Common intersection point

The pHpZc (zero proton condition, point of zero charge) is not affected by the concentration of the inert electrolyte. As Fig. 2.3 shows, there is a common intersection point of the titration curves obtained with different concentrations of inert electrolyte. 

O Figure 4-10a shows a reaction scheme for interactions of enzyme and substrate with a full noncompetitive inhibitor. The inhibitor interacts with a site distinct from the active site, and the ESI complex is incapable of yielding product. It is thus possible, at saturating concentrations of inhibitor, to drive all enzymes to a nonproductive form, and so activity can be completely inhibited. Furthermore, the affinity of the inhibitor for the saturable allosteric inhibitory site remains independent of substrate concentration. A Lineweaver-Burk plot (O Figure 4-1 Ob) reveals a common intersection point on the 1/ [ S] axis for the data obtained at different inhibitor concentrations. It can be seen that as inhibitor concentration increases toward infinity, the slope of the Lineweaver-Burk plot increases toward infinity. Thus, a replot of the slopes versus inhibitor concentrations (O Figure 4-lOc) generates a straight line, which intersects the [i] axis at a value equal to —Ki. 

With perfect data, there will be a common intersection point at coordinates Emax) in the first quadrant. However, for real experimental data, there will be a number of intersection points. The maximum number of intersection points will be (nl2)(n - 1) where n is the number of lines. If different sets of lines have a common intersection point, then that point is treated with weighting. The estimate of the value will be the median value for the x-coordinate of these intersection points. Correspondingly, the median value of the y-coor-dinate of these intersection points provides the value for Ejnax ... 

Consider the standard Uni Uni mechanism (E + A EX E + P). A noncompetitive inhibitor, I, can bind reversibly to either the free enzyme (E) to form an El complex (having a dissociation constant K s), or to the central complex (EX) to form the EXl ternary complex (having a dissociation constant Xu). Both the slope and vertical intercept of the standard double-reciprocal plot (1/v vx. 1/[A]) are affected by the presence of the inhibitor. If the secondary replots of the slopes and the intercepts (thus, slopes or vertical intercepts vx [I]) are linear (See Nonlinear Inhibition), then the values of those dissociation constants can be obtained from these replots. If Kis = Xu, then a plot of 1/v vx 1/[A] at different constant concentrations of the inhibitor will have a common intersection point on the horizontal axis (if not. See Mixed-Type Inhibition). Note that the above analysis assumes that the inhibitor binds in a rapid equilibrium fashion. If steady-state binding conditions are present, then nonlinearity may occur, depending on the magnitude of the [I] and [A] terms in the rate expression. See also Mixed Type Inhibition... 

A] at different constant concentrations of B, a series of straight lines will be obtained having a common intersection point. The intersection point will always be in the second quadrant. A double-reciprocal plot of 1/v vs. 1/[B] at different constant concentrations of A will consist of a series of straight lines all intersecting on the vertical axis. This observation is characteristic of the rapid equilibrium ordered system but not of the steady-state scheme. 

Total proton adsorption, which can be identified with oH, is the sum of adsorption at edges and at exchange sites. The curves run almost parallel to each other, and there is an increase in proton adsorption on decreasing the pH and the electrolyte concentration. The pH where oH = 0 (pH0) decreases when the electrolyte concentration increases. This behavior is markedly different from the behavior exhibited by metal oxides having no structural charge. In these oxides, pH0 does not depend on the electrolyte concentration and appears as a common intersection point of the curves resulting from experiments performed at different electrolyte concentrations. 

This common intersection point in oxides corresponds to the point of zero charge, PZC, which is the pH where the net surface charge is zero.37,38... 

A new feature is that a common intersection point is no longer found. The point of zero charge moves to the left with increasing specific adsorption of cations. This shift Is almost Independent of the inner layer capacitance. Close to the point of zero charge the specific adsorption is superequivalent, as in fig. 3.20c. Making the surface potential more negative, a point is reached where... 

The most general and safe procedure to obtain a point of zero charge is by considering the salt effect on indifferent electrolyte concentrations, the pAg or pH, of the c.l.p. is identified as pAg or pH°. reasoning that when there is no double layer, there Is no charge to be screened and hence no Influence of added indifferent electrolyte. In principle this procedure is correct the main problem is to ensure that the electrolyte is really indifferent, that is, it contains only generlcally adsorbing Ions. 

In flg. 3.34a, a common intersection point is observed. Usually this means that the electrolyte Is Indifferent, so that c.l.p. = pH°. but a caveat is needed. A zero salt effect means that the Esln-Markov coefficient p Is zero see the definitions in 13.4.14 and 15). According to (3.4.16), P is directly related to the fraction of the surface charge that is compensated by cations and anions. For a monovalent electrolyte, at /3 = 0,... 

Figure 3.34. Salt effect on the surface charge near the point of zero charge. Top, a common Intersection point Is found bottom, with Increasing electrolyte concentration, the intersection points shift to lower pH and to more positive surface charge.

For oxides a common Intersection point of (T°(pH) curves at different electroljrte concentrations has also been found in the presence of specifically adsorbed lons . The trend is that if such a c,l.p. Is observed, it is to the left and to more positive charges for specific adsorption of cations and to the right and a more negative surface charge in the case of specific anion adsorption, see fig, 3.57, The physical explanation of such c.i,p, s was already anticipated In connection with the interpretation of fig, 3.34b for the thermodynamics, see . Van Riemsdljk et al. concluded, on theoretical grounds, that surface... 

Figure 3.67. Non-prlstlne common Intersection points, as sometimes observed with oxides, (a) No sf>eclflc adsorption (c.l.p. = p.p.z.c.) (b) specific adsorption of cations (c) specific adsorption of an ion.

Returning to point (ili), considering 13.4.13 or 13al the common intersection point c.i.p. must coincide with a maximum in the adsorption of butanol as a function of pAg or a°, indicated as pAg(max) or CT°(max), respectively. Even if there is no such c.i.p., at each cross-over of two (T°(pAg) curves at different c. is a maximum as a function of a° only in that case does shift with coverage. A maximum in is expected on the grounds that at very... 

Most data are from acid-base titrations at various salt concentrations, leading to a common intersection point. Data obteilned for only two salt concentrations are, as a rule, avoided. This is also the policy for curves where the sample conditions and/or the reversibility of the titrations are insufllclently controlled or which are suspect for other reasons. Isoelectric points or points of zero charge obtained by other methods are sometimes recorded (in italics) if titration data are not available, or if such points are interesting for other reasons. When the temperature Is known = -2.303 J T(pH° - pOH°)/2, see (3.8.16), is also... 

Figure 4.22. Surface charge at the aqueous side of the water-nitrobenzene interface. The aqueous concentration of LiCl is indicated. The nitrobenzene contains tribuiylainmonium tetraphenylborate. The potential is referred to the common intersection point, taken as a zero point. Temperature 22°C. (Redrawn from Samec et al., loc. cit.)...

The pHpzc (zero proton condition, point of zero charge) is not affected by the concentration of the inert electrolyte in the absence of a different specific supporting electrolyte ion boundary for cation and anion. The computations of Dzombak and Morel (1990) employ a difftise layer model coupled with acid-base surface reactions to describe Q versus pH. (This acid-base model incorporates variable capacitance.) As Figure 9.8 shows, there is a common intersection point of the titration curves obtained with different concentrations of inert electrolyte. 

The knowledge of PZC experimental value makes it possible to eliminate one of the four parameters of surface reaction equilibrium constants, even for those few reported cases where CIP was not observed in the system [112]. However, the reported experimental studies show that in most systems the PZC value does not practically depend on salt concentration in the bulk solution, (i.e. a common intersection point (CIP) occurs at pH = PZC) [104,112,113]. Except for the region of very low salt concentrations, one can assume that ac = ax = a. Thus, the independence of PZC of salt concentration can be formally expressed as ... 

Pechenyuk [46] noticed that the apparent PZC (referred to as pH ) of hydrous oxides obtained by hydrolysis of metal salts at certain pH increased as the pH of precipitation increased. The charging curves at three ionic strengths did not intersect, but the plots of apparent PZC as a function of pH of precipitation at three ionic strengths usually showed a common intersection point at pH of precipita-tionssapparent PZC. This pH value was termed true PZC . Unfortunately, with data points every 1 pH unit or more the results depend on rather arbitrarily drawn curves connecting the points representing one ionic strength. 

Barrow reports common intersection points of uptake (pH) curves obtained for sorption of phosphates (constant total concentration) by soils at different NaCl concentrations [25]. The slope of these curves decreases when the ionic strength increases, and the uptake of phosphates from 1 mol dm NaCl is almost independent of pH. The position of these intersection points on the pH scale is a function of the initial phosphate concentration. Similar effect was reported for selenates (IV). Interestingly for borates [26] whose uptake increased with pH over the pH range of interest, a common intersection point (pH of zero salt effect) was also observed but in this case the slope was higher for higher ionic strengths. This type of behavior has not been reported for well defined adsorbents,... 

Common intersection point, 66 coincidence with lEP, 67, 310 in presence of specific adsorption, 77 Component, 586, 587 Constant capacitance model, 603-614 Contact angle, 87 Controlled pore glass (see Glass) Coprecipitation, 7, 313 Cordierite... 

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