statement of Debye huckel limiting law
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The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas. It is a linearized Poisson–Boltzmann model, which assumes an extremely simplified model of electrolyte solution but nevertheless gave accurate predictions of mean activity coefficients for ions in dilute solution. The Debye–Hückel equation provides a starting point for modern treatments of non-ideality of electrolyte solutions.
In the chemistry of electrolyte solutions, an ideal solution is a solution whose colligative properties are proportional to the concentration of the solute. Real solutions show departures from this kind of ideality at all but the very lowest concentrations (see, for example, Raoult's law). In order to accommodate these effects in the thermodynamics of solutions, the concept of activity was introduced: the properties are then proportional to the activities of the ions. Activity, a, is proportional to concentration, c. The proportionality constant is known as an activity coefficient, {\displaystyle \gamma }.
{\displaystyle a=\gamma c/c^{0}}In an ideal electrolyte solution the activity coefficients of all the ions are equal to one. Ideality of electrolyte solution can be achieved only in very dilute solutions. Non-ideality of more concentrated solutions arises principally (but not exclusively) because ions of opposite charge attract each other due to electrostatic forces, while ions of the same charge repel each other. In consequence ions are not randomly distributed throughout the solution, as they would be in an ideal solution.
Activity coefficients of single ions cannot be measured experimentally because an electrolyte solution must contain both positively charged ions and negatively charged ions. Instead, a mean activity coefficient, {\displaystyle \gamma _{\pm }} is defined. For example, with the electrolyte NaCl
{\displaystyle \gamma _{\pm }=\left(\gamma _{\mathrm {Na^{+}} }\gamma _{\mathrm {Cl^{-}} }\right)^{1/2}}In general, the mean activity coefficient of a fully dissociated electrolyte of formula AnBm is given by[4]
{\displaystyle \gamma _{\pm }=\left({\gamma _{A}}^{n}{\gamma _{B}}^{m}\right)^{1/(n+m)}}Activity coefficients are themselves functions of concentration as the amount of inter-ionic interaction increases as the concentration of the electrolyte increases. Debye and Hückel developed a theory with which single ion activity coefficients could be calculated. By calculating the mean activity coefficients from them the theory could be tested against experimental data. It was found to give excellent agreement for "dilute" solutions.
«» ,★ ★ ★★ ★★«. In order to calculate the activity, , of an ion, C, in a solution, one must know the concentration and the activity coefficient: is the concentration of the chosen standard state, e.g. 1 mol/kg if molality is used. is a constant that depends on temperature.
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