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The boiling point of an element or a substance is the temperature at which the vapor pressure of the liquid
equals the environmental pressure surrounding the liquid.[1][2]
A liquid in a vacuum environment has a lower boiling point than when the liquid is at atmospheric
pressure. A liquid in a high pressure environment has a higher boiling point than when the liquid is at
atmospheric pressure. In other words, the boiling point of a liquid varies dependent upon the surrounding
environmental pressure (which tends to vary with elevation). Different liquids (at a given pressure) boil at
different temperatures.
The normal boiling point (also called the atmospheric boiling point or the atmospheric pressure boiling
point) of a liquid is the special case in which the vapor pressure of the liquid equals the defined
atmospheric pressure at sea level, 1 atmosphere.[3][4] At that temperature, the vapor pressure of the liquid
becomes sufficient to overcome atmospheric pressure and lift the liquid to form bubbles inside the bulk of
the liquid. The standard boiling point is now (as of 1982) defined by IUPAC as the temperature at which
boiling occurs under a pressure of 1 bar.[5] The heat of vaporization is the amount of energy required to
convert or vaporize a saturated liquid (i.e., a liquid at its boiling point) into a vapor. Liquids may change to
a vapor at temperatures below their boiling points through the process of evaporation. Evaporation is a
surface phenomenon in which molecules located near the liquid's edge, not contained by enough liquid
pressure on that side, escape into the surroundings as vapor. On the other hand, boiling is a process in
which molecules anywhere in the liquid escape, resulting in the formation of vapor bubbles within the
liquid.
A saturated liquid contains as much thermal energy as it can without boiling (or conversely a saturated
vapor contains as little thermal energy as it can without condensing).
Saturation temperature means boiling point. The saturation temperature is the temperature for a
corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be
saturated with thermal energy. Any addition of thermal energy results in a phase transition.
If the pressure in a system remains constant (isobaric), a vapor at saturation temperature will begin to
condense into its liquid phase as thermal energy (heat) is removed. Similarly, a liquid at saturation
temperature and pressure will boil into its vapor phase as additional thermal energy is applied.
The boiling point corresponds to the temperature at which the vapor pressure of the liquid equals the
surrounding environmental pressure. Thus, the boiling point is dependent on the pressure. Usually,
boiling points are published with respect to atmospheric pressure (101.325 kilopascals or 1 atm). At
higher elevations, where the atmospheric pressure is much lower, the boiling point is also lower. The
boiling point increases with increased pressure up to the critical point, where the gas and liquid properties
become identical. The boiling point cannot be increased beyond the critical point. Likewise, the boiling
point decreases with decreasing pressure until the triple point is reached. The boiling point cannot be
reduced below the triple point.
If the heat of vaporization and the vapor pressure of a liquid at a certain temperature is known, the normal
boiling point can be calculated by using the Clausius-Clapeyron equation thus:
Saturation pressure is the pressure for a corresponding saturation temperature at which a liquid boils
into its vapor phase. Saturation pressure and saturation temperature have a direct relationship: as
saturation pressure is increased so is saturation temperature.
If the temperature in a system remains constant (an isothermal system), vapor at saturation pressure and
temperature will begin to condense into its liquid phase as the system pressure is increased. Similarly, a
liquid at saturation pressure and temperature will tend to flash into its vapor phase as system pressure is
decreased.
The boiling point of water is 100 °C (212 °F) at standard pressure. On top of Mount Everest, at 8,848 m
elevation, the pressure is about 260 mbar (26.39 kPa) and the boiling point of water is 69 °C. (156.2 °F).
The boiling point decreases 1 °C every 285 m of elevation.
For purists, the normal boiling point of water is 99.97 degrees Celsius at a pressure of 1 atm (i.e., 101.325
kPa). Until 1982 this was also the standard boiling point of water, but the IUPAC now recommends a
standard pressure of 1 bar (100 kPa). At this slightly reduced pressure, the standard boiling point of
water is 99.61 degrees Celsius.
The higher the vapor pressure of a liquid at a given temperature, the lower the normal boiling point (i.e.,
the boiling point at atmospheric pressure) of the liquid.
The vapor pressure chart to the right has graphs of the vapor pressures versus temperatures for a variety
of liquids.[6] As can be seen in the chart, the liquids with the highest vapor pressures have the lowest
normal boiling points.
For example, at any given temperature, propane has the highest vapor pressure of any of the liquids in
the chart. It also has the lowest normal boiling point(-42.1 °C), which is where the vapor pressure curve of
propane (the purple line) intersects the horizontal pressure line of one atmosphere (atm) of absolute
vapor pressure.
The melting point of a solid is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends (usually slightly) on pressure and is usually specified at standard atmospheric pressure. When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point or crystallization point. Because of the ability of some substances to supercool, the freezing point is not considered as a characteristic property of a substance. When the "characteristic freezing point" of a substance is determined, in fact the actual methodology is almost always "the principle of observing the disappearance rather than the formation of ice", that is, the melting point.[1] For most
substances, melting and freezing points are approximately equal. For example, the melting point and freezing point of the element mercury is 234.32 kelvins(−38.83 °C or −37.89 °F). However, certain substances possess differing solid-liquid transition temperatures. For example, agar melts at 85 °C (185 °F) and solidifies from 31 °C to 40 °C (89.6 °F to 104 °F); this process is known as hysteresis.
The melting point of ice at 1 atmosphere of pressure is very close [2] to 0 °C (32 °F, 273.15 K), this is also
known as the ice point. In the presence of nucleating substances the freezing point of water is the same
as the melting point, but in the absence of nucleators water can supercool to −42 °C (−43.6 °F, 231 K)
before freezing.
The chemical element with the highest melting point is tungsten, at 3683 K (3410 °C, 6170 °F) making it
excellent for use as filaments in light bulbs. The often-cited carbon does not melt at ambient pressure
but sublimes at about 4000 K; a liquid phase only exists above pressures of 10 MPa and estimated 4300–
4700 K. Tantalum hafnium carbide (Ta4HfC5) is a refractory compound with a very high melting point of
4488 K (4215 °C, 7619 °F).[3] At the other end of the scale, helium does not freeze at all at normal
pressure, even at temperatures very close to absolute zero; pressures over 20 times normal atmospheric
pressure are necessary.
The steps to naming an organic compound are:
1. Identify the parent hydrocarbon chain. This chain must follow the following rules, in order of
precedence:
1. It should have maximum substituent’s of the suffix functional group. By suffix, it is meant
that the parent functional group should have a suffix, unlike halogen substituent’s. If
more than one functional group is present, use the one with highest precedence as
shown here.
2. It should have maximum number of multiple bonds.
3. It should have maximum number of carbons (Side chains included).
4. It should have the maximum length.
5. It should have maximum number of double bonds.
2. Identify the parent functional group, if any, with the highest order of precedence.
3. Identify the side-chains. Side chains are the carbon chains that are not in the parent chain, but
are branched off from it.
4. Identify the remaining functional groups, if any, and name them by the name of their ions (such as
hydroxy for -OH, oxy for =O , oxyalkane for O-R, etc.).
Different side-chains and functional groups will be grouped together in alphabetical order. (The
prefixes di-, tri-, etc. are not taken into consideration for grouping alphabetically. For example,
ethyl comes before dihydroxy or dimethyl, as the "e" in "ethyl" precedes the "h" in "dihydroxy"
and the "m" in "dimethyl" alphabetically. The "di" is not considered in either case). In the case of
there being both side chains and secondary functional groups, they should be written mixed
together in one group rather than in two separate groups.
5. Identify double/triple bonds.
6. Number the chain. To number the chain, first number in both directions (left to right and right to
left), and then choose the numbering which follows these rules, in order of precedence:
1. Has the lowest locant (or locants) for the suffix functional group. Locants are the numbers
on the carbons to which the substituent is directly attached.
2. Has the lowest locants for multiple bonds (The locant of a multiple bond is the number of
the adjacent carbon with a lower number).
3. Has the lowest locants for double bonds
7. Has the lowest locants for prefixes.
8. Number the various substituents and bonds with their locants. If there is more than one of the
same type of substituent/double bond, add the prefix (di-, tri-, etc.) before it. The numbers for that
type of side chain will be grouped in ascending order and written before the name of the side-
chain. If there are two side-chains with the same alpha carbon, the number will be written twice.
Example: 2,2,3-trimethyl- . If there are both double bonds and triple bonds, write the "ene" before
the "yne". In case the main functional group is a terminal functional group (A group which can
only exist at the end of a chain, like formyl and carboxyl groups), there is no need to number it.
9. Arrange everything like this: Group of side chains and secondary functional groups with
numbers made in step 3 + prefix of parent hydrocarbon chain (eth, meth) + double/triple
bonds with numbers (or "ane") + primary functional group suffix with numbers.
Wherever it says "with numbers", it is understood that between the word and the
numbers, you use the prefix(di-, tri-)
1. Add punctuation:
2. Put commas between numbers (2 5 5 becomes 2,5,5)
3. Put a hyphen between a number and a letter (2 5 5 trimethylheptane becomes 2,5,5-
trimethylheptane)
4. Successive words are merged into one word (trimethyl heptane becomes
trimethylheptane)
Note: IUPAC uses one-word names throughout. This is why all parts are connected.
Many laboratory techniques exist for the determination of melting points. A Kofler bench is a metal strip
with a temperature gradient (range from room temperature to 300 °C). Any substance can be placed on a
section of the strip revealing its thermal behaviour at the temperature at that point. Differential scanning
calorimetry gives information on melting point together with its enthalpy of fusion.
A basic melting point apparatus for the analysis of crystalline solids consists of a oil bath with a transparent window (most basic design: a Thiele tube) and a simple magnifier. The several grains of a solid are placed in a thin glass tube and partially immersed in the oil bath. The oil bath is heated (and stirred) and with the aid of the magnifier (and external light source) melting of the individual crystals at a certain temperature can be observed. In large/small devices, the sample is placed in a heating block, and optical detection is automated.
The measurement can also be made continuously with an operating process. For instance, oil refineries
measure the freeze point of diesel fuel online, meaning that the sample is taken from the process and
measured automatically. This allows for more frequent measurements as the sample does not have to be
manually collected and taken to a remote laboratory. With alcohols, hydrogen cyanide, hydrogen chloride,
or carboxylic acids to give vinyl compounds
1,4-Butynediol is produced industrially in this way from formaldehyde and acetylene.
With carbon monoxide to give acrylic acid, or acrylic esters, which can be used to produce acrylic glass.
in Gibbs free energy (ΔG) of the material is zero, but the enthalpy (H) and the entropy (S) of the material
are increasing (ΔH, ΔS > 0</math>). Melting phenomenon happens when the Gibbs free energy of the
liquid becomes lower than the solid for that material. At various pressures this happens at a specific
temperature. It can also be shown that:
Here T, S and ΔH are respectively the temperature at the melting point, change of entropy of melting and
the change of enthalpy of melting.
Unlike the boiling point, the melting point is relatively insensitive to moderate changes
in pressure because the solid/liquid transition represents only a small change in volume.[4][5] If, as
observed in most cases, a substance is more dense in the solid than in the liquid state, the melting point
will increase with increases in pressure. Otherwise the reverse behavior occurs. Notably, this is the case
of water, as illustrated graphically to the right, but also of Si, Ge, Ga, Bi. With extremely large changes in
pressure, substantial changes to the melting point are observed. For example, the melting point of silicon
at ambient pressure (0.1 MPa) is 1415 °C, but at pressures in excess of 10 GPa it decreases to 1000 °C.
[6] Melting points are often used to characterize organic and inorganic compounds and to ascertain
their purity. The melting point of a pure substance is always higher and has a smaller range than the
melting point of an impure substance or, more generally, of mixtures. The higher the quantity of other
components, the lower the melting point and the broader will be the melting point range, often referred to
as the pasty range. The temperature at which melting begins for a mixture is known as the solidus while
the temperature where melting is complete is called the liquidus. Eutectics are special types of mixtures
that behave like single phases. They melt sharply at a constant temperature to form a liquid of the same
composition. Alternatively, on cooling a liquid with the eutectic composition will solidify as uniformly
dispersed, small (fine-grained) mixed crystals with the same composition.
In contrast to crystalline solids, glasses do not possess a melting point; on heating they undergo a
smooth glass transition into a viscous liquid. Upon further heating, they gradually soften, which can be
characterized by certain softening points.
The freezing point of a solvent is depressed when another compound is added, meaning that
a solution has a lower freezing point than a pure solvent. This phenomenon is used in technical
applications to avoid freezing, for instance by adding salt or ethylene glycol to water.
In organic chemistry Carnelley’s Rule, established in 1882 by Thomas Carnelley, stated
that high molecular symmetry is associated with high melting point.[7] Carnelley based his rule on
examination of 15,000 chemical compounds. For example for three structural isomers with molecular
formula C5H12 the melting point increases in the series isopentane −160 °C (113 K) n-pentane −129.8 °C
(143 K) and neopentane −18 °C (255 K). Likewise in xylenes and also dichlorobenzenes[disambiguation
needed] the melting point increases in the order meta, ortho and then para. Pyridine has a lower symmetry
than benzene hence its lower melting point but the melting point again
increases.with diazine and triazines. Many cage-like compounds like adamantane and cubane with high
symmetry have very high melting points. A high melting point results from a high heat of fusion, a
low entropy of fusion, or a combination of both. In highly symmetrical molecules the crystal phase is
densely packed with many efficient intermolecular interactions resulting in a higher enthalpy change on
melting.
An attempt to predict the bulk melting point of crystalline materials was first made in 1910 by Frederick
Lindemann.[8] The idea behind the theory was the observation that the average amplitude of thermal
vibrations increase with increasing temperature. Melting initiates when the amplitude of vibration becomes
large enough for adjacent atoms to partly occupy the same space. The Lindemann criterion states that
melting is expected when the root mean square vibration amplitude exceeds a threshold value. Assuming
that all atoms in a crystal vibrate with the same frequency ν, the average thermal energy can be
estimated using the equipartition theorem as[9]
where m is the atomic mass, ν is the frequency, u is the average vibration amplitude, kB is
the Boltzmann constant, and T is the absolute temperature. If the threshold value
of u2 is c2a2 where c is the Lindemann constant and a is the atomic spacing, then the melting point is
estimated as
Several other expressions for the estimated melting temperature can be obtained depending on
the estimate of the average thermal energy. Another commonly used expression for the
Lindemann criterion is[10]
From the expression for the Debye frequency for ν, we have
where θD is the Debye temperature and h is the Planck constant. Values of c range from
0.15–0.3 for most materials.[11
The liquidus temperature, TL or Tliq, is mostly used for glasses, alloys and rocks. It specifies the maximum
temperature at which crystals can co-exist with the melt in thermodynamic equilibrium. Above the liquidus
temperature the material is homogeneous. Below the liquidus temperature more and more crystals begin
to form in the melt if one waits a sufficiently long time, depending on the material. However, even below
the liquidus temperature homogeneous glasses can be obtained through sufficiently fast cooling, i.e.,
through kinetic inhibition of the crystallization process.
The crystal phase that crystallizes first on cooling a substance to its liquidus temperature is
termed primary crystalline phase or primary phase. The composition range within which the primary
phase remains constant is known as primary crystalline phase field.
The liquidus temperature is important in the glass industry because crystallization can cause severe
problems during the glass melting and forming processes, and it also may lead to product failure.
The liquidus temperature can be contrasted to the solidus temperature. The solidus temperature
quantifies the point at which a material completely solidifies (crystallizes). The liquidus and solidus
temperatures do not necessarily align or overlap; if a gap exists between the liquidus and solidus
temperatures, then within that gap, the material consists of solid and liquid phases simultaneously (like a
"slurry").
Stoichiometry ( / ̩ s t ɔɪ k i ̍ ɒ m ɨ t r i / ) is a branch of chemistry that deals with the relative quantities
of reactants and products in chemical reactions. In a balanced chemical reaction, the relations among
quantities of reactants and products typically form a ratio of whole numbers. For example, in a reaction
that forms ammonia (NH3), exactly one molecule of nitrogen (N2) reacts with three molecules of hydrogen
(H2) to produce two molecules of NH3:
N2 + 3H2 → 2NH3
Stoichiometry can be used to calculate quantities such as the amount of products (in mass, moles,
volume, etc.) that can be produced with given reactants and percent yield (the percentage of the
given reactant that is made into the product). Stoichiometry calculations can predict how elements
and components diluted in a standard solution react in experimental conditions. Stoichiometry is
founded on the law of conservation of mass: the mass of the reactants equals the mass of the
products.
Reaction stoichiometry describes the quantitative relationships among substances as they participate
in chemical reactions. In the example above, reaction stoichiometry describes the 1:3:2 ratio of
molecules of nitrogen, hydrogen, and ammonia.
Composition stoichiometry describes the quantitative (mass) relationships among elements in
compounds. For example, composition stoichiometry describes the nitrogen to hydrogen (mass)
relationship in the compound ammonia: i.e., one mole of nitrogen and three moles of hydrogen are in
every mole of ammonia.
A stoichiometric amount or stoichiometric ratio of a reagent is the amount or ratio where, assuming that
the reaction proceeds to completion:
1. all reagent is consumed,
2. there is no shortfall of reagent, and
3. no residues remain.
A nonstoichiometric mixture, where reactions have gone to completion, will have only the limiting
reagent consumed completely.
While almost all reactions have integer-ratio stoichiometry in amount of matter units (moles, number of
particles), some nonstoichiometric compounds are known that cannot be represented by a ratio of well-
defined natural numbers. These materials therefore violate the law of definite proportions that forms the
basis of stoichiometry along with the law of multiple proportions.
Gas stoichiometry deals with reactions involving gases, where the gases are at a known temperature,
pressure, and volume, and can be assumed to be ideal gases. For gases, the volume ratio is ideally
the same by the ideal gas law, but the mass ratio of a single reaction has to be calculated from
the molecular masses of the reactants and products. In practice, due to the existence
of isotopes, molar masses are used instead when calculating the mass ratio.
"Stoichiometry" is derived from the Greek words στοιχεῖον (stoicheion, meaning element]) and μέτρον (metron, meaning measure.) In patristic Greek, the word Stoichiometria was used by Nicephorus to refer to the number of line counts of the canonical New Testament and some of the Apocrypha.
Stoichiometry rests upon the law of conservation of mass, the law of definite proportions (i.e., the law of
constant composition) and the law of multiple proportions. In general, chemical reactions combine in
definite ratios of chemicals. Since chemical reactions can neither create nor destroy matter,
nor transmute one element into another, the amount of each element must be the same throughout the
overall reaction. For example, the amount of element X on the reactant side must equal the amount of
element X on the product side.
Stoichiometry is often used to balance chemical equations (reaction stoichiometry). For example, the
two diatomic gases, hydrogen and oxygen, can combine to form a liquid, water, in an exothermic reaction,
as described by the following equation:
Reaction stoichiometry describes the 2:1:2 ratio of hydrogen, oxygen, and water molecules in the
above equation.
The term stoichiometry is also often used for the molar proportions of elements in stoichiometric
compounds (composition stoichiometry). For example, the stoichiometry of hydrogen and oxygen
in H2O is 2:1. In stoichiometric compounds, the molar proportions are whole numbers.
Stoichiometry is not only used to balance chemical equations but also used in conversions, i.e.,
converting from grams to moles, or from grams to millilitres. For example, to find the number of moles
in 2.00 g of NaCl, one would do the following:
In the above example, when written out in fraction form, the units of grams form a multiplicative
identity, which is equivalent to one (g/g=1), with the resulting amount of moles (the unit that was
needed), is shown in the following equation,
Stoichiometry is also used to find the right amount of reactants to use in a chemical
reaction (stoichiometric amounts). An example is shown below using the thermite reaction,
This equation shows that 1 mole of aluminium oxide and 2 moles of iron will be
produced with 1 mole of iron(III) oxide and 2 moles of aluminium. So, to completely
react with 85.0 g of iron(III) oxide (0.532 mol), 28.7 g (1.06 mol) of aluminium are
needed.
[edit]Different stoichiometries in competing reactions
Often, more than one reaction is possible given the same starting materials. The
reactions may differ in their stoichiometry. For example,
the methylation of benzene (C6H6), through a Friedel-Crafts reaction usingAlCl3 as
catalyst, may produce singly methylated (C6H5CH3), doubly
methylated (C6H4(CH3)2), or still more highly methylated
products, as shown in the following example,
In this example, which reaction takes place is controlled in part by the relative concentrations of the
reactants.
[edit]Stoichiometric coefficient
In layman's terms, the stoichiometric coefficient (or stoichiometric number in the IUPAC nomenclature[1])
of any given component is the number of molecules which participate in the reaction as written.
For example, in the reaction CH4 + 2 O2 → CO2 + 2 H2O, the stoichiometric coefficient of CH4 would be 1
and the stoichiometric coefficient of O2 would be 2.
In more technically-precise terms, the stoichiometric coefficient in a chemical reaction system of the i–
th component is defined as
or
where Ni is the number of molecules of i, and ξ is the progress variable or extent of reaction (Prigogine
& Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37 & 62).
The extent of reaction ξ can be regarded as a real (or hypothetical) product, one molecule of which is
produced each time the reaction event occurs. It is the extensive quantity describing the progress of a
chemical reaction equal to the number of chemical transformations, as indicated by the reaction equation
on a molecular scale, divided by the Avogadro constant (it is essentially the amount of chemical
transformations). The change in the extent of reaction is given by dξ = dnB/nB, where nB is the
stoichiometric number of any reaction entity B (reactant or product) an dnB is the corresponding amount.[2]
The stoichiometric coefficient νi represents the degree to which a chemical species participates in a
reaction. The convention is to assign negative coefficients to reactants (which are consumed) and positive
ones to products. However, any reaction may be viewed as "going" in the reverse direction, and all the
coefficients then change sign (as does the free energy). Whether a reaction actually will go in the
arbitrarily-selected forward direction or not depends on the amounts of the substances present at any
given time, which determines the kinetics and thermodynamics, i.e., whether equilibrium lies to
the right or the left.
If one contemplates actual reaction mechanisms, stoichiometric coefficients will always be integers, since
elementary reactions always involve whole molecules. If one uses a composite representation of an
"overall" reaction, some may be rational fractions. There are often chemical species present that do not
participate in a reaction; their stoichiometric coefficients are therefore zero. Any chemical species that is
regenerated, such as a catalyst, also has a stoichiometric coefficient of zero.
The simplest possible case is an isomerism
in which νB = 1 since one molecule of B is produced each time the reaction occurs, while νA = −1 since
one molecule of A is necessarily consumed. In any chemical reaction, not only is the total mass
conserved, but also the numbers of atoms of each kind are conserved, and this imposes corresponding
constraints on possible values for the stoichiometric coefficients.
There are usually multiple reactions proceeding simultaneously in any natural reaction system, including those in biology. Since any chemical component can participate in several reactions simultaneously, the stoichiometric coefficient of the i–th component in the k–th reaction is defined as
so that the total (differential) change in the amount of the i–th component is
Extents of reaction provide the clearest and most explicit way of representing compositional change,
although they are not yet widely used.
With complex reaction systems, it is often useful to consider both the representation of a reaction system
in terms of the amounts of the chemicals present { Ni } (state variables), and the representation in terms
of the actual compositional degrees of freedom, as expressed by the extents of reaction { ξk }. The
transformation from a vector expressing the extents to a vector expressing the amounts uses a
rectangular matrix whose elements are the stoichiometric coefficients [ νi k ].
The maximum and minimum for any ξk occur whenever the first of the reactants is depleted for the
forward reaction; or the first of the "products" is depleted if the reaction as viewed as being pushed in the
reverse direction. This is a purely kinematic restriction on the reaction simplex, a hyperplane in
composition space, or N-space, whose dimensionality equals the number of linearly-
independent chemical reactions. This is necessarily less than the number of chemical components, since
each reaction manifests a relation between at least two chemicals. The accessible region of the
hyperplane depends on the amounts of each chemical species actually present, a contingent fact.
Different such amounts can even generate different hyperplanes, all of which share the same algebraic
stoichiometry.
In accord with the principles of chemical kinetics and thermodynamic equilibrium, every chemical reaction
is reversible, at least to some degree, so that each equilibrium point must be an interior point of the
simplex. As a consequence, extrema for the ξ's will not occur unless an experimental system is prepared
with zero initial amounts of some products.
The number of physically-independent reactions can be even greater than the number of chemical
components, and depends on the various reaction mechanisms. For example, there may be two (or more)
reactionpaths for the isomerism above. The reaction may occur by itself, but faster and with different
intermediates, in the presence of a catalyst. The (dimensionless) "units" may be taken to
be molecules or moles. Moles are most commonly used, but it is more suggestive to picture incremental
chemical reactions in terms of molecules. The N's and ξ's are reduced to molar units by dividing
by Avogadro's number. While dimensional mass units may be used, the comments about integers are
then no longer applicable.
[edit]Stoichiometry matrix
In complex reactions, stoichiometries are often represented in a more compact form called the
stoichiometry matrix. The stoichiometry matrix is denoted by the symbol, .
If a reaction network has n reactions and m participating molecular species then the stoichiometry matrix
will have corresponding m rows and n columns.
For example, consider the system of reactions shown below:
S1 → S2
5S3 + S2 → 4S3 + 2S2
S3 → S4
S4 → S5.
This systems comprises fourreactions and five different molecular species. The stoichiometry matrix for
this system can be written as:
where the rows correspond to S1, S2, S3, S4 and S5, respectively. Note that the process of converting a
reaction scheme into a stoichiometry matrix can be a lossy transformation, for example, the
stoichiometries in the second reaction simplify when included in the matrix. This means that it is not
always possible to recover the original reaction scheme from a stoichiometry matrix.
Often the stoichiometry matrix is combined with the rate vector, v to form a compact equation describing
the rates of change of the molecular species:
[edit]Gas stoichiometry---- wrist band/transformer
Gas stoichiometry is the quantitative relationship (ratio) between reactants and products in a chemical
reaction with reactions that produce gases. Gas stoichiometry applies when the gases produced are
assumed to be ideal, and the temperature, pressure, and volume of the gases are all known. The ideal
gas law is used for these calculations. Often, but not always, the standard temperature and
pressure (STP) are taken as 0°C and 1 bar and used as the conditions for gas stoichiometric calculations.
Gas stoichiometry calculations solve for the unknown volume or mass of a gaseous product or reactant.
For example, if we wanted to calculate the volume of gaseous NO2 produced from the combustion of 100
g of NH3, by the reaction:
4NH3 (g) + 7O2 (g) → 4NO2 (g) + 6H2O (l)
Developing a strategy can be difficult, but here is one way of approaching a problem like this.
1. Count the number of each atom on the reactant and on the product side. 2. Determine a term to balance first. When looking at this problem, it appears that the oxygen will be
the most difficult to balance so we'll try to balance the oxygen first. The simplest way to balance the oxygen terms is:
Al + 3 Fe3O4---> 4 Al2O3+ Fe
Be sure to notice that the subscript times the coefficient will give the number of atoms of that element. On the reactant side, we have a coefficient of three (3) multiplied by a subscript of four (4), giving 12 oxygen atoms. On the product side, we have a coefficient of four (4) multiplied by a subscript of three (3), giving 12 oxygen atoms. Now, the oxygens are balanced.
3. Choose another term to balance. We'll choose iron, Fe. Since there are nine (9) iron atoms in the term in which the oxygen is balanced we add a nine (9) coefficient in front of the Fe. We now have:
Al +3 Fe3O4---> 4Al2O3+ 9Fe
4. Balance the last term. In this case, since we had eight (8) aluminum atoms on the product side we need to have eight (8) on the reactant side so we add an eight (8) in front of the Al term on the reactant side. Now, we're done, and the balanced equation is:
5. Sometimes when reactions occur between two or more substances, one reactant runs out before the other. That is called the "limiting reagent". Often, it is necessary to identify the limiting reagent in a problem. Example: A chemist only has 6.0 grams of C2H2 and an unlimited supply of oxygen and he desires to produce as much CO2 as possible. If she uses the equation below, how much oxygen should she add to the reaction?
6. 2C2H2(g) + 5O2(g) ---> 4CO2(g) + 2 H2O(l)7. To solve this problem, it is necessary to determine how much oxygen should be added if all of the
reactants were used up (this is the way to produce the maximum amount of CO2). First, we calculate the number of moles of C2H2 in 6.0 g of C2H2. To be able to calculate the moles we need to look at a periodic table and see that 1 mole of C weighs 12.0 g and H weighs 1.0 g. Therefore we know that 1 mole of C2H2 weighs 26 g (2 × 12 grams + 2 × 1 gram).
6.0 g C2H2 x1 mol C2H2
(24.0 + 2.0)g C2H2
= 0.25 mol C2H2
8. Then, because there are five (5) molecules of oxygen to every two (2) molecules of C2H2, we need to multiply the result by 5/2 to get the total molecules of oxygen. Then we convert to grams to find the amount of oxygen that needs to be added:
0.25 mol C2H2 x5 mol O2
2 mol C2H2
x32.0 g O2
1 mol O2
= 20 g O2
The disiloxane and the TMEDA are positioned on crystallographically independent inversion centres. The disiloxane linkage is linear and the OH groups are anti. The Si-O bonds in the siloxane linkage and the silanol groups are 1.602(2) and 1.599(4) Å respectively. The silanol and the amine molecules are linked via OH...N hydrogen bonds (O...N, H...N, 2.73 and 1.84 Å, OH...N, 169 [ring]) to form a polymer chain in the crystallographic 1 bar1 0 direction. There are small distortions from optimal tetrahedral geometry at silicon, with angles ranging between 105.8(2) and 112.8(2) [ring].
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