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From Wikipedia

Chemical decomposition

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:

2H2O(I) → 2H2 + O2

Additional examples

An example of spontaneous decomposition is that of hydrogen peroxide, which will slowly decompose into water and oxygen:

2H2O2→ 2H2O + O2

Carbonates will decompose when heated, a notable exception being that of carbonic acid, H2CO3. Carbonic acid, the "fizz" in sodas, pop cans and other carbonated beverages, will decompose over time (spontaneously) into carbon dioxide and water

H2CO3→ H2O + CO2

Other carbonates will decompose when heated producing the corresponding metaloxide and carbon dioxide. In the following equation M represents a metal:

MCO3→ MO + CO2

A specific example of this involving calcium carbonate:

CaCO3→ CaO + CO2

Metal chlorates also decompose when heated. A metal chloride and oxygen gas are the products.

2MClO3→ 2MCl + 3O2

A common decomposition of a chlorate to evolve oxygen utilizes potassium chlorate as follows:

2KClO3→ 2KCl + 3O2

Many metal carbonates decompose to form metal oxides and carbon dioxide when heated.


Chemical decomposition

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

Matrix decomposition

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 = QTb = 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

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: m-by-n matrix A
  • Decomposition: A=QR where Q is an orthogonal matrix of size m-by-m, and R is an upper triangular matrix of size m-by-n
  • 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


From Yahoo Answers

Question:The following is an example of reactions involving heterogeneous catalysts: the decomposition og phosphine (PH3) over tungsten (W) (a solid catalyst): 4PH3(g) -> P4(g) + 6H2(g) The rate of the above reaction is found to be independent of the pressure of PH3 as long as the pressure of PH3 is sufficiently high (say >= 1 atm). Explain.

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 TUNGSTEN-BASED 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.

Question:I only know of the thermal decomposition reaction but what are the other three types?? Please help! Need the answer soon.

Answers:decomposition using electrolysis..

Question:can you please give me examples of these chemical reactions 1. Synthesis 2. Decomposition 3. Single Displacement 4. Double Displacement

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

Question:What are 5 real life examples of the 5 type of reactions? Combination/Synthesis Reaction Decomposition Reaction Single-Replacement Reaction Double-Replacement Reaction Combustion Reaction

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)

From Youtube

Decomposition Reaction Example :This is a short explaination, along with an example, of a decomposition reaction for my 9th grade chemistry project.

Chemistry - Synthesis, Decomposition and Combustion Reactions :GET the PowerPoint at www.ZUMAed.com. After a review of chemical reactions, this module presents a discussion of the characteristics of synthesis, decomposition, and combustion reactions, including examples of each. 3 By the end of this presentation, students will be able to * Describe what happens during a chemical reaction. * Identify signs that a chemical reaction has occurred. * Describe what happens during a synthesis, decomposition, and combustion reaction. * Identify and describe examples of synthesis, decomposition, and combustion reactions.