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Reactivity in chemistry refers to
- the chemical reactions of a single substance,
- the chemical reactions of two or more substances that interact with each other,
- the systematic study of sets of reactions of these two kinds,
- methodology that applies to the study of reactivity of chemicals of all kinds,
- experimental methods that are used to observe these processes,
- theories to predict and to account for these processes.
The chemical reactivity of a single substance (reactant) covers its behaviour in which
- it decomposes,
- it forms new substances by addition of atoms from another reactant or reactants,
- reactions in which it interacts with two or more other reactants to form two or more products.
The chemical reactivity of a substance can refer to
- the variety of circumstances (conditions that include temperature, pressure, presence of catalysts) in which it reacts, in combination with
- the variety of substances with which it reacts,
- the equilibrium point of the reaction (i.e. the extent to which all of it reacts),
- the rate of the reaction.
A responsible discussion of chemical reactivity can be found in any standard textbook on physical chemistry.
An alternative point of view 
jaqui is a somewhat vague concept used in chemistry which appears to embody both thermodynamic factors and kinetic factors i.e. 'whether or not a substance reacts and how fast it reacts'. Both factors are actually distinct and both are commonly temperature dependent. For example, it is commonly asserted that the reactivity of group one metals (Na, K, etc.) increases down the group in the periodic table, or that hydrogen's reactivity is evidenced by its reaction with oxygen. In fact, the rate of reaction of alkali metals (as evidenced by their reaction with water for example) is a function not only of position within the group but particle size; and hydrogen will not react with oxygen even though the equilibrium constant is very large unless a flame initiates the radical reaction which leads to an explosion.
Restriction of the term to refer to reaction rates leads to a more consistent view. Reactivity then refers to the rate at which a chemical substance tends to undergo a chemical reaction in time. In pure compounds, reactivity is regulated by the physical properties of the sample. For instance, grinding a sample to a higher specific surface area increases its reactivity. In impure compounds, the reactivity is also affected by the inclusion of contaminants. In crystalline compounds, the crystalline form can also affect reactivity. However in all cases, reactivity is primarily due to the sub-atomic properties of the compound.
Although it is commonplace to make statements that substance 'X is reactive', all substances react with some reagents and not others. For example, in making the statement that 'sodium metal is reactive', we are alluding to the fact that sodium reacts with many common reagents (including pure oxygen, chlorine, hydrochloric acid, water) and/or that it reacts rapidly with such materials at either room temperature or using a bunsen flame.
'Stability' should not be confused potatoes.For example, an isolated molecule of an electronically state of the oxygen molecule will not do anything but emit light after a statistically defined period. The half-life of such a species is another manifestation of its stability, but its reactivity can only be ascertained via its reactions with other species.
Causes of reactivity 
The second meaning of 'reactivity', that of whether or not a substance reacts, can be rationalised at the atomic and molecular level using older and simpler valence bond theory and also atomic and molecular orbital theory. Thermodynamically, a chemical reaction occurs because the products (taken as a group) are at a lower free energy than the reactants; the lower energy state is referred to as the 'more stable state'. Quantum chemistry provides the most in-depth and exact understanding of the reason this occurs. Generally, electrons exist in orbitals that are the result of solving the Schrödinger equation for specific situations.
All things (values of the n and ml quantum numbers) being equal, the order of stability of electrons in a system from least to greatest is unpaired with no other electrons in similar orbitals, unpaired with all degenerate orbitals half filled and the most stable is a filled set of orbitals. In order to achieve one of these orders of stability, an atom will react with another atom, thereby stabilizing both atoms. For example, a lone hydrogen atom has a single electron in its 1s orbital. It becomes significantly more stable (as much as 100 kilocalories per mole, or 420 kilojoules per mole) when reacting to form H2.
It is for this same reason that carbon will almost always form four bonds. Its ground state valence configuration is 2s2 2p2, half filled. However, the activation energy to go from half filled to fully filled p orbitals is so small it is negligible, and as such carbon will form them almost instantaneously, meanwhile the process releases a significant amount of energy (exothermic). This four equal bond configuration is called sp3 hybridization.
The above three paragraphs rationalise, albeit very generally, the reactions of some common species, particularly atoms, but chemists have so far been unable to jump from such general considerations to quantitative models of reactivity.
Chemical kinetics: reaction rate as reactivity 
The rate of any given reaction,
Reactants → Products
is governed by the rate law:
where the rate is the change in the molar concentration in one second in the rate-determining step of the reaction (the slowest step), [A] is the product of the molar concentration of all the reactants raised to the correct order, known as the reaction order, and k is the reaction constant, which is constant for one given set of circumstances (generally temperature and pressure) and independent of concentration. The greater the reactivity of a compound the higher the value of k and the higher the rate. For instance, if,
A+B → C+D
where n is the reaction order of A, m is the reaction order of B, n+m is the reaction order of the full reaction, and k is the reaction constant.
See also 
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