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The Henderson–Hasselbalch equation can be used to model these equilibria. It is important to maintain this pH of 7.4 to ensure enzymes are able to work optimally. [10] Life threatening Acidosis (a low blood pH resulting in nausea, headaches, and even coma, and convulsions) is due to a lack of functioning of enzymes at a low pH. [10]
A strong acid, such as hydrochloric acid, at concentration 1 mol dm −3 has a pH of 0, while a strong alkali like sodium hydroxide, at the same concentration, has a pH of 14. Since pH is a logarithmic scale, a difference of one in pH is equivalent to a tenfold difference in hydrogen ion concentration.
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.
The pH can be calculated using an ICE table. Note that in this example, we are assuming that the acid is not very weak, and that the concentration is not very dilute, so that the concentration of [OH −] ions can be neglected. This is equivalent to the assumption that the final pH will be below about 6 or so. See pH calculations for more details.
Because log(x) is the sum of the terms of the form log(1 + 2 −k) corresponding to those k for which the factor 1 + 2 −k was included in the product P, log(x) may be computed by simple addition, using a table of log(1 + 2 −k) for all k. Any base may be used for the logarithm table. [53]
For example, if the concentration of the conjugate base is 10 times greater than the concentration of the acid, their ratio is 10:1, and consequently the pH is pK a + 1 or pK b + 1. Conversely, if a 10-fold excess of the acid occurs with respect to the base, the ratio is 1:10 and the pH is pK a − 1 or pK b − 1.
The isoionic point is the pH value at which a zwitterion molecule has an equal number of positive and negative charges and no adherent ionic species. It was first defined by S.P.L. Sørensen, Kaj Ulrik Linderstrøm-Lang and Ellen Lund in 1926 [1] and is mainly a term used in protein sciences.
The prime number race generalizes to other moduli and is the subject of much research; Pál Turán asked whether it is always the case that π c,a (x) and π c,b (x) change places when a and b are coprime to c. [34] Granville and Martin give a thorough exposition and survey. [33] Graph of the number of primes ending in 1, 3, 7, and 9 up to n ...
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