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An **acid–base reaction** is a chemical reaction that occurs between an acid and a base. Several concepts exist that provide alternative definitions for the reaction mechanisms involved and their application in solving related problems. Despite several differences in definitions, their importance becomes apparent as different methods of analysis when applied to acid–base reactions for gaseous or liquid species, or when acid or base character may be somewhat less apparent. The first of these scientific concepts of acids and bases was provided by the French chemist Antoine Lavoisier, circa 1776.

**Equilibrium chemistry** is a concerned with systems in chemical equilibrium. The unifying principle is that the free energy of a system at equilibrium is the minimum possible, so that the slope of the free energy with respect to the reaction coordinate is zero. This principle, applied to mixtures at equilibrium provides a definition of an equilibrium constant. Applications include acid-base, host-guest, metal-complex, solubility, partition, chromatography and redox equilibria.

A chemical system is said to be in equilibrium when the quantities of the chemical entities involved do not and *cannot* change in time without the application of an external influence. In this sense a system in chemical equilibrium is in a stable state. The system at chemical equilibrium will be at a constant temperature, pressure (or volume) and composition. It will be insulated from exchange of heat with the surroundings, that is, it is a closed system. A change of temperature, pressure (or volume) constitutes an external influence and the equilibrium quantities will change as a result of such a change. If there is a possibility that the composition might change, but the rate of change is negligibly slow, the system is said to be in a metastable state. The equation of chemical equilibrium can be expressed symbolically as

**Equations**
In chemistry, the **Henderson–Hasselbalch equation** describes the derivation of pH as a measure of acidity (using pK_{a}, the negative log of the acid dissociation constant) in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions (it is widely used to calculate the isoelectric point of proteins).

The equation is given by:

A **Respiratory Therapist** is specialized healthcare practitioner who has graduated from a college or a university and passed a national board certifying examination. Respiratory therapists work under the general supervision of a primary provider, such as physician or nurse practitioner most often in intensive care and operating rooms, but also in outpatient clinics.

Respiratory therapists are specialists and educators in cardiology and pulmonology. Respiratory therapists are also advanced-practice clinicians in airway management; establishing and maintaining the airway during management of trauma, intensive care, and may administer anaesthesia for surgery or conscious sedation.

A **buffer** is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. Its pH changes very little when a small amount of strong acid or base is added to it and thus it is used to prevent changes in the pH of a solution. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications. Many life forms thrive only in a relatively small pH range so they utilize a buffer solution to maintain a constant pH. One example of a buffer solution found in nature is blood.

Buffer solutions achieve their resistance to pH change because of the presence of an equilibrium between the acid HA and its conjugate base A-.

**Science**
**Nature**
**Applied mathematics** is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems; as a profession focused on practical problems, *applied mathematics* focuses on the formulation and study of mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for its own sake. Thus, the activity of applied mathematics is vitally connected with research in pure mathematics.

Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis); and applied probability. These areas of mathematics were intimately tied to the development of Newtonian physics, and in fact the distinction between mathematicians and physicists was not sharply drawn before the mid-19th century. This history left a legacy as well: until the early 20th century subjects such as classical mechanics were often taught in applied mathematics departments at American universities rather than in physics departments, and fluid mechanics may still be taught in applied mathematics departments. Engineering and computer science departments have traditionally made use of applied mathematics.

**Education**