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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.
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.
Conversely, when pH = pK a, the concentration of HA is equal to the concentration of A −. The buffer region extends over the approximate range pK a ± 2. Buffering is weak outside the range pK a ± 1. At pH ≤ pK a − 2 the substance is said to be fully protonated and at pH ≥ pK a + 2 it is fully dissociated (deprotonated).
A quantity in square brackets, [X], represents the concentration of the chemical substance X. It is understood that the symbol H + stands for the hydrated hydronium ion. K a is an acid dissociation constant. The Henderson–Hasselbalch equation can be applied to a polybasic acid only if its consecutive pK values differ by at least 3.
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 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).
For a strong acid-strong base titration monitored by pH, we have at any i'th point in the titration = [+] [] where K w is the water autoprotolysis constant.. If titrating an acid of initial volume and concentration [+] with base of concentration [], then at any i'th point in the titration with titrant volume ,