurs in solution and that the direction of rotation of the normal (open-chain) and epoxide forms is reversed (8). Synthetic (racemic) R,.9-ma1ic acid can be resolved into the two enantiomers by crystallisation of its cinchonine salts. 

RNA is relatively resistant to the effects of dilute acid, but gentle treatment of DNA with 1 mM HCl leads to hydrolysis of purine glycosidic bonds and the loss of purine bases from the DNA. The glycosidic bonds between pyrimidine bases and 2 -deoxyribose are not affected, and, in this case, the polynucleotide s sugar-phosphate backbone remains intact. The purine-free polynucleotide product is called apurinic acid. 

FIg. 6.5. Effect of dilution rate on cell density, substrate concentration and cell production rate. 

Li Jiang, Dahong Yang, and Shing Bor Chen. Electroviscous Effects of Dilute Sodium Poly(styrenesulfonate) Solutions in Simple Shear Flow. Macromolecules 2001, 34, 3730-3735. 

Historically, gas lubrication theory was developed from the classical liquid lubrication equation—Re5molds equation [4]. The first gas lubrication equation was derived by Harrison [5] in 1913, taking the compressibility of gases into account. Because the classical gas lubrication equation is based on the Navier-Stokes equation, it does not incorporate some gas flow characteristics rooted in the rarefaction effects of dilute gases. As early as 1959, Brunner s experiment [6] showed that the classical gas lubrication equation was... 

Table III. Effect of Dilution on the Dispersion of Supported Metal Catalysts...

Under some conditions, it is difficult to incorporate an internal standard into a method. If the chromatogram is very complex, an internal standard may interfere with quantitation of a peak of interest. The development of highly precise sample transfer techniques, including modem autoinjectors, reduces the dependence of the experimentalist on the use of an internal standard to correct for effects of dilution and transfer losses. In many cases, external standardization can be used effectively. The weight percent purity is determined by comparing the area of each peak in a chromatogram with those generated by separately injected pure standards of known concentration. 

Fig. 28 Top Effect of dilution on Rh and Kc/lg o of the mesoglobules ( ) formed upon heating of 0.2 gL1 aqueous solution of PVCL-g-18. Bottom Scattering intensity at 90° from polymer solution of different concentration. (Reprinted with permission from Ref. [180] copyright 2005 Elsevier)... 

However, many possible sources of error other than the accuracy of the measurements deserve attention. These sources of error are inherent in the assumptions that we made about average E, chemical expansion factor, and effect of dilution. 

Effect of dilution—In addition to the water present in the ambient air, the materials contained a certain amount of water. The water evaporated from the materials diluted the exhaust gases. This water is not accounted for in the chemical expansion factor. The magnitude of the error depends on the evaporation rate of water and the total... 

As shown in Figure 22.1, quenching is effective at producing fluorite. The process, however, is somewhat less efficient than simple cooling because of the counter-effect of dilution, which limits precipitation and eventually begins to cause the fluorite that formed early in the reaction path to redissolve. Each mechanism of fluorite deposition is quite efficient, nonetheless, producing - over a temperature drop of just 50 °C - about a cm3 or more mineral per kg of water in the ore fluid. 

The solution experiments may be made in aqueous media at around ambient temperatures, or in metallic or inorganic melts at high temperatures. Two main types of ambient temperature solution calorimeter are used adiabatic and isoperibol. While the adiabatic ones tend to be more accurate, they are quite complex instruments. Thus most solution calorimeters are of the isoperibol type [33]. The choice of solvent is obviously crucial and aqueous hydrofluoric acid or mixtures of HF and HC1 are often-used solvents in materials applications. Very precise enthalpies of solution, with uncertainties approaching 0.1% are obtained. The effect of dilution and of changes in solvent composition must be considered. Whereas low temperature solution calorimetry is well suited for hydrous phases, its ability to handle refractory oxides like A1203 and MgO is limited. 

Dearden JC, Tomlinson E (1971) Correction for effect of dilution on diffusion through a membrane. J Pharm Sci 60 1278-1279... 

FIGURE 8.17 Effect of dilution and temperature reduction, resulting from inert addition to the fuel, on soot formation. A 100% Ethene, B 50% Ethene/50% Nitrogen, C same as B except temperature has been adjusted to be equal to that of A by replacing a portion of the nitrogen in the oxidizer with an equal molar amount of argon. From Ref. [79]. 

A. superior end point is obtained if the effects of dilution are compensated for by using an abscissa axis of V +AV/2. 

The effect of dilution by shallow aquifers can also be quantified. It invariably results in scattered saturation curves, proportional to the extent of contamination. 

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