The Ion Product

Before we begin considering shifts in an equilibrium system, we need a quantitative way to describe the state of the system at any time, whether it has established equilibrium or not. In Chapter 12, you learned about the reaction quotient, Q, which was used to describe equilibrium systems. In solubility equilibria, we re not really dealing with a quotient—just a product. Because the expression is the product of the concentrations of two differentions, the equilibrium expression that describes solubility equilibria is known as the ion product. Q is calculated in the same way as K p, except it does not necessarily describe a system at equilibrium. Referring to our initial example, for the equilibrium shown below  

The value of Q can be interpreted according to three possible relationships between Q and 

This condition means that the concentration of ions is higher than it is at equilibrium. The way to get rid of the excess ions is for them to form additional solid (precipitate). This process will occur until Q = K p 

This means that the concentration of ions is smaller than it should be. the way to increase the concentration of ions is for more of the solid to dissolve until Q = K p 

The solution is at equilibrium. That means the solution is saturated and there is some solid present. 

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Ion Product. The ion product of water is the product of the molality of the hydrogen and hydroxide ions, oh - temperature... 

Ionic Equilibria.. The ion product constant of D2O (see Table 3) is an order of magnitude less than the value for H2O (24,31,32). The relationship pD = pH + 0.41 (molar scale 0.45 molal scale) for pD ia the range 2—9 as measured by a glass electrode standardized ia H2O has been established (33). For many phenomena strongly dependent on hydrogen ion activity, as is the case ia many biological contexts, the difference between pH and pD may have a large effect on the iaterpretation of experiments. 

Indeed, because most hydrogen atoms in liquid water are hydrogen-bonded to a neighboring water molecule, this protonic hydration is an instantaneous process and the ion products of water are and OH ... 

These equations say that the Kh of an amine multiplied by the of the corresponding ammonium ion is equal to Kw, the ion-product constant for water (1.00 x 10 14). Thus, if we know Ka for an ammonium ion, we also know for the corresponding amine base because /stronger base has an ammonium ion with a larger p... 

If Q > K, the solution contains a higher concentration of ions than it can hold at equilibrium. A precipitate forms, decreasing the concentrations until the ion product becomes equal to Ksp and equilibrium is established. 

This time the trial product, 4 X 10-4, is greater than Klp = 2.4 X 10 s so a precipitate does form. Solid calcium sulfate, CaS04, will continue to form, lowering the concentrations [Ca+2] and [SO -2] until they are low enough that the ion product equals Kcp. Then equilibrium exists and no more precipitation occurs. 

Kw is also widely called the autoionization constant and sometimes the ion product constant of water. 

The molar concentration of water, 55.56 mol/L, is too great to be significantly affected by dissociation. It therefore is considered to be essentially constant. This constant may then be incorporated into the dissociation constant K to provide a useful new constant termed the ion product for water. The relationship between and is shown below ... 

Note that the dimensions of K are moles per hter and those of are moles per hter. As its name suggests, the ion product is numerically equal to the product of the molar concentrations of and OH ... 

Kgp values can be compared with the ion product, 2sp, to determine whether or not a precipitate will form for a given solution. How would you describe a solution of AgCl with = 1.4 x 10 i° and =... 

Subsequently, Bos and Dahmen used in m-cresol65 (e = 12.29 at 25° C) a potentiometric titration method combined with conductometry. Essential precautions were the preparation of water-free m-cresol (<0.01% of water), the use of a genuine Bronsted base B, e.g., tetramethylguanidine (TMG), and the application of a glass electrode combined with an Ag-AgCl reference electrode filled with a saturated solution of Me4NCl in m-cresol. The ion product of the self-dissociation of m-cresol, Ks, was determined from the part beyond the equivalence point of the potentiometric titration curve of HBr with TMG comparison with titration curves calculated with various Ka values showed the best fit for Ks = 2 10 19... 

This equilibrium is characterized by the ion product of the solvent— thermodynamic... 

The activity of the solvent molecule HS in a single-component solvent is constant and is included in Kus. The concentration of ions is mostly quite low. For example, self-ionization occurs in water according to the equation 2H20— H30+ + OH". The conductivity of pure water at 18°C is only 3.8 X 10"8 Q"1 cm-1, yielding a degree of self-ionization of 1.4xl0"19. Thus, one H30+ or OH" ion is present for every 7.2 x 108 molecules of water. Some values of Kus are listed in Table 1.5 and the temperature dependence of the ion product of water Kw is given in Table 1.6. 

In order to measure cross sections, a beam of electrons of known energy is directed through a gas sample of known pressure and the resulting ion and electron currents measured.63 If mass selective ion detection is used, then partial ionization cross sections oz may be determined. These cross sections correspond to the production of z electrons and an ion or ions having total charge +ze. Some instruments allow the counting cross section oc, also known as the ion production cross section, to be determined ... 

For some nonaqueous solvents, the autoionization, if it occurs at all, must be to a degree so small that virtually no ions are present. If the ion product constant for a solvent is as low as 10-40, the concentra-... 

For this equilibrium, the ion product constant has a value of approximately 2.7 X 1CP4. However, the discussion is complex and other species are present in sulfuric acid as a result of equilibria that can be written as... 

Now compute the value of the ion product in this solution and compare it with the value of for Mg(OH)2. 

The ion product has the same format as the solubility product expression, but it involves initial rather than equilibrium concentrations. 

An ion pair is a close association of a cation and an anion in solution, whereas the ion product is the value obtained when the initial concentrations for the dissolved ions involved in the solubility equilibrium are inserted into the equilibrium constant expression. 

The presence of KI in a solution produces a significant [l ] in the solution. Not as much Agl can dissolve in such a solution as in pure water, since the ion product, [Ag+][r], cannot exceed the value of K (i.e. the T from the KI that dissolves represses the dissociation of Agl(s). In similar fashion, AgN03 produces a significant [Ag+] in solution, again influencing the value of the ion product not as much Agl can dissolve as in... 

Then we determine the value of the ion product and compare it to the solubility product constant value. 

Thus, when all concentrations are the same, the ion product, Q, equals 1.00. From the negative standard cell potential, it is clear that Keq must be (slightly) less than one. Therefore, all the concentrations cannot be 0.500 M at the same time. 

The laser induces instantaneous vaporization of a microvolume (called a plume), and a mixture of ionized matrix and analyte molecules is released into the vacuum of the ion source. The relationship between the laser irradiance, I ascn and the number of molecules formed, Gma di, is most peculiar. There exists a threshold irradiance, peculiar to each matrix, below which ionization is not observed. Above this level, the ion production increases in a very strong, nonlinear, manner (often Gma di grows as Ilaser is raised to the eighth power). 

Recognize that this problem is one involving the ion product, Q. We calculate Q in the same manner as Ksp, except that we use initial concentrations of the species instead of equilibrium concentrations. We then compare the value of Q to that of Ksp ... 

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