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In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different ...
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.
The stability of solutions in holds as follows: a locally uniform limit of a sequence of solutions (or subsolutions, or supersolutions) is a solution (or subsolution, or supersolution). More generally, the notions of viscosity sub- and supersolution are also conserved by half-relaxed limits.
However, for weak acids, a quadratic equation must be solved, and for weak bases, a cubic equation is required. In general, a set of non-linear simultaneous equations must be solved. Water itself is a weak acid and a weak base, so its dissociation must be taken into account at high pH and low solute concentration (see Amphoterism).
Also acid ionization constant or acidity constant. A quantitative measure of the strength of an acid in solution expressed as an equilibrium constant for a chemical dissociation reaction in the context of acid-base reactions. It is often given as its base-10 cologarithm, p K a. acid–base extraction A chemical reaction in which chemical species are separated from other acids and bases. acid ...
A weak base is a base that, upon dissolution in water, does not dissociate completely, so that the resulting aqueous solution contains only a small proportion of hydroxide ions and the concerned basic radical, and a large proportion of undissociated molecules of the base.
The main use of litmus is to test whether a solution is acidic or basic, as blue litmus paper turns red under acidic conditions, and red litmus paper turns blue under basic or alkaline conditions, with the color change occurring over the pH range 4.5–8.3 at 25 °C (77 °F). Neutral litmus paper is purple. [2]
Although hydrofluoric acid is regarded as a weak acid, it is very corrosive, even attacking glass when hydrated. [20] Dilute solutions are weakly acidic with an acid ionization constant K a = 6.6 × 10 −4 (or pK a = 3.18), [10] in contrast to corresponding solutions of the other hydrogen halides, which are strong acids (pK a < 0).