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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.


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

Chemical change

In a chemical change, bonds are broken and new bonds are formed between different atoms. This breaking and forming of bonds takes place when particles of the original materials collide with one another. Some exothermic reactions may be hot enough to cause certain chemicals to also undergo a change in state; for example in the case of aqueous solutions, bubbles may not necessarily be newly produced gas but instead water vapor.

Whenever chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an energy change as new products are generated. An example of a chemical change is the reaction between sodium hydroxide and hydrogen chloride to produce sodium chloride, or table salt. This reaction is so exothermic, meaning it releases heat in the form of energy, that even flames are generated. This is an example of a chemical change because the end product is molecularly different from the starting molecules.

Chemical changes are happening all the time. There are several different types of chemical change, including: synthesis, decomposition, single displacement, double displacement, neutralization, precipitation, combustion and redox.

Examples of chemical changes

A primary example of chemical change is the combustion of methane to produce carbon dioxide and water.

Other examples of chemical changes are:

Evidence of a chemical change:

The following can indicate that a chemical change took place, although this evidence is not conclusive:

  • Change of odor
  • Change of color (for example, silver to reddish-brown when iron rusts).
  • Change in temperature or energy, such as the production (exothermic) or loss (endothermic) of heat.
  • Change of form (for example, burning paper).
  • Light, heat, or sound is given off.
  • Formation of gases, often appearing as bubbles.
  • Formation of precipitate (insoluble particles).
  • The decomposition of organic matter (for example, rotting food).

A chemical change can have a huge impact on a physical change.

Laws of chemical changes

Chemical law

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: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:This is an old assignment, and I got 20 points taken off for not doing it correctly, and it's REALLY bugging me that I can't get it right. I imagine I'd have to make a loop of some sort, or it's a glaringly obvious solution that I am missing. That's for any help. 2. Decomposition into Prime Factors (50 points): Taken from Wikipedia: In number theory and algebraic number theory, the Fundamental Theorem of Arithmetic (or Unique-Prime-Factorization Theorem) states that any integer greater than 1 can be written as a unique product (up to ordering of the factors) of prime numbers. For example, Your task is to develop a function that takes a positive integer number greater than or equal to 2 and prints the factorization of the number into its prime factors and the powers for each prime factor. To keep things simple, the algorithm should check that the integer is less than or equal to 100.000. Look that if the number is a prime number no decomposition can be performed. In this case the algorithm should print that the number is prime. An example of the input and output of the program is Please write an integer number greater than or equal to 2 and less than or equal to 100000? 1200 1200 is decomposed as follows Prime factor 2 , power 4 Prime factor 3 , power 1 Prime factor 5 , power 2 Here's the block of code that pertains to this (the whole program is pretty lengthy) as it's a menu with a few different capabilites: case 2: /* Case 2 is the code for decomposing the inputted number into prime numbers */ printf("Enter number (up to 100000): "); scanf("%d", &n); prime = 2; if (n <= 100000) /* sets the range for the program to be under or equal to 100,000 */ { do /* starts the loop */ { check2 = n % prime; /* checks the prime factors of the inputted number */ if (check2 == 0 ) /* if there is no remaind, then it is a factor and printed as such */ { printf("%d ", prime); n = n / prime; } else /* if there is a remaind then add one to the divisor and go through the loop again */ prime = prime + 1; } while ( n > 1 ); /* The loop is broken when the number is no longer divisible */ } else printf("You went over the 100000 mark. Stay under that number!"); /* Message for any who go over the range */ getch(); break; I forgot to mention..the 20 points was taken off for not creating the power for each factor. Instead I listed each factor. For example: I had 2 2 2 4 5 6 6 as factors; instead of: Prime factor: 2, power: 3. Prime factor: 4, power: 1. Prime factor: 5, power: 1. Prime factor: 6, power: 2. I know I did it wrong, I just can't figure out how to get from a to b.

Answers:Read Again: ---- Edited: I forgot to mention that if you are dealing with 32 bit integers, the maximum number of factors with power of 1 happens is 32. It is when in theory the prime factors are the smallest possible value: 2^32 (2 x 2 x 2 ... x 2). Although it is written as 2 ^ 32, it guarantees that no factorized expression would have more than 32 different prime factors. Therefore, you could simple defines two integer arrays of maximum 32 elements like: int prime_factor [32]; int frequency [32]; The first array indicates the found prime factors. The second array indicates the number of times each prim factors is appeared. You could also use a count variable to denote the actual number of the distinct prime numbers found. for example, for the expression: 2^3 * 5^2 * 7^4, the arrays would be: prime_factor : {2, 5, 7} frequency : {3, 2, 4} count: 3 You could modify the code given in the article to fill these arrays rather then simply append each factor to the std::string object. The function getPrimeFactor always return the samllest prime factor of the number, so you could only need to check if it is repeated factor or a new factor by comparing it with the most recent found prime factor. ---- Do have a look at the following article: C++: Factorizing an Integer http://911programming.wordpress.com/2010/05/23/c-factorizing-an-integer/ You would need a very simple modification to do it as specified in your assignment.

Question:How do acidity and alkalinity affect the rate of decomp and which of the two results in a faster rate of decomp? How do pH levels affect the rate of decomp? Thanks.

Answers:This is such a complex issue that organisations such as the FBI conduct research using real human bodies buried in all sorts of different conditions in order to investigate what happens. Extreme acidity or alkalinity will often slow the rate of decomposition by restricting the growth rate of microorganisms but many other factors also have an impact, for example:- - temperature - humidity - exposure to the air - condition of the corpse (damaged by injury, body mass, health when alive, etc) - seasonal variations in weather - nearby flora and fungi

From Youtube

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.

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