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For any substance, the number density can be expressed in terms of its amount concentration c (in mol/m 3) as = where N A is the Avogadro constant. This is still true if the spatial dimension unit, metre, in both n and c is consistently replaced by any other spatial dimension unit, e.g. if n is in cm −3 and c is in mol/cm 3 , or if n is in L ...
This is true for ideal solutions only, as occasionally ion pairing occurs in solution. At a given instant a small percentage of the ions are paired and count as a single particle. Ion pairing occurs to some extent in all electrolyte solutions. This causes the measured van 't Hoff factor to be less than that predicted in an ideal solution.
The concentration of measure phenomenon was put forth in the early 1970s by Vitali Milman in his works on the local theory of Banach spaces, extending an idea going back to the work of Paul Lévy. [ 2 ] [ 3 ] It was further developed in the works of Milman and Gromov , Maurey , Pisier , Schechtman , Talagrand , Ledoux , and others.
The result is that in dilute ideal solutions, the extent of boiling-point elevation is directly proportional to the molal concentration (amount of substance per mass) of the solution according to the equation: [2] ΔT b = K b · b c. where the boiling point elevation, is defined as T b (solution) − T b (pure solvent).
Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution. [1] For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase : [2]
The solubility of a specific solute in a specific solvent is generally expressed as the concentration of a saturated solution of the two. [1] Any of the several ways of expressing concentration of solutions can be used, such as the mass, volume, or amount in moles of the solute for a specific mass, volume, or mole amount of the solvent or of the solution.
The concentration gradient, in turn, is affected by the concentration of species at the electrode, and how fast the species can diffuse through solution. By changing the cell voltage, the concentration of the species at the electrode surface is also changed, as set by the Nernst equation. Therefore, a faster voltage sweep causes a larger ...
This article describes how to use a computer to calculate an approximate numerical solution of the discretized equation, in a time-dependent situation. In order to be concrete, this article focuses on heat flow, an important example where the convection–diffusion equation applies. However, the same mathematical analysis works equally well to ...