Хемијске једначине — разлика између измена

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{{Short description|Симболички приказ хемијске реакције}}
[[Датотека:Combustion reaction of methane.jpg|мини|Оксидација метана]]
[[Датотека:H3PO4 balancing chemical equation phosphorus pentoxide and water becomes phosphoric acid.gif|мини|Ова хемијска једначина је уравнотежена тако што се прво помножи H3PО4 са четири да би број P атома био једнак, а затим множењем Н2О са шест да би бројеви Н и О атома били једнаки.]]
'''Хемијске једначине''' приказују у [[стехиометрија|стехиометријским]] односима реакције различитих [[хемијски елемент|хемијских елемената]] и [[хемијско једињење|једињења]], тј. [[хемијски процес]].{{напомена|[[стехиометрија]], хемијско мерење: учење о пропорцији}} На левој страни једначине су хемијски елементи које улазе у процес, а на десној једињења која хемијским процесом настају. Уместо знака једнакости пише се стрелица (→) која означава смер у коме се промена догађа.<ref name="goldbook">[[Међународна унија за чисту и примењену хемију|IUPAC]]. Compendium of Chemical Terminology, 2nd ed. {{ISBN|0-9678550-9-8}}.</ref><ref>{{cite journal |author= Crosland, M.P. |year= 1959 |title= The use of diagrams as chemical 'equations' in the lectures of William Cullen and Joseph Black |journal= Annals of Science |volume= 15 |issue= 2 |pages= 75–90 }}</ref>
Стехиометријски коефицијенти (бројеви испред хемијских формула) резултат су закона о одржању масе и закона о одржању наелектрисања. Закон о одржању масе диктира да се количина сваког елемента у хемијској реакцији не мења. Дакле, свака страна хемијске једначине мора представљати исту количину било којег одређеног елемента. Исто тако, наелектрисање се чува у хемијској реакцији. Према томе, исто наелектрисање мора бити присутно на обе стране уравнотежене једначине.
== Формирање хемијске реакције ==
A chemical equation consists of the [[chemical formula]]s of the reactants (the starting substances) and the chemical formula of the products (substances formed in the chemical reaction). The two are separated by an [[arrow (symbol)|arrow symbol]] (→, usually read as "yields") and each individual substance's chemical formula is separated from others by a [[plus sign]].
As an example, the equation for the reaction of [[hydrochloric acid]] with [[sodium]] can be denoted:
:2 {{chem|HCl}} + 2 {{chem|Na}} → 2 {{chem|NaCl}} + {{chem|H|2}}
This equation would be read as "two HCl plus two Na yields two NaCl and H two." But, for equations involving complex chemicals, rather than reading the letter and its subscript, the chemical formulas are read using [[IUPAC nomenclature]]. Using IUPAC nomenclature, this equation would be read as "hydrochloric acid plus sodium yields [[sodium chloride]] and [[hydrogen]] gas."
This equation indicates that sodium and HCl react to form NaCl and H<sub>2</sub>. It also indicates that two sodium molecules are required for every two hydrochloric acid molecules and the reaction will form two sodium chloride molecules and one [[Diatomic molecule|diatomic]] molecule of hydrogen gas molecule for every two hydrochloric acid and two sodium molecules that react. The [[stoichiometric coefficients]] (the numbers in front of the chemical formulas) result from the [[conservation of mass|law of conservation of mass]] and the [[charge conservation|law of conservation of charge]] (see [[#Balancing chemical equations|"Balancing chemical equations" section]] below for more information).
== Уобичајени симболи ==
[[File:Baker-Venkataraman-Rearrangement V.1.svg|thumb|250px|<small>Baker-Venkataraman rearrangement</small>]]
Symbols are used to differentiate between different types of reactions. To denote the type of reaction:<ref name="goldbook" />
* "<math>=</math>" symbol is used to denote a [[stoichiometric]] relation.
* "<math>\rightarrow</math>" symbol is used to denote a net forward reaction.
* "<math>\rightleftarrows</math>" symbol is used to denote a reaction in both directions.<ref>The notation <math>\rightleftarrows</math> was proposed in 1884 by the Dutch chemist [[Jacobus Henricus van 't Hoff]]. See: {{cite book|last1=van 't Hoff|first1=J.H.|title=Études de Dynamique Chemique|trans-title=Studies of chemical dynamics|date=1884|publisher=Frederik Muller & Co.|location=Amsterdam, Netherlands|pages=4–5|url=https://archive.org/stream/etudesdedynamiqu00hoff#page/4/mode/2up|language=fr}} Van 't Hoff called reactions that didn't proceed to completion "limited reactions". From pp. 4–5: ''"Or M. Pfaundler a relié ces deux phénomênes … s'accomplit en même temps dans deux sens opposés."'' (Now Mr. Pfaundler has joined these two phenomena in a single concept by considering the observed limit as the result of two opposing reactions, driving the one in the example cited to the formation of sea salt [i.e., NaCl] and nitric acid, [and] the other to hydrochloric acid and sodium nitrate. This consideration, which experiment validates, justifies the expression "chemical equilibrium", which is used to characterize the final state of limited reactions. I would propose to translate this expression by the following symbol:
: HCl + NO<sub>3</sub> Na <math>\rightleftarrows</math> NO<sub>3</sub> H + Cl Na.
I thus replace, in this case, the = sign in the chemical equation by the sign <math>\rightleftarrows</math>, which in reality doesn't express just equality but shows also the direction of the reaction. This clearly expresses that a chemical action occurs simultaneously in two opposing directions.)</ref>
* "<chem><=></chem>" symbol is used to denote an [[chemical equilibrium|equilibrium]].<ref>The notation <chem><=></chem> was suggested by [[Hugh Marshall]] in 1902. See: {{cite journal |last1=Marshall |first1=Hugh |date=1902 |title=Suggested Modifications of the Sign of Equality for Use in Chemical Notation |journal=Proceedings of the Royal Society of Edinburgh |volume=24 |pages=85–87 |doi=10.1017/S0370164600007720 }}</ref>
The physical state of chemicals is also very commonly stated in parentheses after the chemical symbol, especially for ionic reactions. When stating physical state, (s) denotes a solid, (l) denotes a liquid, (g) denotes a gas and (aq) denotes an [[aqueous solution]].
If the reaction requires energy, it is indicated above the arrow. A capital Greek letter delta (<math>\Delta</math><ref>The symbol is more properly denoted as a simple triangle (△), which was originally the alchemical symbol for fire.</ref>) is put on the reaction arrow to show that energy in the form of heat is added to the reaction. The expression <math>h\nu</math><ref>This symbol comes from the Planck equation for the energy of a photon, <math>E = h\nu</math>. It is sometimes mistakenly written with a 'v' ("vee") instead of the Greek letter '<math>\nu</math>' ("nu")</ref> is used as a symbol for the addition of energy in the form of light. Other symbols are used for other specific types of energy or radiation.
== Балансирање хемијских једначина ==
[[File:Combustion reaction of methane.jpg|thumb|250px|As seen from the equation {{chem|CH|4}} + 2 {{chem|O|2}} → {{chem|CO|2}} + 2 {{chem|H|2|O}}, a coefficient of 2 must be placed before the [[oxygen]] gas on the reactants side and before the [[properties of water|water]] on the products side in order for, as per the law of conservation of mass, the quantity of each element does not change during the reaction]][[File:H3PO4 balancing chemical equation phosphorus pentoxide and water becomes phosphoric acid.gif|thumb|[[Phosphorus pentoxide|P<sub>4</sub>O<sub>10</sub>]] + 6 [[water|H<sub>2</sub>O]] → 4 [[Phosphoric acid|H<sub>3</sub>PO<sub>4</sub>]]<br>This chemical equation is being balanced by first multiplying H<sub>3</sub>PO<sub>4</sub> by four to match the number of P atoms, and then multiplying H<sub>2</sub>O by six to match the numbers of H and O atoms.]]
The [[law of conservation of mass]] dictates that the quantity of each [[Chemical element|element]] does not change in a [[chemical reaction]]. Thus, each side of the chemical equation must represent the same quantity of any particular element. Likewise, the charge is conserved in a [[chemical reaction]]. Therefore, the same charge must be present on both sides of the balanced [[equation]].
One balances a chemical equation by changing the scalar number for each chemical formula. Simple chemical equations can be balanced by inspection, that is, by trial and error. Another technique involves solving a [[system of linear equations]].
Balanced equations are often written with smallest whole-number coefficients. If there is no coefficient before a chemical formula, the coefficient is 1.
The method of inspection can be outlined as putting a coefficient of 1 in front of the most complex chemical formula and putting the other coefficients before everything else such that both sides of the arrows have the same number of each atom. If any [[fraction (mathematics)|fractional]] coefficient exists, multiply every coefficient with the smallest number required to make them whole, typically the [[denominator]] of the fractional coefficient for a reaction with a single fractional coefficient.
As an example, seen in the above image, the burning of methane would be balanced by putting a coefficient of 1 before the CH<sub>4</sub>:
:1 CH<sub>4</sub> + O<sub>2</sub> → CO<sub>2</sub> + H<sub>2</sub>O
Since there is one carbon on each side of the arrow, the first atom (carbon) is balanced.
Looking at the next atom (hydrogen), the right-hand side has two atoms, while the left-hand side has four. To balance the hydrogens, 2 goes in front of the H<sub>2</sub>O, which yields:
:1 CH<sub>4</sub> + O<sub>2</sub> → CO<sub>2</sub> + 2 H<sub>2</sub>O
Inspection of the last atom to be balanced (oxygen) shows that the right-hand side has four atoms, while the left-hand side has two. It can be balanced by putting a 2 before O<sub>2</sub>, giving the balanced equation:
:CH<sub>4</sub> + 2 O<sub>2</sub> → CO<sub>2</sub> + 2 H<sub>2</sub>O
This equation does not have any coefficients in front of CH<sub>4</sub> and CO<sub>2</sub>, since a coefficient of 1 is dropped.
Note that in some circumstances it is not correct to write a balanced reaction with all whole-number coefficients. For example, the reaction corresponding to the [[standard enthalpy of formation]] must be written such that one mole of a single product is formed. This will often require that some reactant coefficients be fractional, as is the case with the formation of lithium fluoride:
:Li(s) + {{1/2}}&thinsp;F<sub>2</sub>(g) → LiF(s)
=== Матрична метода ===
Generally, any chemical equation involving ''J'' different molecules can be written as:
:<math>\sum_{j=1}^J \nu_j R_j=0</math>
where ''R<sub>j</sub>'' is the symbol for the ''j-th'' molecule, and &nu;<sub>j</sub> is the stoichiometric coefficient for the ''j-th'' molecule, positive for products, negative for reactants (or vice versa). A properly balanced chemical equation will then obey:
:<math>\sum_{j=1}^J a_{ij} \nu_j=0</math>
where the composition matrix ''a<sub>ij</sub>'' is the number of atoms of element ''i'' in molecule ''j''. Any vector which, when operated upon by the composition matrix yields a zero vector, is said to be a member of the [[kernel (linear algebra)|kernel]] or null space of the operator. Any member &nu;<sub>j</sub> of the null space of ''a<sub>ij</sub>'' will serve to balance a chemical equation involving the set of ''J'' molecules comprising the system. A "preferred" stoichiometric vector is one for which all of its elements can be converted to integers with no common divisors by multiplication by a suitable constant.
Generally, the composition matrix is degenerate: That is to say, not all of its rows will be linearly independent. In other words, the [[Matrix rank|rank]] (''J<sub>R</sub>'') of the composition matrix is generally less than its number of columns (''J''). By the [[rank-nullity]] theorem, the null space of ''a<sub>ij</sub>'' will have ''J-J<sub>R</sub>'' dimensions and this number is called the nullity (''J<sub>N</sub>'') of ''a<sub>ij</sub>''. The problem of balancing a chemical equation then becomes the problem of determining the ''J<sub>N</sub>''-dimensional null space of the composition matrix. It is important to note that only for ''J<sub>N</sub>''=1, will there be a unique solution. For ''J<sub>N</sub>''>1 there will be an infinite number of solutions to the balancing problem, but only ''J<sub>N</sub>'' of them will be independent: If ''J<sub>N</sub>'' independent solutions to the balancing problem can be found, then any other solution will be a linear combination of these solutions. If ''J<sub>N</sub>''=0, there will be no solution to the balancing problem.
Techniques have been developed <ref name="Thorne2010">{{cite journal |last1=Thorne |first1=Lawrence R. |date=2010 |title=An Innovative Approach to Balancing Chemical-Reaction Equations: A Simplified Matrix-Inversion Technique for Determining the Matrix Null Space |journal=Chem. Educator |volume=15 |pages=304–308 |arxiv=1110.4321 }}</ref><ref name="Holmes2015">{{cite web |url=http://www.logical.ai/chemistry/html/chem-nullspace.html |title=The null space's insight into chemical balance |last=Holmes |first=Dylan |date=2015 |publisher=Dylan Holmes |access-date=Oct 10, 2017 }}</ref> to quickly calculate a set of ''J<sub>N</sub>'' independent solutions to the balancing problem and are superior to the inspection and algebraic method in that they are determinative and yield all solutions to the balancing problem.
== Јонске једначине ==
An ionic equation is a chemical equation in which [[electrolyte]]s are written as dissociated [[ion]]s. Ionic equations are used for [[single displacement reaction|single]] and [[double displacement reaction]]s that occur in [[aqueous solution]]s.
For example, in the following precipitation reaction:
:<chem>CaCl2 + 2AgNO3 -> Ca(NO3)2 + 2 AgCl(v)</chem>
the full ionic equation is:
:<chem>Ca^2+ + 2Cl^- + 2Ag+ + 2NO3^- -> Ca^2+ + 2NO3^- + 2AgCl(v)</chem>
or, with all physical states included:
:<chem>Ca^2+(aq) + 2Cl^-(aq) + 2Ag+(aq) + 2NO3^{-}(aq) -> Ca^2+(aq) + 2NO3^{-}(aq) + 2AgCl(v)</chem>
In this reaction, the Ca<sup>2+</sup> and the NO<sub>3</sub><sup>&minus;</sup> ions remain in solution and are not part of the reaction. That is, these ions are identical on both the reactant and product side of the chemical equation. Because such ions do not participate in the reaction, they are called [[spectator ion]]s. A ''net ionic'' equation is the full ionic equation from which the spectator ions have been removed.<ref>{{cite book |title=Chemistry: matter and its changes |author1=James E. Brady |author2=Frederick Senese |author3=Neil D. Jespersen |isbn=9780470120941 |lccn=2007033355 |date=December 14, 2007 |url=https://books.google.com/books?id=A1UvAQAAIAAJ&q=%22a+net+ionic+equation+is+obtained+by+eliminating+spectator+ions+from+the+ionic+equation%22 |publisher=John Wiley & Sons}}</ref> The net ionic equation of the proceeding reactions is:
:<chem>2Cl^- + 2Ag+ -> 2AgCl(v)</chem>
or, in ''reduced'' balanced form,
:<chem>Ag+ + Cl^- -> AgCl(v)</chem>
In a [[Neutralization (chemistry)|neutralization]] or [[acid]]/[[Base (chemistry)|base]] reaction, the net ionic equation will usually be:
:H<sup>+</sup>(aq) + OH<sup>&minus;</sup>(aq) → H<sub>2</sub>O(l)
There are a few acid/base reactions that produce a precipitate in addition to the water molecule shown above. An example is the reaction of [[barium hydroxide]] with [[phosphoric acid]], which produces not only water but also the insoluble salt [[barium phosphate]]. In this reaction, there are no spectator ions, so the net ionic equation is the same as the full ionic equation.
:<chem>3Ba(OH)2 + 2H3PO4 -> 6H2O + Ba3(PO4)2(v)</chem>
:<math chem="">\ce{{3Ba^2+} + {6OH^-} + {6H+}} + \underbrace\ce{2PO4^3-}_\ce{phosphate} \ce{-> {6H2O} + \underbrace{Ba3(PO4)2(v)}_{barium~phosphate}}</math>
Double displacement reactions that feature a [[carbonate]] reacting with an acid have the net ionic equation:
:<math chem>\ce{2H+} + \underbrace\ce{CO3^2-}_\ce{carbonate} \ce{-> H2O + CO2 (^)}</math>
If every ion is a "spectator ion" then there was no reaction, and the net ionic equation is null.
Generally, if ''z<sub>j</sub>'' is the multiple of elementary charge on the ''j-th'' molecule, charge neutrality may be written as:
:<math>\sum_{j=1}^J z_j \nu_j=0</math>
where the ''&nu;<sub>j</sub>'' are the stoichiometric coefficients described above. The ''z<sub>j</sub>'' may be incorporated<ref name="Thorne2010"/><ref name="Holmes2015"/>
as an additional row in the ''a<sub>ij</sub>'' matrix described above, and a properly balanced ionic equation will then also obey:
:<math>\sum_{j=1}^J a_{ij} \nu_j=0</math>
== Напомене ==
== Спољашње везе ==
* [ Хемијске једначине]{{Мртва веза|date=10. 2018 |bot=InternetArchiveBot |fix-attempted=yes }}
* [http://www.berkeleychurchill.com/software/chembal.php Уравнотеживање хемијских једначина]
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