Ionic concentrations

The expression for v shows that it is the product of the ionic concentration c and e lzJcT, which is called the... 

Bjemim parameter. The virial series is an expansion in the total ionic concentration c at a fixed value of... 

Ionic conductors arise whenever there are mobile ions present. In electrolyte solutions, such ions are nonually fonued by the dissolution of an ionic solid. Provided the dissolution leads to the complete separation of the ionic components to fonu essentially independent anions and cations, the electrolyte is tenued strong. By contrast, weak electrolytes, such as organic carboxylic acids, are present mainly in the undissociated fonu in solution, with the total ionic concentration orders of magnitude lower than the fonual concentration of the solute. Ionic conductivity will be treated in some detail below, but we initially concentrate on the equilibrium stmcture of liquids and ionic solutions. 

It is important to recognize the approximations made here the electric field is supposed to be sulficiently small so that the equilibrium distribution of velocities of the ions is essentially undisturbed. We are also assuming that the we can use the relaxation approximation, and that the relaxation time r is independent of the ionic concentration and velocity. We shall see below that these approximations break down at higher ionic concentrations a primary reason for this is that ion-ion interactions begin to affect both x and F, as we shall see in more detail below. However, in very dilute solutions, the ion scattering will be dominated by solvent molecules, and in this limiting region A2.4.31 will be an adequate description. 

NH4. HCO3. CU and Na and the least soluble salt sodium hydrogen carbonate, is precipitated when ionic concentrations increase, and is removed by vacuum filtration. 

A solution containing a relatively high concentration of inert electrolytes such that its composition fixes the ionic concentration of all solutions to which it is added. 

Fig. 4. Hypothetical leakage curves to show effect of ionic concentration and flow rate, where the dashed line corresponds to the leakage shutdown level...

Fig. 14. The cellular ionic environment depicting representative intracellular ionic concentrations and the equiUbrium potentials, for individual ions. Excitatory and inhibitory events are represented by — and +, respectively. Thus, K" channel agonists and antagonists are inhibitory and excitatory, respectively Ca " channel antagonists and activators are inhibitory and excitatory, respectively.

Fig. 1. (a) Ionic concentrations in static state. Thejy-axis represents the cellulose surface, (b) Distribution of ions in practice. 

Surface charge pH, ionic concentration Resistance to liquid flowthrough the filter medium and support... 

The concentration of salt in physiological systems is on the order of 150 mM, which corresponds to approximately 350 water molecules for each cation-anion pair. Eor this reason, investigations of salt effects in biological systems using detailed atomic models and molecular dynamic simulations become rapidly prohibitive, and mean-field treatments based on continuum electrostatics are advantageous. Such approximations, which were pioneered by Debye and Huckel [11], are valid at moderately low ionic concentration when core-core interactions between the mobile ions can be neglected. Briefly, the spatial density throughout the solvent is assumed to depend only on the local electrostatic poten-... 

Hygroscopic Panicle Deposition Determined by Initial Ionic Concentration... 

In this partial derivative the temperature T and the ionic concentrations and p in the bulk phase are kept constant. Hereafter we assume that we have a 1 1 electrolyte, = p = Pb/2- Taking the derivative of (1) relative to (j) we get... 

Instead of an exact calculation, Gouy and Chapman have assumed that (4) can be approximated by combining the Poisson equation with a Boltzmann factor which contains the mean electrical potential existing in the interface. (This approximation will be rederived below). From this approach the distribution of the potential across the interface can be calculated as the function of a and from (2) we get a differential capacitance Cqc- It has been shown by Grahame that Cqc fits very well the measurements in the case of low ionic concentrations [11]. For higher concentrations another capacitance in series, Q, had to be introduced. It is called the inner layer capacitance and it was first considered by Stern [1,2]. Then the experimental capacitance Cexp is analyzed according to ... 

Total Salinity. The salinity control of oil-base mud is very important for stabilizing water-sensitive shales and clays. Depending upon the ionic concentration of the shale waters and of the mud water phase, an osmotic flow of pure water from the weaker salt concentration (in shale) to the stronger salt concentration (in mud) will occur. This may cause a dehydration of the shale and, consequently, affect its stabilization. 

With respect to general corrosion, once a surface film is formed the rate of corrosion is essentially determined by the ionic concentration gradient across the film. Consequently the corrosion rate tends to be independent of water flow rate across the corroding surface. However, under impingement conditions where the surface film is unable to form or is removed due to the shear stress created by the flow, the corrosion rate is theoretically velocity (10 dependent and is proportional to the power for laminar flow and... 

It is important to note that the solubility product relation applies with sufficient accuracy for purposes of quantitative analysis only to saturated solutions of slightly soluble electrolytes and with small additions of other salts. In the presence of moderate concentrations of salts, the ionic concentration, and therefore the ionic strength of the solution, will increase. This will, in general, lower the activity coefficients of both ions, and consequently the ionic concentrations (and therefore the solubility) must increase in order to maintain the solubility product constant. This effect, which is most marked when the added electrolyte does not possess an ion in common with the sparingly soluble salt, is termed the salt effect. 

The great importance of the solubility product concept lies in its bearing upon precipitation from solution, which is, of course, one of the important operations of quantitative analysis. The solubility product is the ultimate value which is attained by the ionic concentration product when equilibrium has been established between the solid phase of a difficultly soluble salt and the solution. If the experimental conditions are such that the ionic concentration product is different from the solubility product, then the system will attempt to adjust itself in such a manner that the ionic and solubility products are equal in value. Thus if, for a given electrolyte, the product of the concentrations of the ions in solution is arbitrarily made to exceed the solubility product, as for example by the addition of a salt with a common ion, the adjustment of the system to equilibrium results in precipitation of the solid salt, provided supersaturation conditions are excluded. If the ionic concentration product is less than the solubility product or can arbitrarily be made so, as (for example) by complex salt formation or by the formation of weak electrolytes, then a further quantity of solute can pass into solution until the solubility product is attained, or, if this is not possible, until all the solute has dissolved. 

Since water is only slightly ionised, the ionic concentrations will be small, and their activity coefficients may be regarded as unity the activity of the un-ionised molecules may also be taken as unity. The expression thus becomes ... 

The ionic product varies with the temperature, but under ordinary experimental conditions (at about 25 °C) its value may be taken as 1 x 10 14 with concentrations expressed in molL-1. This is sensibly constant in dilute aqueous solutions. If the product of [H + ] and [OH-] in aqueous solution momentarily exceeds this value, the excess ions will immediately combine to form water. Similarly, if the product of the two ionic concentrations is momentarily less than 10-14, more water molecules will dissociate until the equilibrium value is attained. 

The logarithmic or exponential form has also been found useful for expressing other small quantities which arise in quantitative analysis. These include (i) dissociation constants (Section 2.13), (ii) other ionic concentrations, and (iii) solubility products (Section 2.6). 

If a buffer solution is diluted, the ionic concentrations are decreased and so, as shown in Section 2.5, the ionic activity coefficients are increased. It follows from equation (26) that the pH is increased. 

This is not strictly true, since the dissolved silver chloride will contribute silver and chloride ions to the solution the actual concentration is ca 1 x 10-5 gions L . If the excess of silver ions added is greater than 10 times this value, i.e. > 10 /Af, ol AgC1, the error introduced by neglecting the ionic concentration produced by the dissolved salt may be taken as negligible for the purpose of the ensuing discussion. 

If the relevant ionic concentration in the solution is c, and the ion concerned has a charge number of 2, then at a temperature of 25 °C, the cathode potential... 

If the ionic concentration is reduced by deposition to one ten-thousandth of its original value, thus giving an accuracy of 0.01 per cent in the determination, the new cathode potential will be ... 

Direct measurement of conductivity is potentially a very sensitive procedure for measuring ionic concentrations, but it must be used with caution since any charged species present in a solution will contribute to the total conductance. 

Ion chromatography (see Section 7.4). Conductivity cells can be coupled to ion chromatographic systems to provide a sensitive method for measuring ionic concentrations in the eluate. To achieve this end, special micro-conductivity cells have been developed of a flow-through pattern and placed in a thermostatted enclosure a typical cell may contain a volume of about 1.5 /iL and have a cell constant of approximately 15 cm-1. It is claimed15 that sensitivity is improved by use of a bipolar square-wave pulsed current which reduces polarisation and capacitance effects, and the changes in conductivity caused by the heating effect of the current (see Refs 16, 17). 

In the Nernst equation the term RT/nF involves known constants, and introducing the factor for converting natural logarithms to logarithms to base 10, the term has a value at a temperature of 25 °C of 0.0591 V when n is equal to 1. Hence, for an ion M+, a ten-fold change in ionic activity will alter the electrode potential by about 60 millivolts, whilst for an ion M2 +, a similar change in activity will alter the electrode potential by approximately 30 millivolts, and it follows that to achieve an accuracy of 1 per cent in the value determined for the ionic concentration by direct potentiometry, the electrode potential must be capable of measurement to within 0.26 mV for the ion M+, and to within 0.13 mV for the ion M2 +. ... 

Fabiato, A. (1988). Computer programs for calculating total from specified free or free from specified total ionic concentrations in aqueous solutions containing multiple metals and ligands. Method. Enzymol. 157 378-417. 

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