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The Boltzmann constant (k B or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. [2] It occurs in the definitions of the kelvin (K) and the gas constant , in Planck's law of black-body radiation and Boltzmann's entropy formula , and is used in ...
In thermodynamics, the ebullioscopic constant K b relates molality b to boiling point elevation. [1] It is the ratio of the latter to the former: = i is the van 't Hoff factor, the number of particles the solute splits into or forms when dissolved. b is the molality of the solution.
The concentration of water, [H 2 O], is omitted by convention, which means that the value of K w differs from the value of K eq that would be computed using that concentration. The value of K w varies with temperature, as shown in the table below. This variation must be taken into account when making precise measurements of quantities such as pH.
An often considered quantity is the dissociation constant K d ≡ 1 / K a , which has the unit of concentration, despite the fact that strictly speaking, all association constants are unitless values. The inclusion of units arises from the simplification that such constants are calculated solely from concentrations, which is not the case.
kT (also written as k B T) is the product of the Boltzmann constant, k (or k B), and the temperature, T.This product is used in physics as a scale factor for energy values in molecular-scale systems (sometimes it is used as a unit of energy), as the rates and frequencies of many processes and phenomena depend not on their energy alone, but on the ratio of that energy and kT, that is, on E ...
with an on-rate (k on) and off-rate (k off) related to the dissociation constant through K d =k off /k on. When the system equilibrates, [] [] = [] so that the average number of ligands bound to each receptor is given by
The analytical (total) concentration of a reactant R at the i th titration point is given by = + [] + where R 0 is the initial amount of R in the titration vessel, v 0 is the initial volume, [R] is the concentration of R in the burette and v i is the volume added. The burette concentration of a reactant not present in the burette is taken to be ...
depending on whether the electrode is calibrated in millivolts or pH. For convenience the concentration, [H +], is used in place of activity. In a titration of strong acid with strong alkali, the analytical concentration of the hydrogen ion is obtained from the initial concentration of acid, C i and the amount of alkali added during titration.