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A '''chemical equation''' is the symbolic representation of a [[chemical reaction]] wherein the [[reactant]] entities are given on the left-hand side and the [[Product (chemistry)|product]] entities on the right-hand side.<ref name="goldbook">[[IUPAC]]. Compendium of Chemical Terminology, 2nd ed. ISBN 0-9678550-9-8.</ref> The coefficients next to the symbols and formulae of entities are the absolute values of the [[stoichiometric coefficient|stoichiometric numbers]]. The first chemical equation was diagrammed by [[Jean Beguin]] in 1615.<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 |doi=10.1080/00033795900200088}}</ref>
In [[electronics]] a '''relaxation oscillator''' is a [[linear circuit|nonlinear]] [[electronic oscillator]] circuit that produces a [[sinusoid|nonsinusoidal]] repetitive output signal, such as a [[triangle wave]] or [[square wave]].<ref name="Graf">{{cite book
| isbn = 1139485768}}</ref> The circuit consists of a [[feedback loop]] containing a switching device such as a [[transistor]], [[comparator]], [[relay]],<ref name="Varigonda">{{cite journal
| last = Varigonda
| first = Subbarao
| coauthors = Tryphon T. Georgiou
| title = Dynamics of Relay Relaxation Oscillators
| journal = IEEE Trans. on Automatic Control
| volume = 46
| issue = 1
| pages = 65
| publisher = Inst. of Electrical and Electronic Engineers
| accessdate = February 22, 2014}}</ref> [[op amp]], or a [[negative resistance]] device like a [[tunnel diode]], that repetitively charges a [[capacitor]] or [[inductor]] through a resistance until it reaches a threshold level, then discharges it again.<ref name="Du" /><ref name="HyperPhysics">{{cite web
| last = Nave
| first = Carl R.
| title = Relaxation Oscillator Concept
| work = [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
| publisher = Dept. of Physics and Astronomy, Georgia State Univ.
| accessdate = February 22, 2014}}</ref> The [[frequency|period]] of the oscillator depends on the [[time constant]] of the capacitor or inductor circuit.<ref name="Edson" /> The active device switches abruptly between charging and discharging modes, and thus produces a discontinuously changing repetitive waveform.<ref name="Edson" /><ref name="Du" /> This contrasts with the other type of electronic oscillator, the harmonic or [[electronic oscillator#linear oscillator|linear oscillator]], which uses an [[amplifier]] with feedback to excite [[resonant]] oscillations in a [[resonator]], producing a [[sine wave]].<ref name="Oliveira">{{cite book
| last = Oliveira
| first = Luis B.
| authorlink =
| coauthors = et al
| title = Analysis and Design of Quadrature Oscillators
| isbn = 1402085168}}</ref> The difference between the two types is that in a linear oscillator the circuit operates close to [[linearity]], while in a relaxation oscillator one of the components, the switching device, operates in an extremely nonlinear fashion, in a saturated condition, during most of the cycle.<ref name="Oliveira" />
The term ''relaxation oscillator'' is also applied to [[dynamic system]]s in many diverse areas of science that produce nonlinear oscillations and can be analyzed using the same mathematical model as electronic relaxation oscillators.<ref name="Wang">{{cite conference
A chemical equation consists of the [[chemical formulas]] 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)|<math>\rightarrow</math>]], usually read as "yields") and each individual substance's chemical formula is separated from others by a [[plus sign]].
| first = Wang
| last = DeLiang
| title = Relaxation oscillators and networks
| booktitle = Wiley Encyclopedia of Electrical and Electronics Engineering, Vol. 18
| isbn = 0521033330}}</ref> networks of firing [[nerve cell]]s,<ref name="Letellier1" /> [[thermostat]] controlled heating systems,<ref name="Pippard1">[http://books.google.com/books?id=F8-9UNvsCBoC&pg=PA41 Pippard, The Physics of Vibration, p. 41-42]</ref> coupled chemical reactions,<ref name="Sauro" /> the beating human heart,<ref name="Letellier1" /><ref name="Pippard1" /> earthquakes,<ref name="Enns" /> the squeaking of chalk on a blackboard,<ref name="Pippard1" /> the cyclic populations of predator and prey animals, and [[gene activation]] systems<ref name="Sauro" /> have been modeled as relaxation oscillators. Relaxation oscillations are characterized by two alternating processes on different time scales: a long [[relaxation (physics)|relaxation]] period during which the system approaches an [[equilibrium point]], alternating with a short impulsive period in which the equilibrium point shifts.<ref name="Enns" /><ref name="Letellier1" /><ref name="Pippard" /><ref name="Kinoshita">{{cite conference
| first = Shuichi
| last = Kinoshita
| title = Introduction to Nonequilibrium Phenomena
| booktitle = Pattern Formations and Oscillatory Phenomena
| accessdate = February 24, 2014}}</ref> The [[frequency|period]] of a relaxation oscillator is mainly determined by the [[relaxation time]] constant.<ref name="Letellier1" /> Relaxation oscillations are a type of [[limit cycle]] and are studied in [[nonlinear control]] theory.<ref name="Leigh">see Ch. 9, "Limit cycles and relaxation oscillations" in {{cite book
As an example, the equation for the reaction of [[hydrochloric acid]] with [[sodium]] can be denoted:
The first relaxation oscillator circuit, the [[astable multivibrator]], was invented by [[Henri Abraham]] and Eugene Bloch using [[vacuum tube]]s during World War 1.<ref name="Abraham">{{cite journal
| last = Abraham
| first = H.
| coauthors = E. Bloch
| title = Mesure en valeur absolue des périodes des oscillations électriques de haute fréquence (Measurement of the periods of high frequency electrical oscillations)
| isbn = 9814374423}}</ref> [[Balthasar van der Pol]] originated the term, first distinguished relaxation oscillations from harmonic oscillations, and derived the first mathematical model of a relaxation oscillator, the [[Van der Pol oscillator]], in 1920.<ref name="Van Der Pol">{{cite journal
| last = Van Der Pol
| first = Balthasar
| title = On Relaxation-Oscillations
| journal = The London, Edinburgh, and Dublin Philosophical Magazine 2
| volume = 2
| issue =
| pages = 978-992
| publisher =
| date = 1927
| url =
| issn =
| doi =
| id =
| accessdate = }}</ref><ref name="Letellier" /> Van der Pol borrowed the term ''[[relaxation (physics)|relaxation]]'' from mechanics; the discharge of the capacitor is analogous to the process of ''[[stress relaxation]]'', the gradual disappearance of deformation and return to equilibrium in a [[inelastic]] medium.<ref name="Shukla">{{cite paper
| first = Jai Karan N.
| last = Shukla
| title = Discontinuous Theory of Relaxation Oscillators
| version = Master of Science thesis
| publisher = Dept. of Electrical Engineering, Kansas State Univ.
Relaxation oscillators are generally used to produce low [[frequency]] signals for such applications as blinking lights, electronic beepers, horizontal deflection circuits and time bases for CRT [[oscilloscope]]s, and [[clock signal]]s in some digital circuits. They are also used in [[voltage controlled oscillator]]s (VCOs),<ref name="Abidi">{{cite conference
| accessdate = 0780311493}}</ref> [[inverter (electrical)|inverter]]s and [[switching power supply|switching power supplies]], [[dual-slope ADC|dual-slope analog to digital converters]], and in [[function generator]]s to produce square and triangle waves. One large application in modern society is the [[electronic ballast]] in the base of [[compact fluorescent lamp]]s. Relaxation oscillators are widely used because they are easier to design than linear oscillators, are easier to fabricate on [[integrated circuit]] chips because they do not require inductors like LC oscillators,<ref name="Abidi" /><ref name="van der Tang" /> and can be tuned over a wide frequency range.<ref name="van der Tang">{{cite book
| last = van der Tang
| first = J.
| coauthors = Dieter Kasperkovitz, Arthur H.M. van Roermund
| title = High-Frequency Oscillator Design for Integrated Transceivers
| isbn = 0306487160}}</ref> However they have more [[phase noise]]<ref name="Abidi" /> and poorer [[frequency stability]] than linear oscillators.<ref name="Edson" /><ref name="Abidi" /> Before the advent of microelectronics, simple relaxation oscillators often used a [[negative resistance]] device with [[hysteresis]] such as a [[thyratron]] tube, [[neon lamp]], or [[unijunction transistor]], however today they are more often built with dedicated integrated circuits such as the [[555 timer IC|555 timer]] chip.
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."
[[Image:NeonBulbRelaxationOscillator.svg|thumb|[[Circuit diagram]] of a capacitive relaxation oscillator with a neon lamp threshold device]]
{{main|Pearson-Anson effect}}
This example can be implemented with a [[capacitor|capacitive]] or [[RC circuit|resistive-capacitive integrating circuit]] driven respectively by a constant [[Current source|current]] or [[voltage source]], and a threshold device with [[hysteresis]] ([[neon lamp]], [[thyratron]], [[diac]], reverse-biased [[bipolar transistor]],<ref>http://members.shaw.ca/roma/twenty-three.html</ref> or [[unijunction transistor]]) connected in parallel to the capacitor. The capacitor is charged by the input source causing the voltage across the capacitor to rise. The threshold device does not conduct at all until the capacitor voltage reaches its threshold (trigger) voltage. It then increases heavily its conductance in an avalanche-like manner because of the inherent positive feedback, which quickly discharges the capacitor. When the voltage across the capacitor drops to some lower threshold voltage, the device stops conducting and the capacitor begins charging again, and the cycle repeats [[ad infinitum]].
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 Equation" section below for more information).
If the threshold element is a [[neon lamp]],<ref group="nb">When a (neon) cathode glow lamp or thyratron are used as the trigger devices a second resistor with a value of a few tens to hundreds ohms is often placed in series with the gas trigger device to limit the current from the discharging capacitor and prevent the electrodes of the lamp rapidly [[sputter]]ing away or the cathode coating of the thyratron being damaged by the repeated pulses of heavy current.</ref><ref group="nb">Trigger devices with a third control connection, such as the thyratron or unijunction transistor allow the timing of the discharge of the capacitor to be synchronized with a control pulse. Thus the sawtooth output can be synchronized to signals produced by other circuit elements as it is often used as a scan waveform for a display, such as a [[cathode ray tube]].</ref> the circuit also provides a flash of light with each discharge of the capacitor. This lamp example is depicted below in the typical circuit used to describe the [[Pearson–Anson effect]]. The discharging duration can be extended by connecting an additional resistor in series to the threshold element. The two resistors form a voltage divider; so, the additional resistor has to have low enough resistance to reach the low threshold.
== Common symbols==
Symbols are used to differentiate between different types of reactions. To denote the type of reaction:<ref name="goldbook"/>
=== Alternative implementation with 555 timer ===
* "<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.
* "<math>\rightleftharpoons</math>" symbol is used to denote an [[chemical equilibrium|equilibrium]].
A similar relaxation oscillator can be built with a [[555 timer|555 timer IC]] (acting in astable mode) that takes the place of the neon bulb above. That is, when a chosen capacitor is charged to a design value, (e.g., 2/3 of the power supply voltage) [[comparator]]s within the 555 timer flip a transistor switch that gradually discharges that capacitor through a chosen resistor (RC Time Constant) to ground. At the instant the capacitor falls to a sufficiently low value (e.g., 1/3 of the power supply voltage), the switch flips to let the capacitor charge up again. The popular 555's comparator design permits accurate operation with any supply from 5 to 15 volts or even wider.
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]].
Other, non-comparator oscillators may have unwanted timing changes if the supply voltage changes.
If the reaction requires energy, it is indicated above the arrow. A capital Greek letter delta (<math>\Delta</math>) is put on the reaction arrow to show that energy in the form of heat is added to the reaction. <math>h\nu</math> is used if the energy is added in the form of light.
[[File:Combustion reaction of methane.jpg|thumb|450px|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]]
Alternatively, when the capacitor reaches each threshold, the charging source can be switched from the positive power supply to the negative power supply or vice versa. This case is shown in the [[comparator]]-based implementation here.
The [[law of conservation of mass]] dictates that the quantity of each 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]].
This relaxation oscillator is a hysteretic oscillator, named this way because of the [[hysteresis]] created by the [[positive feedback]] loop implemented with the [[comparator]] (similar to, but different from, an [[operational amplifier|op-amp]]). A circuit that implements this form of hysteretic switching is known as a [[Schmitt trigger]]. Alone, the trigger is a [[bistable multivibrator]]. However, the slow [[negative feedback]] added to the trigger by the RC circuit causes the circuit to oscillate automatically. That is, the addition of the RC circuit turns the hysteretic bistable [[multivibrator]] into an [[astable multivibrator]].
Balanced equations are written with smallest whole-number coefficients. If there is no coefficient before a chemical formula, the coefficient 1 is understood.
=== General Concept ===
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 exist, 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.
The system is in unstable equilibrium if both the inputs and outputs of the comparator are at zero volts. The moment any sort of noise, be it thermal or [[Electromagnetic radiation|electromagnetic]] [[noise]] brings the output of the comparator above zero (the case of the comparator output going below zero is also possible, and a similar argument to what follows applies), the positive feedback in the comparator results in the output of the comparator saturating at the positive rail.
In other words, because the output of the comparator is now positive, the non-inverting input to the comparator is also positive, and continues to increase as the output increases, due to the [[voltage divider]]. After a short time, the output of the comparator is the positive voltage rail, <math>V_{DD}</math>.
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>:
The inverting input and the output of the comparator are linked by a [[Series and parallel circuits#Series_circuits|series]] [[RC circuit]]. Because of this, the inverting input of the comparator asymptotically approaches the comparator output voltage with a [[time constant]] RC. At the point where voltage at the inverting input is greater than the non-inverting input, the output of the comparator falls quickly due to positive feedback.
Since there is one carbon on each side of the arrow, the first atom (carbon) is balanced.
This is because the non-inverting input is less than the inverting input, and as the output continues to decrease, the difference between the inputs gets more and more negative. Again, the inverting input approaches the comparator's output voltage asymptotically, and the cycle repeats itself once the non-inverting input is greater than the inverting input, hence the system oscillates.
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:
=== Example: Differential Equation Analysis of comparator-based Relaxation Oscillator ===
[[Image:opamprelaxationoscillator.svg|thumb|300px|Transient analysis of a comparator-based relaxation oscillator.]]
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:
<math>\, \! V_+</math> is set by <math>\, \! V_{out}</math> across a resistive [[voltage divider]]:
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:
In this reaction, the Ca<sup>2+</sup> and the NO<sub>3</sub><sup>−</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. The net ionic equation of the proceeding reactions is:
Notice there are two solutions to the differential equation, the driven or particular solution and the homogeneous solution. Solving for the driven solution, observe that for this particular form, the solution is a constant. In other words, <math>\, \! V_-=A</math> where A is a constant and <math>\frac{dV_-}{dt}=0</math>.
Using the [[Laplace transform]] to solve the [[Homogeneous polynomial|homogeneous equation]] <math>\frac{dV_-}{dt}+\frac{V_-}{RC}=0</math> results in
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.
If every ion is a "spectator ion" then there was no reaction, and the net ionic equation is null.
Solving for B requires evaluation of the initial conditions. At time 0, <math>V_{out}=V_{dd}</math> and <math>\, \! V_-=0</math>. Substituting into our previous equation,
==References==
:<math>\, \! 0=V_{dd}+B</math>
:<math>\, \! B=-V_{dd}</math>
==== Frequency of Oscillation ====
First let's assume that <math>V_{dd} = -V_{ss}</math> for ease of calculation. Ignoring the initial charge up of the capacitor, which is irrelevant for calculations of the frequency, note that charges and discharges oscillate between <math>\frac{V_{dd}}{2}</math> and <math>\frac{V_{ss}}{2}</math>. For the circuit above, V<sub>ss</sub> must be less than 0. Half of the period (T) is the same as time that <math>V_{out}</math> switches from V<sub>dd</sub>. This occurs when V<sub>-</sub> charges up from <math>-\frac{V_{dd}}{2}</math> to <math>\frac{V_{dd}}{2}</math>.
When V<sub>ss</sub> is not the inverse of V<sub>dd</sub> we need to worry about asymmetric charge up and discharge times. Taking this into account we end up with a formula of the form:
Which reduces to the above result in the case that <math>V_{dd} = -V_{ss}</math>.
== Practical examples of the use of the relaxation oscillator ==
This type of circuit was used as the [[time base]] in early [[oscilloscope]]s and television receivers. Variants of this circuit find use in [[stroboscope]]s used in machine shops and nightclubs. Electronic camera flashes are a monostable version of this circuit, generating ''one cycle'' of the sawtooth. The rising edge develops as the flash capacitor is charged, and the rapid falling edge as the capacitor is discharged. The flash is produced upon receiving the firing signal from the shutter button.
Use as a timebase in oscilloscopes was discontinued when the much more linear [[Miller Integrator]] timebase circuit (invented by [[Alan Blumlein]]), using "hard" valves (vacuum tubes) as a constant current source, was developed.
<ref>Book: Time Bases, by Owen Standige Puckle, ca. 1946</ref>
== See also ==
* [[Multivibrator]]
* [[FitzHugh–Nagumo model]] – A hysteretic model of, for example, a neuron.
* [[Schmitt trigger]] – The circuit on which the comparator-based relaxation oscillator is based.
* [[Unijunction transistor]] A transistor capable of relaxation oscillations.
* [[Robert Kearns]] – Used relaxation oscillator in intermittent wiper patent dispute.
* [[stable limit cycle]] – a more abstract concept; a relaxation oscillator has a stable limit cycle
* [[FitzHugh–Nagumo model]] – A hysteretic model of, for example, a pokémon.
A chemical equation consists of the chemical formulas 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 (, 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:
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 H2. 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 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 law of conservation of mass and the law of conservation of charge (see "Balancing Chemical Equation" section below for more information).
Common symbols
Symbols are used to differentiate between different types of reactions. To denote the type of reaction:[1]
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 () is put on the reaction arrow to show that energy in the form of heat is added to the reaction. is used if the energy is added in the form of light.
Balancing chemical equations
As seen from the equation Template:Chem + 2 Template:Chem → Template:Chem + 2 Template:Chem, a coefficient of 2 must be placed before the oxygen gas on the reactants side and before the 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
The law of conservation of mass dictates that the quantity of each 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 written with smallest whole-number coefficients. If there is no coefficient before a chemical formula, the coefficient 1 is understood.
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 fractional coefficient exist, 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 CH4:
1 CH4 + O2 → CO2 + H2O
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 H2O, which yields:
1 CH4 + O2 → CO2 + 2 H2O
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 O2, giving the balanced equation:
CH4 + 2 O2 → CO2 + 2 H2O
This equation does not have any coefficients in front of CH4 and CO2, since a coefficient of 1 is dropped.
In this reaction, the Ca2+ and the NO3− 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 ions. A net ionic equation is the full ionic equation from which the spectator ions have been removed. The net ionic equation of the proceeding reactions is:
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.
Double displacement reactions that feature a carbonate reacting with an acid have the net ionic equation:
2 H+(aq) + CO32−(aq) → H2O(l) + CO2(g)
If every ion is a "spectator ion" then there was no reaction, and the net ionic equation is null.
References
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↑ 1.01.1IUPAC. Compendium of Chemical Terminology, 2nd ed. ISBN 0-9678550-9-8.
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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
