Electrolyte volume, calculation

Anion exclusion volumes calculated on the disk model [34] for a particle with a large radius (ro > 250 nm) are similar to those obtained from the infinite-plane model because, for a large particle, the anion exclusion volume contributed from the region outside the edge surface is relatively smaller than that from above the basal plane. Very large values of the anion exclusion volume are found on the disk model for small particles (r0 = lOnm) in dilute electrolyte solutions because anion depletion outside the edge surface becomes very important for small particles [34]. 

An investigation on the effect of added electrolyte valence and species on polyelectrolytes studied using ACM was made in Reference [46], First-order differences in polyelectrolyte conformations, interactions, and hydrodynamics were reported by the authors when electrolytes of different valence and symmetry were added to the polyelectrolyte solution. Each relevant characteristic, however, followed the same scaling relationship to ionic strength but the prefactors were different. Electrostatic persistence length/electrostatic excluded volume calculations without adjustable parameters suggested that the effective linear charge density is considerably lower in the presence of divalent ions than monovalent ions. Consideration of the... 

Note that the derivation is based on the passage of ions in and out of fixed electrode portions determined by the planes of reference A and B, and the gain or loss of electrolyte is calculated for a constant quantity of solvent. Appreciable volume changes at the electrodes would affect this picture, and are allowed for in very accurate work. A... 

Equations 57 and 58 assume that aU change in electrode volume is compensated by change in electrolyte volume fraction. This assumption neglects any effects of mechanical stress on changes in electrode area and/or thickness, and may be a poor assumption for alloy or phase-change electrodes [81]. Calculation of such changes in eleetrode volume would require knowledge of the mechanical properties of the battery container. 

Reliable pH data and activities of ions in strong electrolytes are not readily available. For this reason calculation of corrosion rate has been made using weight-loss data (of which a great deal is available in the literature) and concentration of the chemical in solution, expressed as a percentage on a weight of chemical/volume of solution basis. Because the concentration instead of the activity has been used, the equations are empirical nevertheless useful predictions of corrosion rate may be made using the equations. 

Nucleation Consider an idealized spherical nucleus of a gas with the radius on the surface of an electrode immersed in an electrolyte solution. Because of the small size of the nucleus, the chemical potential, of the gas in it will be higher than that ( To) in a sufficiently large phase volume of the same gas. Let us calculate this quantity. 

Influence on Electrolyte Conductivity In porous separators the ionic current passes through the liquid electrolyte present in the separator pores. Therefore, the electrolyte s resistance in the pores has to be calculated for known values of porosity of the separator and of conductivity, o, of the free liquid electrolyte. Such a calculation is highly complex in the general case. Consider the very simple model where a separator of thickness d has cylindrical pores of radius r which are parallel and completely electrolyte-filled (Fig. 18.2). Let / be the pore length and N the number of pores (all calculations refer to the unit surface area of the separator). The ratio p = Ud (where P = cos a > 1) characterizes the tilt of the pores and is called the tortuosity factor of the pores. The total pore volume is given by NnrH, the porosity by... 

In aqueous solutions, concentrations are sometimes expressed in terms of normality (gram equivalents per liter), so that if C is concentration, then V = 103/C and a = 103 K/C. To calculate C, it is necessary to know the formula of the solute in solution. For example, a one molar solution of Fe2(S04)3 would contain 6 1CT3 equivalents cm-3. It is now clear as to why A is preferred. The derivation provided herein clearly brings out the fact that A is the measure of the electrolytic conductance of the ions which make up 1 g-equiv. of electrolyte of a particular concentration - thereby setting conductance measurements on a common basis. Sometimes the molar conductance am is preferred to the equivalent conductance this is the conductance of that volume of the electrolyte which contains one gram molecule (mole) of the ions taking part in the electrolysis and which is held between parallel electrodes 1 cm apart. 

If the resistance of any other electrolyte is found by measurement to be Rx when using the same conductance cell, then the specific conductance of this electrolyte is L1/ . Thus, on multiplying the value of specific conductance so obtained by V, the volume of solution in milliliters containing one gram equivalent weight of the electrolyte under investigation, the equivalent conductance A is calculated. 

While the gases used in stripping are usually air, nitrogen, or helium, electrolytically evolved hydrogen has been used as a collector for hydrocarbons [49]. In this technique, the gas is not passed through a column of adsorbent, but instead collects in the headspace of the container. Since the volume of seawater and of hydrogen are known, the hydrocarbon concentration in the headspace can be used to calculate the partition coefficients and the concentration of hydrocarbon in the seawater. 

Figure 2.16 The pair potential calculated for rutile particles with a radius of 100 nm, background electrolyte concentration of 10 4moldm 3 and a -potential of —50 mV. Curve a was calculated for an isolated pair of particles and curve b corresponds to the potential for a pair ofparticles in a dispersion at a volume fraction of 0.45. Note how the increased electrolyte content due to the counterions introduced with the particles shorten the range of the repulsion enough for a small secondary minimum to be found at h 70 nm...

Figure 5.18 The high frequency shear modulus versus volume fraction for a polystyrene latex for three different electrolyte concentrations. The symbols are the experimental data and the solid lines are calculated fits using a cell model. The radius of the latex particles was 38 nm...

The pressure-volume-temperature (PVT) properties of aqueous electrolyte and mixed electrolyte solutions are frequently needed to make practical engineering calculations. For example precise PVT properties of natural waters like seawater are required to determine the vertical stability, the circulation, and the mixing of waters in the oceans. Besides the practical interest, the PVT properties of aqueous electrolyte solutions can also yield information on the structure of solutions and the ionic interactions that occur in solution. The derived partial molal volumes of electrolytes yield information on ion-water and ion-ion interactions (1,2 ). The effect of pressure on chemical equilibria can also be derived from partial molal volume data (3). 

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