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From Wikipedia
Chemical decomposition, analysis or breakdown is the separation of a chemical compound into elements or simpler compounds. It is sometimes defined as the exact opposite of a chemical synthesis. Chemical decomposition is often an undesired chemical reaction. The stability that a chemical compound ordinarily has is eventually limited when exposed to extreme environmental conditions like heat, radiation, humidity or the acidity of a solvent. The details of decomposition processes are generally not well defined, as a molecule may break up into a host of smaller fragments. Chemical decomposition is exploited in several analytical techniques, notably mass spectrometry, traditional gravimetric analysis, and thermogravimetric analysis.
A broader definition of the term decomposition also includes the breakdown of one phase into two or more phases.
There are broadly three types of decomposition reactions: thermal, electrolytic and catalytic.
Reaction formula
The generalized reaction for chemical decomposition is:
 AB → A + B
with a specific example being the electrolysis of water to gaseous hydrogen and oxygen:
 2H_{2}O(I) → 2H_{2} + O_{2}
Additional examples
An example of spontaneous decomposition is that of hydrogen peroxide, which will slowly decompose into water and oxygen:
 2H_{2}O_{2}→ 2H_{2}O + O_{2}
Carbonates will decompose when heated, a notable exception being that of carbonic acid, H_{2}CO_{3}. Carbonic acid, the "fizz" in sodas, pop cans and other carbonated beverages, will decompose over time (spontaneously) into carbon dioxide and water
 H_{2}CO_{3}→ H_{2}O + CO_{2}
Other carbonates will decompose when heated producing the corresponding metaloxide and carbon dioxide. In the following equation M represents a metal:
 MCO_{3}→ MO + CO_{2}
A specific example of this involving calcium carbonate:
 CaCO_{3}→ CaO + CO_{2}
Metal chlorates also decompose when heated. A metal chloride and oxygen gas are the products.
 2MClO_{3}→ 2MCl + 3O_{2}
A common decomposition of a chlorate to evolve oxygen utilizes potassium chlorate as follows:
 2KClO_{3}→ 2KCl + 3O_{2}
Many metal carbonates decompose to form metal oxides and carbon dioxide when heated.
Chemical decomposition, analysis or breakdown is the separation of a chemical compound into elements or simpler compounds. It is sometimes defined as the exact opposite of a chemical synthesis. Chemical decomposition is often an undesired chemical reaction. The stability that a chemical
In the mathematical discipline of linear algebra, a matrix decomposition is a factorization of a matrix into some canonical form. There are many different matrix decompositions; each finds use among a particular class of problems.
Example
In numerical analysis, different decompositions are used to implement efficient matrix algorithms.
For instance, when solving a system of linear equations Ax=b, the matrix A can be decomposed via the LU decomposition. The LU decomposition factorizes a matrix into a lower triangular matrixL and an upper triangular matrixU. The systems L(Ux)=b and Ux=L^{1}b require fewer additions and multiplications to solve, though one might require significantly more digits in inexact arithmetic such as floating point. Similarly the QR decomposition expresses A as QR with Q a unitary matrix and R an upper triangular matrix. The system Q(Rx) = b is solved by Rx = Q^{T}b = c, and the system Rx = c is solved by "back substitution". The number of additions and multiplications required is about twice that of using the LU solver, but no more digits are required in inexact arithmetic because the QR decomposition is numerically stable.
Decompositions related to solving systems of linear equations
 Applicable to: square matrixA
 Decomposition: A=LU, where L is lower triangular and U is upper triangular
 Related: the LDU decomposition is A=LDU, where L is lower triangular with ones on the diagonal, U is upper triangular with ones on the diagonal, and D is a diagonal matrix.
 Related: the LUP decomposition is A=LUP, where L is lower triangular, U is upper triangular, and P is a permutation matrix.
 Existence: An LUP decomposition exists for any square matrix A. When P is an identity matrix, the LUP decomposition reduces to the LU decomposition. If the LU decomposition exists, the LDU decomposition does too.
 Comments: The LUP and LU decompositions are useful in solving an nbyn system of linear equations Ax=b. These decompositions summarize the process of Gaussian elimination in matrix form. Matrix P represents any row interchanges carried out in the process of Gaussian elimination. If Gaussian elimination produces the row echelon form without requiring any row interchanges, then P=I, so an LU decomposition exists.
LU Reduction
Block LU decomposition
Rank factorization
 Applicable to: square, symmetric, positive definite matrix A
 Decomposition: A=U^TU, where U is upper triangular with positive diagonal entries
 Comment: the Cholesky decomposition is a special case of the symmetric LU decomposition, with L=U^T.
 Comment: the Cholesky decomposition is unique
 Comment: the Cholesky decomposition is also applicable for complex hermitian positive definite matrices
 Comment: An alternative is the LDL decomposition which can avoid extracting square roots.
 Applicable to: mbyn matrix A
 Decomposition: A=QR where Q is an orthogonal matrix of size mbym, and R is an upper triangular matrix of size mbyn
 Comment: The QR decomposition provides an alternative way of solving the system of equations Ax=b without inverting the matrix A. The fact that Q is orthogonal means that Q^TQ=I, so that Ax=b is equivalent to Rx=Q^Tb, which is easier to solve since R is triangular.
Singular value decomposition
 Applicable to: mbyn matrix A.
 Decomposition: A=UDV^H, where D is a nonnegative diagonal matrix, and U and V are unitary matrices, and V^H denotes the conjugate transpose of V (or simply the transpose, if V contains real numbers
From Yahoo Answers
Answers:Lancenigo di Villorba (TV), Italy LET ME RECOVER THE EXPERIMENTAL FACTs, HENCE I SHOW MY REASONINGs. EXPERIMENTAL FACTs Phosphine undergoes decomposition in Its Chemical Elements if it flows upon a TUNGSTENBASED powder which is able to acts as a CATALYST : meanwhile TUNGSTEN maintain its chemical nature, it enhances the Decomposition's Rate which runs VERY FASTER THAN when Catalyst there wasn't. If the Partial Pressure of Phosphine results GREATER THAN a THRESHOLD VALUE, Kinetic Data show a Decomposition's Rate iniflunced by Partial Pressure. DISCUSSION The mechanism related to this Decomposition experiment involves FIVE MAIN STEPs, as the following ones : ) Phosphine must diffuse from Gas Bulk toward the TUNGSTEN's surface ; ) Phosphine interact with Tungsten's surface, e.g. Tungsten ADSORBs Phosphine ; ) Adsorbed Phosphine forms Secundary Chemical Bonds with Tungsten, so the Decomposition take place giving Phosphorus Atoms and Hydrogen Ones in the BOUND FORM TO TUNGSTEN ; ) Phosphorus and Hydrogen's BOUND FORMs break its Chemical Bonds ; ) Phosphorus and Hydrogen diffuse outward. RATE DETERMINING STEP's approach assumes that the Decomposition's Rate results EQUAL THAN the Lowest's One among Its Five Elementar Step's Rates. In particular way, ii) STEP is related to ISOTHERMAL BEHAVIOUR of ADSORPTION, e.g. it states that it exists a THRESHOLD VALUE of Gas Molarity leading the Adsorption Equilibria to Its Maximum's Values. I hope this helps you.
Answers:decomposition using electrolysis..
Answers:1. 2 H2(g) + O2(g)>2 H2O,(l) synthesis 2 .2 H2O(l)> O2)g)+2 H2 (g) , decomposition 3. 2NaCl(aq)+ F2(g)>2 NaF(aq)+ Cl2(g), single displacement 4. AgNO3(aq)+ NaCl(aq)> AgCl(s) + NaNO3(aq), double displacement
Answers:Combination: the rusting of iron (4Fe + 3O2 2Fe2O3) Decomposition: the production of quicklime (Ca(OH)2 CaO + H2O) Single displacement: the polishing of silverware by soaking with aluminium (2Al + 3Ag2S 6Ag + Al2S3) Double displacement: the extraction of magnesium from seawater (MgCl2 + 2NaOH Mg(OH)2 + 2NaCl) Combustion: burning natural gas for heat (CH4 + 2O2 CO2 + 2H2O)
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