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A buffer solution is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature. [1] Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical ...
A simple buffer solution consists of a solution of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetate . The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant , K a of the acid ...
A buffer solution contains an acid and its conjugate base or a base and its conjugate acid. [2] Addition of the conjugate ion will result in a change of pH of the buffer solution. For example, if both sodium acetate and acetic acid are dissolved in the same solution they both dissociate and ionize to produce acetate ions .
which is an eigenvalue equation. Very often, only numerical solutions to the Schrödinger equation can be found for a given physical system and its associated potential energy. However, there exists a subset of physical systems for which the form of the eigenfunctions and their associated energies, or eigenvalues, can be found.
The bicarbonate buffer system is an acid-base homeostatic mechanism involving the balance of carbonic acid (H 2 CO 3), bicarbonate ion (HCO − 3 ), and carbon dioxide (CO 2 ) in order to maintain pH in the blood and duodenum , among other tissues, to support proper metabolic function. [ 1 ]
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
The Riemann problem is very useful for the understanding of equations like Euler conservation equations because all properties, such as shocks and rarefaction waves, appear as characteristics in the solution. It also gives an exact solution to some complex nonlinear equations, such as the Euler equations.