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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 specific values for C a and K a this quadratic equation can be solved for x. Assuming [4] that pH = −log 10 [H +] the pH can be calculated as pH = −log 10 x. If the degree of dissociation is quite small, C a ≫ x and the expression simplifies to = and pH = 1 / 2 (pK a − log C a).
Therefore, the buffer regions will be centered at about pH 1.3 and pH 4.3. The buffer regions carry the information necessary to get the pK a values as the concentrations of acid and conjugate base change along a buffer region. Between the two buffer regions there is an end-point, or equivalence point, at about pH 3.
For K′ 3 there are three different dissociation constants — there are only three possibilities for which pocket is filled last (I, II or III) — and one state (I–II–III). Even when the microscopic dissociation constant is the same for each individual binding event, the macroscopic outcome (K′ 1, K′ 2 and K′ 3) is not equal. This ...
Buffer capacity falls to 33% of the maximum value at pH = pK a ± 1, to 10% at pH = pK a ± 1.5 and to 1% at pH = pK a ± 2. For this reason the most useful range is approximately p K a ± 1. When choosing a buffer for use at a specific pH, it should have a p K a value as close as possible to that pH.
The Charlot equation, named after Gaston Charlot, is used in analytical chemistry to relate the hydrogen ion concentration, and therefore the pH, with the formal analytical concentration of an acid and its conjugate base. It can be used for computing the pH of buffer solutions when the approximations of the Henderson–Hasselbalch equation ...
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Figure 2 gives an example; in this example, the two x-intercepts differ by about 0.2 mL but this is a small discrepancy, given the large equivalence volume (0.5% error). Similar equations can be written for the titration of a weak base by strong acid (Gran, 1952; Harris, 1998).
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