In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula . The informal use of the term formula in science refers to the general construct of a relationship between given quantities.
The plural of formula can be either formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin). [2]
In mathematics, a formula generally refers to an equation or inequality relating one mathematical expression to another, with the most important ones being mathematical theorems. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. [3] However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius:
Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Here, notice that the volume V and the radius r are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex. [4] Mathematical formulas are often algebraic, analytical or in closed form. [5]
In a general context, formulas often represent mathematical models of real world phenomena, and as such can be used to provide solutions (or approximate solutions) to real world problems, with some being more general than others. For example, the formula
is an expression of Newton's second law, and is applicable to a wide range of physical situations. Other formulas, such as the use of the equation of a sine curve to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations.
Expressions are distinct from formulas in the sense that they don't usually contain relations like equality (=) or inequality (<). Expressions denote a mathematical object, where as formulas denote a statement about mathematical objects. [6] [7] [ dubious – discuss ] This is analogous to natural language, where a noun phrase refers to an object, and a whole sentence refers to a fact. For example, is an expression, while is a formula.
However, in some areas mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to true or false , depending on the values that are given to the variables occurring in the expressions. For example takes the value false if x is given a value less than 1, and the value true otherwise. (See Boolean expression)
In mathematical logic, a formula (often referred to as a well-formed formula ) is an entity constructed using the symbols and formation rules of a given logical language. [8] For example, in first-order logic,
is a formula, provided that is a unary function symbol, a unary predicate symbol, and a ternary predicate symbol.
In modern chemistry, a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. [9] For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom. Similarly, O−
3 denotes an ozone molecule consisting of three oxygen atoms [10] and a net negative charge.
A chemical formula identifies each constituent element by its chemical symbol, and indicates the proportionate number of atoms of each element.
In empirical formulas, these proportions begin with a key element and then assign numbers of atoms of the other elements in the compound—as ratios to the key element. For molecular compounds, these ratio numbers can always be expressed as whole numbers. For example, the empirical formula of ethanol may be written C2H6O, [11] because the molecules of ethanol all contain two carbon atoms, six hydrogen atoms, and one oxygen atom. Some types of ionic compounds, however, cannot be written as empirical formulas which contains only the whole numbers. An example is boron carbide, whose formula of CBn is a variable non-whole number ratio, with n ranging from over 4 to more than 6.5.
When the chemical compound of the formula consists of simple molecules, chemical formulas often employ ways to suggest the structure of the molecule. There are several types of these formulas, including molecular formulas and condensed formulas. A molecular formula enumerates the number of atoms to reflect those in the molecule, so that the molecular formula for glucose is C6H12O6 rather than the glucose empirical formula, which is CH2O. Except for the very simple substances, molecular chemical formulas generally lack needed structural information, and might even be ambiguous in occasions.
A structural formula is a drawing that shows the location of each atom, and which atoms it binds to.
In computing, a formula typically describes a calculation, such as addition, to be performed on one or more variables. A formula is often implicitly provided in the form of a computer instruction such as.
In computer spreadsheet software, a formula indicating how to compute the value of a cell, say A3, could be written as
where A1 and A2 refer to other cells (column A, row 1 or 2) within the spreadsheet. This is a shortcut for the "paper" form A3 = A1+A2, where A3 is, by convention, omitted because the result is always stored in the cell itself, making the stating of the name redundant.
Formulas used in science almost always require a choice of units. [12] Formulas are used to express relationships between various quantities, such as temperature, mass, or charge in physics; supply, profit, or demand in economics; or a wide range of other quantities in other disciplines.
An example of a formula used in science is Boltzmann's entropy formula. In statistical thermodynamics, it is a probability equation relating the entropy S of an ideal gas to the quantity W, which is the number of microstates corresponding to a given macrostate:
where k is the Boltzmann constant, equal to 1.380649×10−23 J⋅K−1, and W is the number of microstates consistent with the given macrostate.
In chemistry, amines are compounds and functional groups that contain a basic nitrogen atom with a lone pair. Formally, amines are derivatives of ammonia, wherein one or more hydrogen atoms have been replaced by a substituent such as an alkyl or aryl group. Important amines include amino acids, biogenic amines, trimethylamine, and aniline. Inorganic derivatives of ammonia are also called amines, such as monochloramine.
In organic chemistry, an alkyne is an unsaturated hydrocarbon containing at least one carbon—carbon triple bond. The simplest acyclic alkynes with only one triple bond and no other functional groups form a homologous series with the general chemical formula CnH2n−2. Alkynes are traditionally known as acetylenes, although the name acetylene also refers specifically to C2H2, known formally as ethyne using IUPAC nomenclature. Like other hydrocarbons, alkynes are generally hydrophobic.
In chemistry, an acid–base reaction is a chemical reaction that occurs between an acid and a base. It can be used to determine pH via titration. Several theoretical frameworks provide alternative conceptions of the reaction mechanisms and their application in solving related problems; these are called the acid–base theories, for example, Brønsted–Lowry acid–base theory.
A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, commas and plus (+) and minus (−) signs. These are limited to a single typographic line of symbols, which may include subscripts and superscripts. A chemical formula is not a chemical name since it does not contain any words. Although a chemical formula may imply certain simple chemical structures, it is not the same as a full chemical structural formula. Chemical formulae can fully specify the structure of only the simplest of molecules and chemical substances, and are generally more limited in power than chemical names and structural formulae.
Diatomic molecules are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen or oxygen, then it is said to be homonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such as carbon monoxide or nitric oxide, the molecule is said to be heteronuclear. The bond in a homonuclear diatomic molecule is non-polar.
In chemistry, the empirical formula of a chemical compound is the simplest whole number ratio of atoms present in a compound. A simple example of this concept is that the empirical formula of sulfur monoxide, or SO, would simply be SO, as is the empirical formula of disulfur dioxide, S2O2. Thus, sulfur monoxide and disulfur dioxide, both compounds of sulfur and oxygen, have the same empirical formula. However, their molecular formulas, which express the number of atoms in each molecule of a chemical compound, are not the same.
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and molecule is often used when referring to polyatomic ions.
In chemistry, the molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of the compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.
A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas. The reactant entities are given on the left-hand side and the product entities are on the right-hand side with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the products to show the direction of the reaction. The chemical formulas may be symbolic, structural, or intermixed. The coefficients next to the symbols and formulas of entities are the absolute values of the stoichiometric numbers. The first chemical equation was diagrammed by Jean Beguin in 1615.
In atomic physics, a partial charge is a non-integer charge value when measured in elementary charge units. It is represented by the Greek lowercase delta (𝛿), namely 𝛿− or 𝛿+.
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems. In their most basic form, they consist of a set of objects, plus relations on how to transform those objects.
In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers (constants), variables, operations, functions. Other symbols include punctuation signs and brackets.
In chemistry, the amount of substance (symbol n) in a given sample of matter is defined as a ratio (n = N/NA) between the number of elementary entities (N) and the Avogadro constant (NA). The entities are usually molecules, atoms, ions, or ion pairs of a specified kind. The particular substance sampled may be specified using a subscript, e.g., the amount of sodium chloride (NaCl) would be denoted as nNaCl. The unit of amount of substance in the International System of Units is the mole (symbol: mol), a base unit. Since 2019, the value of the Avogadro constant NA is defined to be exactly 6.02214076×1023 mol−1. Sometimes, the amount of substance is referred to as the chemical amount or, informally, as the "number of moles" in a given sample of matter.
In theoretical computer science and mathematical logic a string rewriting system (SRS), historically called a semi-Thue system, is a rewriting system over strings from a alphabet. Given a binary relation between fixed strings over the alphabet, called rewrite rules, denoted by , an SRS extends the rewriting relation to all strings in which the left- and right-hand side of the rules appear as substrings, that is , where , , , and are strings.
A bond graph is a graphical representation of a physical dynamic system. It allows the conversion of the system into a state-space representation. It is similar to a block diagram or signal-flow graph, with the major difference that the arcs in bond graphs represent bi-directional exchange of physical energy, while those in block diagrams and signal-flow graphs represent uni-directional flow of information. Bond graphs are multi-energy domain and domain neutral. This means a bond graph can incorporate multiple domains seamlessly.
In mathematical logic, an atomic formula is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining the atomic formulas using the logical connectives.
The mass recorded by a mass spectrometer can refer to different physical quantities depending on the characteristics of the instrument and the manner in which the mass spectrum is displayed.
This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions; it features an extensive vocabulary and a significant amount of jargon.
In chemistry, isomers are molecules or polyatomic ions with identical molecular formula – that is, the same number of atoms of each element – but distinct arrangements of atoms in space. Isomerism refers to the existence or possibility of isomers.
A chemical graph generator is a software package to generate computer representations of chemical structures adhering to certain boundary conditions. The development of such software packages is a research topic of cheminformatics. Chemical graph generators are used in areas such as virtual library generation in drug design, in molecular design with specified properties, called inverse QSAR/QSPR, as well as in organic synthesis design, retrosynthesis or in systems for computer-assisted structure elucidation (CASE). CASE systems again have regained interest for the structure elucidation of unknowns in computational metabolomics, a current area of computational biology.
