Titration mass balance

Figure 4.42. Trend analysis over 46 batches of a bulk chemical produced according to the same manufacturing procedure Small and scaled-up batch size [kg], HPLC and Titration assays [%], resp. individual HPLC impurity levels [%], versus batch number. The lack of full correlation between assays indicates that the titration is insensitive to some impurities detected by HPLC. The mass balance, where available, suggests that all relevant impurities are quantified. Impurities B and C, for instance, are highly correlated (r = 0.884, p = 0.0002).

Consider the sodium nltrate/goethite suspension titrated in the presence and absence of lead ion. The following equations governing the titrations are easily derived from the charge and mass balance equations ... 

Let s see how to reproduce the EDTA titration curves in Figure 12-11 by using one equation that applies to the entire titration. Because the reactions are carried out at fixed pH. the equilibria and mass balances are sufficient to solve for all unknowns. 

By substituting expressions for [ML] and [ML2J into the mass balance, show that the master equation for a titration of metal by ligand is... 

The potentiometric procedure requires that the mass balance of hydrogen ion or metal ion be known at each condition of pH or pM (15, 16). Considering the analysis using pH, it is necessary that the pH of the solution containing M and L be accurately determined throughout the titration. The hydrogen ion concentration [H+] is related to pH as follows ... 

The fraction of Ca(0H)2 reacted at any given time can be calculated by integrating the S02 versus time curve obtained by the recorder on the SO2 analyzer and doing a mass balance in the reactor. As a backup, the reacted solids are analyzed for sulfite and hydroxide using acid/base and iodine titrations. 

As a strong acid mixes with a strong base (i.e., titration), the pH of the solution changes with increasing amounts of a strong acid added to an initial volume of a strong base. The units for the mass balance equation should be moles, not moles/liter (i.e., concentration unit). Suppose a volume Vb of NaOH with concentration Cb is titrated with a volume Va of HC1 with concentration Ca. Then,... 

As illustrated in Section 2.1.2, the titration curve of a weak acid with a strong base can be constructed in terms of pH versus volume of the strong base. Consider a weak acid (e.g., HA) of volume Va its concentration Ca is titrated with a strong base (e.g., NaOH) of volume Vb and concentration Cb. The mass balances and electroneutrality equation can be given by ... 

When a volume Va of the mixture of a strong acid (e.g., HC1) with a concentration Cal and a monoprotic weak acid (HA) with a concentration Ca2 is titrated with a strong base (e.g., NaOH) with a concentration Cb and a volume Vb, the charge balance and mass balance can be written ... 

Consider the titration of a concentration Ca and a volume Va of a weak acid salt KH2A with a concentration Cb and a volume Vb of the strong base NaOH. The electroneutrality equation and the mass balance equation are given by ... 

All of the treated zeolite solids, both "filtrate" samples and "slurry" samples, were further analyzed by X-ray powder diffraction. The chemical compositions were determined by standard wet chemical analysis, and the filtrates were analyzed for Si02 and AI2O3 following titration. The results show that crystallinity was fully maintained in the solids and that the chemical reactions described in this work are confirmed by the analytical data and mass balances. 

To check the mass balance of the reaction, the reaction products were analyzed after each run by a thorium nitrate method for fluoride and by a sodium hydroxide titration for hydrogen ions. 

In order to fully define the titration system it is essential to account for the total metal ion added to solution, and the total ligand concentrations, Cn and Cl2, available to complex metal. This is done via mass balance equations shown in equations 16 thru 18. 

The theoretical equation describing the titration curve, [M ] v.v. Mt, is available by solution of one equation system considering the equations 9,11 and 12. By the expression of the conditional stability constant and the mass balance for the ligand one can obtain ... 

Substituting the equation (24) in the metal mass balance, equation (20), for all the i ligands, the theoretical equation of the titration curve is obtained (104) ... 

In the region of a few tenths of a milliliter beyond the first equivalence point, the solution is primarily HM with some formed as a result of the titration. So, the mass balance is... 

To derive a function for the buffer index of a weak monoprotic acid, HA, we begin as before with equilibrium, mass-balance, and charge-balance equations, and first derive an equation for the titration curve. We are given the following expressions ... 

Various chemical surface complexation models have been developed to describe potentiometric titration and metal adsorption data at the oxide—mineral solution interface. Surface complexation models provide molecular descriptions of metal adsorption using an equilibrium approach that defines surface species, chemical reactions, mass balances, and charge balances. Thermodynamic properties such as solid-phase activity coefficients and equilibrium constants are calculated mathematically. The major advancement of the chemical surface complexation models is consideration of charge on both the adsorbate metal ion and the adsorbent surface. In addition, these models can provide insight into the stoichiometry and reactivity of adsorbed species. Application of these models to reference oxide minerals has been extensive, but their use in describing ion adsorption by clay minerals, organic materials, and soils has been more limited. 

If water is a product of the reaction, its removal by evaporation is induced, and if no other volatile component is present, the progress of the reaction can also be monitored by calculating the mass of water evaporated. The latter is determined from a mass balance, using the overall loss of mass from the system, determined gravimetrically, or using Karl-Fischer titration to monitor water concentration changes. ... 

When the necessary condition that the chemistry at point A does not change with time is met, inverse mass balance models are still applicable when the chemistry at point B changes with time. An example is a laboratory column study, in which the chemistry of influent is maintained in the experiments while the effluent chemistry continues to change. In this case, we are assured that the effluent is chemically evolved from the influent. The variation of chemistry with time in the effluent does not violate the steady-state assumption. Another example is field injection of reactive tracers, during which the injectate chemistry is constant. Actually, laboratory titration experiments would also fit into this category because we know the initial solution chemistry from which the final solution evolves. Inverse mass balance modeling should find applications in these situations. 

Association constants were calculated by fitting the experimental titration curves to a 1 1 binding model based on (Equation (9.3)) and the mass balance (Equations (9.4) and (9.5)), by applying a least squares optimization routine ... 

Ultraviolet/visible (UV/vis) titrations were performed with a Varian Australia Pty Cary 3E UV/vis spectrophotometer. Titrations of Zn-porphyrin 1 were carried out by adding 5 pL aliquots (0.5 equiv.) of 10 2 M solutions of pyridine 2 or 4 to 1 mL of a 10-4 M Zn-porphyrin 1 solution, up to a maximum of 10 pyridine equivalents. Association constants were calculated by fitting the experimental titration curves to a 1 1 binding model based on (Equation (9.3)), on the mass balances (Equations (9.4) and (9.5)) and the Lambert-Beer law by applying a least squares optimization routine. 

Solution of the mass-balance equations at any titration point provides the concentration of free hydrogen ions [H ] so that a potential can be calculated for Eq. 10. The objective function to minimize can be written (in simplified form) as - )". It is immediately... 

A general titration curve equation can be derived from the mass balance equation for the ligand, i.e., to state that the total ligand concentration is the sum of the bound and free ligand concentrations. By the bound ligand is meant the ligand incorporated into the metal complex(es). Thus, for Ag ... 

For example, in the cell pictured above, with a copper sulphate solution with a concentration of 5x10 mol L it takes about two hours of electrolysis with the current set at 20 mA to observe significant concentration changes (about 20%). With an accurate measurement of these variations from complexation or precipitation titration reactions, the transport number of Cu ions can be determined t+ = 0.4 to the nearest few %, close to the values stated in scientific reports. As expected from the Hittorf mass balance, the concentration in the central compartment does not fluctuate a great deal. 

For example, iron(II) can be determined by titration with dichromate, so combination of the appropriate half-reactions [VII] and [XIII], so as to achieve a charge and mass balance, gives the overall reaction [XVI] ... 

The primary standard is the reference standard used in other methods and is characterised by its high purity and stability. A primary standard has its purity determined by mass balance and can be used to caUhrate secondary standards such as volumetric solutirms. These secondary standards are then used in the titrimetric analysis of samples. The titrant may degrade over time so this may need to be checked by titration with another secondary standard... 

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