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{{Use dmy datesInfobox physical quantity|datebgcolour=February 2015}{default}{{chembox| Verifiedfields name = changedKinetic energy| Watchedfields image= changed| verifiedrevid = 477003420| Name = Calcium carbonate| ImageFileL1 = calcium carbonate.png| ImageFileR1 = Calcium-carbonate-xtal-3D-SF.png| ImageFile2 = Calcium carbonate[[File:Wooden roller coaster txgi.jpg| IUPACName = Calcium carbonate220px]]| OtherNames caption= The cars of a [[calciteroller coaster]]; reach their maximum kinetic energy when at the bottom of the path. When they start rising, the kinetic energy begins to be converted to gravitational [[aragonitepotential energy]]; . The sum of kinetic and potential energy in the system remains constant, ignoring losses to [[chalkfriction]]; .|unit = [[Lime joule]] (materialJ)]]; [[Limestone]]; [[marble]]; [[oyster]]; [[pearl]]; |Section1symbols ={{Chembox Identifiers| UNII_Ref = {{fdacite|correct|FDA}}| UNII = H0G9379FGK| ChEMBL_Ref = {{ebicite|changed|EBI}}| ChEMBL = 1200539| KEGG_Ref = {{keggcite|correct|kegg}}| KEGG = D00932| InChI = 1/CH2O3.CaKE, ''E''<sub>k</c2-1(3)4;/h(H2,2,3sub>,4);/q;+2/p-2or T| ChEBI_Ref derivations = {{ebicite|correct|EBI}}| ChEBI ''E''<sub>k</sub> = 3311½''[[mass| SMILES = [Ca+2m]].[O-]C([O-])=O| InChIKey = VTYYLEPIZMXCLO-NUQVWONBASvelocity| SMILES1 = C(=O)([O-v])[O-].[Ca+''<sup>2]</sup> <br>| StdInChI_Ref = {{stdinchicite|correct|chemspider}}| StdInChI ''E''<sub>k</sub> = 1S/CH2O3.Ca/c2-1(3)4;/h(H2,2,3,4);''E''<sub>t</q;sub>+2''E''<sub>r</p-2| StdInChIKey_Ref = {{stdinchicite|correct|chemspider}}| StdInChIKey = VTYYLEPIZMXCLO-UHFFFAOYSA-L| CASNo = 471-34-1| CASNo_Ref = {{cascite|correct|CAS}}| ChemSpiderID_Ref = {{chemspidercite|correct|chemspider}}| ChemSpiderID = 9708| EINECS = 207-439-9| PubChem = 10112| RTECS = FF9335000sub>
}}
==Chemistry=Kinetic energy of rigid bodies===Calcium carbonate shares the typical properties of other carbonates. Notably,* it reacts with In [[acidclassical mechanics]]s, releasing [[carbon dioxide]]::CaCO<sub>3</sub>the kinetic energy of a ''point object'' (s) + 2H<sup>+</sup>(aq) → Ca<sup>2+</sup>(aq) + CO<sub>2</sub>(g) + H<sub>2</sub>O (lan object so small that its mass can be assumed to exist at one point)* it releases carbon dioxide upon heating, called or a non-rotating [[thermal decompositionrigid body]] reaction, or depends on the [[calcinationmass]] (to above 840 °C in of the case of CaCO<sub>3</sub>), to form body as well as its [[calcium oxidespeed]], commonly called . The kinetic energy is equal to 1/2 the [[quicklimeMultiplication|product]], with reaction [[enthalpy]] 178 kJ/moleof the mass and the square of the speed. In formula form::CaCO<sub>3</sub> (s) → CaO (s) + CO<sub>2</sub> (g)
:<math>F s ==Preparation==The vast majority of calcium carbonate used in industry is extracted by mining or quarrying. Pure calcium carbonate (e.g. for food or pharmaceutical use), can be produced from a pure quarried source (usually [[marble]]).\tfrac{1}{2} mv^2</math>
The kinetic energy of an object is related to its [[momentum]] by the equation: CaO + H<sub>2</sub>O → Ca(OH)<sub>2</sub>:<chemmath>Ca(OH)E_\text{k} = \frac{p^2 + CO2 -> CaCO3(v) + H2O}{2m}</chemmath>
===Extraterrestrial=Derivation====Beyond Earth, strong evidence suggests The work done in accelerating a particle with mass ''m'' during the infinitesimal time interval ''dt'' is given by the presence dot product of calcium carbonate on [[Mars]]. Signs of calcium carbonate have been detected at more than one location (notably at [[Gusev crater|Gusev]] ''force'' '''F''' and [[Huygens (crater)|Huygens]] craters). This provides some evidence for the past presence of liquid water.infinitesimal ''displacement ''d'''x''''':<refmath>\mathbf{F} \cdot d \mathbf{cite journal| last1x} =Boynton |first1\mathbf{F} \cdot \mathbf{v} d t =WV| last2\frac{d \mathbf{p}}{d t} \cdot \mathbf{v} d t =Ming |first2\mathbf{v} \cdot d \mathbf{p} =DW| last3=Kounaves |first3=SP| last4=Young |first4=SM| last5=Arvidson |first5=RE| last6=Hecht |first6=MH| last7=Hoffman |first7=J| last8=Niles |first8=PB| last9=Hamara |first9=DK| last10=Quinn| first10=R. C.| last11=Smith| first11=P. H.| last12=Sutter| first12=B| last13=Catling| first13=D. C.| last14=Morris| first14=R. V.| title=Evidence for Calcium Carbonate at the Mars Phoenix Landing Site| url=http://planetary.chem.tufts.edu/Boynton%20etal%20Science%202009v325p61.pdf| journal=Science |volume=325 |issue=5936 |pages= 61–64| year=2009 |pmid=19574384 |bibcode=2009Sci...325...61B| display-authors=3| doi=10.1126/science.1172768| doi-broken-date=2017-01-31 \mathbf{v}\cdot d (m \mathbf{v})\,,</ref><ref name=Clark2007math>{{cite journal| author1where we have assumed the relationship '''p''' =Clark| year=2007| title=Evidence for montmorillonite or its compositional equivalent in Columbia Hills ''m'' '''v''' and the validity of [[Newton's Second Law]]. (However, Mars| journal=also see the special relativistic derivation [[Journal Kinetic energy#Relativistic kinetic energy of Geophysical Researchrigid bodies|below]]| volume=112 |pages=E06S01| doi=10.1029/2006JE002756| last2=Arvidson| first2=R. E.| last3=Gellert| first3=R.| last4=Morris| first4=R. V.| last5=Ming| first5=D. W.| last6=Richter| first6=L.| last7=Ruff| first7=S. W.| last8=Michalski| first8=J. R.| last9=Farrand| first9=W. H.| last10=Yen| first10=A.| last11=Herkenhoff| first11=K. E.| last12=Li| first12=R.| last13=Squyres| first13=S. W.| last14=Schröder| first14=C.| last15=Klingelhöfer| first15=G.| last16=Bell| first16=J. F.| bibcode = 2007JGRE..112.6S01C| displayauthors=3 | url=http://dspace.stir.ac.uk/bitstream/1893/17119/1/Clark2007_Evidence_for_montmorillonite_or_its_compositional_equivalent_in_Columbia_Hills_Mars.pdf}}</ref>)
===Role in taphonomyRotating bodies===Calcium carbonate can [[taphonomy|preserve fossils]] If a rigid body Q is rotating about any line through [[permineralization]]. Most of the vertebrate fossils center of the mass then it has [[Two Medicine Formationrotational energy|''rotational kinetic energy'']]—a [[geologic formation]] known for its [[duck-billed dinosaur]] eggs—are preserved by CaCO(<submath>3E_\text{r}\,</submath> permineralization.<ref name="twoturn" /> This type ) which is simply the sum of preservation conserves high levels the kinetic energies of detailits moving parts, even down to the microscopic level. However, it also leaves specimens vulnerable to [[weathering]] when exposed to the surface.<ref name="twoturn">Trexler, D. (2001) [httpsand is thus given by://books.google.com/books?id=mgc6CS4EUPsC&pg=PA98 "Two Medicine Formation, Montana: geology and fauna"], pp. 298–309 in ''Mesozoic Vertebrate Life'', Tanke, D. H., and Carpenter, K. (eds), Indiana University Press. {{ISBN|0-253-33907-3}}</ref>
===Household use=Relativistic kinetic energy of rigid bodies==Calcium carbonate is a key ingredient {{See also|Mass in many household cleaning powders like [[Comet (cleanser)]] special relativity|Tests of relativistic energy and is used as a scrubbing agent.momentum}}
:<math>E_\text{k} \approx m c^2 \left(1 + \frac{1}{2} v^2/c^2\right) - m c^2 ==Solubility==\frac{1}{2} m v^2</math>
This can also be expanded as a [[Taylor series]], the first term of which is the simple expression from Newtonian mechanics:<ref>{{cite web |url=http://farside.ph.utexas.edu/teaching/qmech/Quantum/node107.html |title=Fine Structure of Hydrogen |first=Richard |last=Fitzpatrick | widthdate="500"20 July 2010 | stylework="width:50%; height:25px;"Quantum Mechanics |H<sub>2accessdate=20 August 2016}}</subref>CO:<sub>3</submath> E_\text{k} \approx \frac{p^2}{eqm2 m}- \frac{p^4} H<sup>+</sup> + HCO<sub>{8 m^3</sub><sup>−</sup> | ''K''<sub>a1</sub> = c^2} .5×10<sup>−4</supmath> at 25 °C|}This suggests that the formulae for energy and momentum are not special and axiomatic, but concepts emerging from the equivalence of mass and energy and the principles of relativity.
and the kinetic energy can be expressed as the total energy minus the rest energy:{| width="450"| style="width:50%; height:25px;"| H<submath>2</sub>O E_{k} \, = \, - \, p_{\beta} \, u_{\text{eqmobs}}^{\beta} H<sup>+</sup> + OH<sup>−</sup>| ''K'' = 10<sup>−14\, - \, m \, c^2 \, .</supmath> at 25 °C|}
Consider the case of a metric that is diagonal and spatially isotropic (which is true for all aqueous solutions''g''<sub>tt</sub>,''g''<sub>ss</sub>,''g''<sub>ss</sub>,''g''<sub>ss</sub>). Since:<math>u^{\alpha} = \frac{d x^{\alpha}}{d t} \frac{d t}{d \tau} = v^{\alpha} u^{t} \, and the fact that the solution must be electrically neutral,</math>
In this situation, the dissociation constants for the much faster reactions HNewtonian approximation to general relativity:<submath>g_{t t} = - \left( c^2</sub>CO<sub>3</sub> ⇌ H<sup>+</sup> + HCO<sub>3</sub><sup>‾</sup> ⇌ 2 H<sup>+</sup> + CO<sub>3</sub><sup>2−</sup> allow the prediction of concentrations of each dissolved inorganic carbon species in solution\Phi \right) \, from the added concentration of HCO<sub>3</submath>:<supmath>−</sup> (which constitutes more than 90% of [[Bjerrum plot]] species from pH 7 to pH 8 at 25 °C in fresh water).<ref nameg_{s s} ="Mook 2000">Mook, W. (2000) [http://www1 -naweb.iaea.org/napc/ih/documents/global_cycle/vol%20I/cht_i_09.pdf "Chemistry of carbonic acid in water"], pp. 143–165 in ''Environmental Isotopes in the Hydrological Cycle: Principles and Applications''. INEA/UNESCO: Paris.</ref> Addition of HCO<sub>3</sub><sup>−</sup> will increase CO<sub>3</sub><sup>2−</sup> concentration at any pH. Rearranging the equations given above, we can see that [Ca<sup>\frac{2 \Phi}{c^2+</sup>] = Ksp / [CO<sub>3</sub><sup>2−</sup>], and [CO<sub>3</sub><sup>2−</sup>] = K<sub>a2</sub> × [HCO<sub>3</sub><sup>−</sup>] / [H<sup>+</sup>]. Therefore} \, when HCO<sub>3</sub><sup>−</sup> concentration is known, the maximum concentration of Ca<sup>2+</supmath> ions before scaling through CaCO<sub>3</sub> precipitation can be predicted from the formula:
The expectation value of the electron kinetic energy, <math>\langle\hat{| border="1" cellspacing="0" cellpadding="4" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;" class="wikitable"|-! width="160" {{chembox header}T} |[A] (mol/L)| 1| 10<sup>−1\rangle</supmath>, for a system of ''N'' electrons described by the [[Wave function| 10wavefunction]] <supmath>−2\vert\psi\rangle</supmath>is a sum of 1-electron operator expectation values:| 10:<supmath>−3</sup>| 10<sup>−4</sup>| 10<sup>−5</sup>| 10<sup>−6</sup>| 10<sup>−7</sup>| 10<sup>−10</sup>|-! width\langle\hat{T}\rangle ="160" \bigg\langle\psi \bigg\vert \sum_{i=1}^N \frac{chembox header-\hbar^2}} |Initial pH| 1.08||1.62||{2.25||3.05||4.01||5.00||5.97||6.74||7.00|-! width="160" {m_\text{chembox headere}} |Final pH| 6.71||7.17||7.63||8.06||8.24||8.26||8.26||8.26||8.27|\nabla^2_i \bigg\vert \psi \bigg\rangle = -! width="160" \frac{\hbar^2}{2 m_\text{chembox headere}} |Dissolved CaCO\sum_{i=1}^N \bigg\langle\psi \bigg\vert \nabla^2_i \bigg\vert \psi \bigg\rangle</math>where <submath>3m_\text{e}</submath> is the mass of the electron and <math>\nabla^2_i<br /math>(g/is the [[liter|LLaplacian]] operator acting upon the coordinates of acid)| 62.0||7.39||0.874||0.123||0.0536||0.0477||0the ''i''<sup>th</sup> electron and the summation runs over all electrons.0471||0.0471||0.0470|}
==See also==
{{div colPortal|colwidth=22emEnergy}}* [[CuttleboneEscape velocity]]* [[CuttlefishJoule]]* [[GessoKE-Munitions]]* [[LimescaleProjectile#Typical projectile speeds|Kinetic energy per unit mass of projectiles]]* [[MarbleProjectile#Kinetic projectiles|Kinetic projectile]]* [[Ocean acidificationParallel axis theorem]]* [[Potential energy]]* [[Recoil]] ==Notes=={{div col endreflist}}
==References==
*{{reflistcite web |30emurl = http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy | title = Kinetic Energy | accessdate = 2015-07-19 | author = Physics Classroom | year = 2000 }}*[[Oxford Dictionary]] 1998*{{cite web | url = http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Coriolis.html | title = Biography of Gaspard-Gustave de Coriolis (1792-1843) | accessdate = 2006-03-03 | author = School of Mathematics and Statistics, University of St Andrews | year = 2000 }}*{{cite book | last = Serway | first = Raymond A. |author2=Jewett, John W. | title = Physics for Scientists and Engineers | edition = 6th | publisher = Brooks/Cole | year = 2004 | isbn = 0-534-40842-7 }}*{{cite book | last = Tipler | first = Paul | title = Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics | edition = 5th | publisher = W. H. Freeman | year = 2004 | isbn = 0-7167-0809-4 }}*{{cite book | last = Tipler | first = Paul |author2=Llewellyn, Ralph | title = Modern Physics | edition = 4th | publisher = W. H. Freeman | year = 2002 | isbn = 0-7167-4345-0 }}
==External links==
* {{ICSC|1193|11}}* {{PubChemLink|516889}}* [[ATC codes]]: {{ATC|A02|AC01}} and {{ATC|A12|AA04Commonscat-inline}}* [http://calcium-carbonatewww.orgkineticenergys.uk/calciumcom kinetic energy] -carbonate.asp The British Calcium Carbonate Association – What what it is calcium carbonate]* [https://www.cdc.gov/niosh/npg/npgd0090.html CDC – NIOSH Pocket Guide to Chemical Hazards – Calcium Carbonate] {{Calcium compounds}}{{Antacids}}{{Drugs for treatment of hyperkalemia and hyperphosphatemia}}how it works
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