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Similarly, in a basic solution, the concentration of hydroxide ions (OH-) can be considered equal to the concentration of the base. The pH of a solution is defined as the negative logarithm of the concentration of H +, and the pOH is defined as the negative logarithm of the concentration of OH −.
The distribution coefficient, log D, is the ratio of the sum of the concentrations of all forms of the compound (ionized plus un-ionized) in each of the two phases, one essentially always aqueous; as such, it depends on the pH of the aqueous phase, and log D = log P for non-ionizable compounds at any pH.
When the acidic medium in question is a dilute aqueous solution, the is approximately equal to the pH value, which is a negative logarithm of the concentration of aqueous + in solution. The pH of a simple solution of an acid in water is determined by both K a {\displaystyle K_{{\ce {a}}}} and the acid concentration.
The logarithm of a product is the sum of the logarithms of the numbers being multiplied; the logarithm of the ratio of two numbers is the difference of the logarithms. The logarithm of the p -th power of a number is p times the logarithm of the number itself; the logarithm of a p -th root is the logarithm of the number divided by p .
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]
Like Log P, Log D is positive for lipophilic and negative for hydrophilic substances. While P values are largely independent of the pH value of the aqueous phase due to their restriction to only one species, D values are often strongly dependent on the pH value of the aqueous phase.
The pH scale is by far the most commonly used acidity function, and is ideal for dilute aqueous solutions. Other acidity functions have been proposed for different environments, most notably the Hammett acidity function , H 0 , [ 3 ] for superacid media and its modified version H − for superbasic media.
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...