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Analysis of variance | 634 | Generalizations | Below we make clear the connection between multi-way ANOVA and linear regression. |
Analysis of variance | 634 | Generalizations | Linearly re-order the data so that k {\displaystyle k} -th observation is associated with a response y k {\displaystyle y_{k}} and factors Z k , b {\displaystyle Z_{k,b}} where b ∈ { 1 , 2 , … , B } {\displaystyle b\in \{1,2,\ldots ,B\}} denotes the different factors and B {\displaystyle B} is the total number of factors. In one-way ANOVA B = 1 {\displaystyle B=1} and in two-way ANOVA B = 2 {\displaystyle B=2} . Furthermore, we assume the b {\displaystyle b} -th factor has I b {\displaystyle I_{b}} levels, namely { 1 , 2 , … , I b } {\displaystyle \{1,2,\ldots ,I_{b}\}} . Now, we can one-hot encode the factors into the ∑ b = 1 B I b {\textstyle \sum _{b=1}^{B}I_{b}} dimensional vector v k {\displaystyle v_{k}} . |
Analysis of variance | 634 | Generalizations | The one-hot encoding function g b : { 1 , 2 , … , I b } ↦ { 0 , 1 } I b {\displaystyle g_{b}:\{1,2,\ldots ,I_{b}\}\mapsto \{0,1\}^{I_{b}}} is defined such that the i {\displaystyle i} -th entry of g b ( Z k , b ) {\displaystyle g_{b}(Z_{k,b})} is |
Analysis of variance | 634 | Generalizations | The vector v k {\displaystyle v_{k}} is the concatenation of all of the above vectors for all b {\displaystyle b} . Thus, v k = [ g 1 ( Z k , 1 ) , g 2 ( Z k , 2 ) , … , g B ( Z k , B ) ] {\displaystyle v_{k}=[g_{1}(Z_{k,1}),g_{2}(Z_{k,2}),\ldots ,g_{B}(Z_{k,B})]} . In order to obtain a fully general B {\displaystyle B} -way interaction ANOVA we must also concatenate every additional interaction term in the vector v k {\displaystyle v_{k}} and then add an intercept term. Let that vector be X k {\displaystyle X_{k}} . |
Analysis of variance | 634 | Generalizations | With this notation in place, we now have the exact connection with linear regression. We simply regress response y k {\displaystyle y_{k}} against the vector X k {\displaystyle X_{k}} . However, there is a concern about identifiability. In order to overcome such issues we assume that the sum of the parameters within each set of interactions is equal to zero. From here, one can use F-statistics or other methods to determine the relevance of the individual factors. |
Analysis of variance | 634 | Generalizations | We can consider the 2-way interaction example where we assume that the first factor has 2 levels and the second factor has 3 levels. |
Analysis of variance | 634 | Generalizations | Define a i = 1 {\displaystyle a_{i}=1} if Z k , 1 = i {\displaystyle Z_{k,1}=i} and b i = 1 {\displaystyle b_{i}=1} if Z k , 2 = i {\displaystyle Z_{k,2}=i} , i.e. a {\displaystyle a} is the one-hot encoding of the first factor and b {\displaystyle b} is the one-hot encoding of the second factor. |
Analysis of variance | 634 | Generalizations | With that, |
Analysis of variance | 634 | Generalizations | where the last term is an intercept term. For a more concrete example suppose that |
Analysis of variance | 634 | Generalizations | Then, |
Alkane | 639 | In organic chemistry, an alkane, or paraffin (a historical trivial name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which all the carbon–carbon bonds are single. Alkanes have the general chemical formula CnH2n+2. The alkanes range in complexity from the simplest case of methane (CH4), where n = 1 (sometimes called the parent molecule), to arbitrarily large and complex molecules, like pentacontane (C50H102) or 6-ethyl-2-methyl-5-(1-methylethyl) octane, an isomer of tetradecane (C14H30). |
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Alkane | 639 | The International Union of Pure and Applied Chemistry (IUPAC) defines alkanes as "acyclic branched or unbranched hydrocarbons having the general formula CnH2n+2, and therefore consisting entirely of hydrogen atoms and saturated carbon atoms". However, some sources use the term to denote any saturated hydrocarbon, including those that are either monocyclic (i.e. the cycloalkanes) or polycyclic, despite their having a distinct general formula (i.e. cycloalkanes are CnH2n). |
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Alkane | 639 | In an alkane, each carbon atom is sp-hybridized with 4 sigma bonds (either C–C or C–H), and each hydrogen atom is joined to one of the carbon atoms (in a C–H bond). The longest series of linked carbon atoms in a molecule is known as its carbon skeleton or carbon backbone. The number of carbon atoms may be considered as the size of the alkane. |
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Alkane | 639 | One group of the higher alkanes are waxes, solids at standard ambient temperature and pressure (SATP), for which the number of carbon atoms in the carbon backbone is greater than about 17. With their repeated –CH2 units, the alkanes constitute a homologous series of organic compounds in which the members differ in molecular mass by multiples of 14.03 u (the total mass of each such methylene-bridge unit, which comprises a single carbon atom of mass 12.01 u and two hydrogen atoms of mass ~1.01 u each). |
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Alkane | 639 | Methane is produced by methanogenic bacteria and some long-chain alkanes function as pheromones in certain animal species or as protective waxes in plants and fungi. Nevertheless, most alkanes do not have much biological activity. They can be viewed as molecular trees upon which can be hung the more active/reactive functional groups of biological molecules. |
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Alkane | 639 | The alkanes have two main commercial sources: petroleum (crude oil) and natural gas. |
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Alkane | 639 | An alkyl group is an alkane-based molecular fragment that bears one open valence for bonding. They are generally abbreviated with the symbol for any organyl group, R, although Alk is sometimes used to specifically symbolize an alkyl group (as opposed to an alkenyl group or aryl group). |
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Alkane | 639 | Structure and classification | Ordinarily the C-C single bond distance is 1.53 ångströms (1.53×10 m). Saturated hydrocarbons can be linear, branched, or cyclic. The third group is sometimes called cycloalkanes. Very complicated structures are possible by combining linear, branch, cyclic alkanes. |
Alkane | 639 | Isomerism | Alkanes with more than three carbon atoms can be arranged in various ways, forming structural isomers. The simplest isomer of an alkane is the one in which the carbon atoms are arranged in a single chain with no branches. This isomer is sometimes called the n-isomer (n for "normal", although it is not necessarily the most common). However, the chain of carbon atoms may also be branched at one or more points. The number of possible isomers increases rapidly with the number of carbon atoms. For example, for acyclic alkanes: |
Alkane | 639 | Isomerism | Branched alkanes can be chiral. For example, 3-methylhexane and its higher homologues are chiral due to their stereogenic center at carbon atom number 3. The above list only includes differences of connectivity, not stereochemistry. In addition to the alkane isomers, the chain of carbon atoms may form one or more rings. Such compounds are called cycloalkanes, and are also excluded from the above list because changing the number of rings changes the molecular formula. For example, cyclobutane and methylcyclopropane are isomers of each other (C4H8), but are not isomers of butane (C4H10). |
Alkane | 639 | Isomerism | Branched alkanes are more thermodynamically stable than their linear (or less branched) isomers. For example, the highly branched 2,2,3,3-tetramethylbutane is about 1.9 kcal/mol more stable than its linear isomer, n-octane. |
Alkane | 639 | Nomenclature | The IUPAC nomenclature (systematic way of naming compounds) for alkanes is based on identifying hydrocarbon chains. Unbranched, saturated hydrocarbon chains are named systematically with a Greek numerical prefix denoting the number of carbons and the suffix "-ane". |
Alkane | 639 | Nomenclature | In 1866, August Wilhelm von Hofmann suggested systematizing nomenclature by using the whole sequence of vowels a, e, i, o and u to create suffixes -ane, -ene, -ine (or -yne), -one, -une, for the hydrocarbons CnH2n+2, CnH2n, CnH2n−2, CnH2n−4, CnH2n−6. In modern nomenclature, the first three specifically name hydrocarbons with single, double and triple bonds; while "-one" now represents a ketone. |
Alkane | 639 | Nomenclature | Straight-chain alkanes are sometimes indicated by the prefix "n-" or "n-"(for "normal") where a non-linear isomer exists. Although this is not strictly necessary and is not part of the IUPAC naming system, the usage is still common in cases where one wishes to emphasize or distinguish between the straight-chain and branched-chain isomers, e.g., "n-butane" rather than simply "butane" to differentiate it from isobutane. Alternative names for this group used in the petroleum industry are linear paraffins or n-paraffins. |
Alkane | 639 | Nomenclature | The first eight members of the series (in terms of number of carbon atoms) are named as follows: |
Alkane | 639 | Nomenclature | The first four names were derived from methanol, ether, propionic acid and butyric acid. Alkanes with five or more carbon atoms are named by adding the suffix -ane to the appropriate numerical multiplier prefix with elision of any terminal vowel (-a or -o) from the basic numerical term. Hence, pentane, C5H12; hexane, C6H14; heptane, C7H16; octane, C8H18; etc. The numeral prefix is generally Greek; however, alkanes with a carbon atom count ending in nine, for example nonane, use the Latin prefix non-. |
Alkane | 639 | Nomenclature | Simple branched alkanes often have a common name using a prefix to distinguish them from linear alkanes, for example n-pentane, isopentane, and neopentane. |
Alkane | 639 | Nomenclature | IUPAC naming conventions can be used to produce a systematic name. |
Alkane | 639 | Nomenclature | The key steps in the naming of more complicated branched alkanes are as follows: |
Alkane | 639 | Nomenclature | Though technically distinct from the alkanes, this class of hydrocarbons is referred to by some as the "cyclic alkanes." As their description implies, they contain one or more rings. |
Alkane | 639 | Nomenclature | Simple cycloalkanes have a prefix "cyclo-" to distinguish them from alkanes. Cycloalkanes are named as per their acyclic counterparts with respect to the number of carbon atoms in their backbones, e.g., cyclopentane (C5H10) is a cycloalkane with 5 carbon atoms just like pentane (C5H12), but they are joined up in a five-membered ring. In a similar manner, propane and cyclopropane, butane and cyclobutane, etc. |
Alkane | 639 | Nomenclature | Substituted cycloalkanes are named similarly to substituted alkanes – the cycloalkane ring is stated, and the substituents are according to their position on the ring, with the numbering decided by the Cahn–Ingold–Prelog priority rules. |
Alkane | 639 | Nomenclature | The trivial (non-systematic) name for alkanes is 'paraffins'. Together, alkanes are known as the 'paraffin series'. Trivial names for compounds are usually historical artifacts. They were coined before the development of systematic names, and have been retained due to familiar usage in industry. Cycloalkanes are also called naphthenes. |
Alkane | 639 | Nomenclature | Branched-chain alkanes are called isoparaffins. "Paraffin" is a general term and often does not distinguish between pure compounds and mixtures of isomers, i.e., compounds of the same chemical formula, e.g., pentane and isopentane. |
Alkane | 639 | Nomenclature | The following trivial names are retained in the IUPAC system: |
Alkane | 639 | Nomenclature | Some non-IUPAC trivial names are occasionally used: |
Alkane | 639 | Physical properties | All alkanes are colorless. Alkanes with the lowest molecular weights are gases, those of intermediate molecular weight are liquids, and the heaviest are waxy solids. |
Alkane | 639 | Physical properties | Alkanes experience intermolecular van der Waals forces. The cumulative effects of these intermolecular forces give rise to greater boiling points of alkanes. |
Alkane | 639 | Physical properties | Two factors influence the strength of the van der Waals forces: |
Alkane | 639 | Physical properties | Under standard conditions, from CH4 to C4H10 alkanes are gaseous; from C5H12 to C17H36 they are liquids; and after C18H38 they are solids. As the boiling point of alkanes is primarily determined by weight, it should not be a surprise that the boiling point has an almost linear relationship with the size (molecular weight) of the molecule. As a rule of thumb, the boiling point rises 20–30 °C for each carbon added to the chain; this rule applies to other homologous series. |
Alkane | 639 | Physical properties | A straight-chain alkane will have a boiling point higher than a branched-chain alkane due to the greater surface area in contact, and thus greater van der Waals forces, between adjacent molecules. For example, compare isobutane (2-methylpropane) and n-butane (butane), which boil at −12 and 0 °C, and 2,2-dimethylbutane and 2,3-dimethylbutane which boil at 50 and 58 °C, respectively. |
Alkane | 639 | Physical properties | On the other hand, cycloalkanes tend to have higher boiling points than their linear counterparts due to the locked conformations of the molecules, which give a plane of intermolecular contact. |
Alkane | 639 | Physical properties | The melting points of the alkanes follow a similar trend to boiling points for the same reason as outlined above. That is, (all other things being equal) the larger the molecule the higher the melting point. There is one significant difference between boiling points and melting points. Solids have a more rigid and fixed structure than liquids. This rigid structure requires energy to break down. Thus the better put together solid structures will require more energy to break apart. For alkanes, this can be seen from the graph above (i.e., the blue line). The odd-numbered alkanes have a lower trend in melting points than even-numbered alkanes. This is because even-numbered alkanes pack well in the solid phase, forming a well-organized structure which requires more energy to break apart. The odd-numbered alkanes pack less well and so the "looser"-organized solid packing structure requires less energy to break apart. For a visualization of the crystal structures see. |
Alkane | 639 | Physical properties | The melting points of branched-chain alkanes can be either higher or lower than those of the corresponding straight-chain alkanes, again depending on the ability of the alkane in question to pack well in the solid phase. |
Alkane | 639 | Physical properties | Alkanes do not conduct electricity in any way, nor are they substantially polarized by an electric field. For this reason, they do not form hydrogen bonds and are insoluble in polar solvents such as water. Since the hydrogen bonds between individual water molecules are aligned away from an alkane molecule, the coexistence of an alkane and water leads to an increase in molecular order (a reduction in entropy). As there is no significant bonding between water molecules and alkane molecules, the second law of thermodynamics suggests that this reduction in entropy should be minimized by minimizing the contact between alkane and water: Alkanes are said to be hydrophobic as they are insoluble in water. |
Alkane | 639 | Physical properties | Their solubility in nonpolar solvents is relatively high, a property that is called lipophilicity. Alkanes are, for example, miscible in all proportions among themselves. |
Alkane | 639 | Physical properties | The density of the alkanes usually increases with the number of carbon atoms but remains less than that of water. Hence, alkanes form the upper layer in an alkane–water mixture. |
Alkane | 639 | Physical properties | The molecular structure of the alkanes directly affects their physical and chemical characteristics. It is derived from the electron configuration of carbon, which has four valence electrons. The carbon atoms in alkanes are described as sp hybrids; that is to say that, to a good approximation, the valence electrons are in orbitals directed towards the corners of a tetrahedron which are derived from the combination of the 2s orbital and the three 2p orbitals. Geometrically, the angle between the bonds are cos(−1/3) ≈ 109.47°. This is exact for the case of methane, while larger alkanes containing a combination of C–H and C–C bonds generally have bonds that are within several degrees of this idealized value. |
Alkane | 639 | Physical properties | An alkane has only C–H and C–C single bonds. The former result from the overlap of an sp orbital of carbon with the 1s orbital of a hydrogen; the latter by the overlap of two sp orbitals on adjacent carbon atoms. The bond lengths amount to 1.09 × 10 m for a C–H bond and 1.54 × 10 m for a C–C bond. |
Alkane | 639 | Physical properties | The spatial arrangement of the bonds is similar to that of the four sp orbitals—they are tetrahedrally arranged, with an angle of 109.47° between them. Structural formulae that represent the bonds as being at right angles to one another, while both common and useful, do not accurately depict the geometry. |
Alkane | 639 | Physical properties | The spatial arrangement of the C-C and C-H bonds are described by the torsion angles of the molecule is known as its conformation. In ethane, the simplest case for studying the conformation of alkanes, there is nearly free rotation about a carbon–carbon single bond. Two limiting conformations are important: eclipsed conformation and staggered conformation. The staggered conformation is 12.6 kJ/mol (3.0 kcal/mol) lower in energy (more stable) than the eclipsed conformation (the least stable). In highly branched alkanes, the bond angle may differ from the optimal value (109.5°) to accommodate bulky groups. Such distortions introduce a tension in the molecule, known as steric hindrance or strain. Strain substantially increases reactivity.. |
Alkane | 639 | Physical properties | Spectroscopic signatures for alkanes are obtainable by the major characterization techniques. |
Alkane | 639 | Physical properties | The C-Hstretching mode gives a strong absorptions between 2850 and 2960 cm and weaker bands for the C-C stretching mode absorbs between 800 and 1300 cm. The carbon–hydrogen bending modes depend on the nature of the group: methyl groups show bands at 1450 cm and 1375 cm, while methylene groups show bands at 1465 cm and 1450 cm. Carbon chains with more than four carbon atoms show a weak absorption at around 725 cm. |
Alkane | 639 | Physical properties | The proton resonances of alkanes are usually found at δH = 0.5–1.5. The carbon-13 resonances depend on the number of hydrogen atoms attached to the carbon: δC = 8–30 (primary, methyl, –CH3), 15–55 (secondary, methylene, –CH2–), 20–60 (tertiary, methyne, C–H) and quaternary. The carbon-13 resonance of quaternary carbon atoms is characteristically weak, due to the lack of nuclear Overhauser effect and the long relaxation time, and can be missed in weak samples, or samples that have not been run for a sufficiently long time. |
Alkane | 639 | Physical properties | Since alkanes have high ionization energies, their electron impact mass spectra show weak currents for their molecular ions. The fragmentation pattern can be difficult to interpret, but in the case of branched chain alkanes, the carbon chain is preferentially cleaved at tertiary or quaternary carbons due to the relative stability of the resulting free radicals. The mass spectra for straight-chain alkanes is illustrated by that for dodecane: the fragment resulting from the loss of a single methyl group (M − 15) is absent, fragments are more intense than the molecular ion and are spaced by intervals of 14 mass units, corresponding to loss of CH2 groups. |
Alkane | 639 | Chemical properties | Alkanes are only weakly reactive with most chemical compounds. They only reacts with the strongest of electrophilic reagents by virtue of their strong C–H bonds (~100 kcal/mol) and C–C bonds (~90 kcal/mol). They are also relatively unreactive toward free radicals. This inertness is the source of the term paraffins (with the meaning here of "lacking affinity"). In crude oil the alkane molecules have remained chemically unchanged for millions of years. |
Alkane | 639 | Chemical properties | The acid dissociation constant (pKa) values of all alkanes are estimated to range from 50 to 70, depending on the extrapolation method, hence they are extremely weak acids that are practically inert to bases (see: carbon acids). They are also extremely weak bases, undergoing no observable protonation in pure sulfuric acid (H0 ~ −12), although superacids that are at least millions of times stronger have been known to protonate them to give hypercoordinate alkanium ions (see: methanium ion). Thus, a mixture of antimony pentafluoride (SbF5) and fluorosulfonic acid (HSO3F), called magic acid, can protonate alkanes. |
Alkane | 639 | Chemical properties | All alkanes react with oxygen in a combustion reaction, although they become increasingly difficult to ignite as the number of carbon atoms increases. The general equation for complete combustion is: |
Alkane | 639 | Chemical properties | In the absence of sufficient oxygen, carbon monoxide or even soot can be formed, as shown below: |
Alkane | 639 | Chemical properties | For example, methane: |
Alkane | 639 | Chemical properties | See the alkane heat of formation table for detailed data. The standard enthalpy change of combustion, ΔcH, for alkanes increases by about 650 kJ/mol per CH2 group. Branched-chain alkanes have lower values of ΔcH than straight-chain alkanes of the same number of carbon atoms, and so can be seen to be somewhat more stable. |
Alkane | 639 | Chemical properties | Some organisms are capable of metalbolizing alkanes. The methane monooxygenases convert methane to methanol. For higher alkanes, cytochrome P450 convert alkanes to alcohols, which are then susceptible to degradation. |
Alkane | 639 | Chemical properties | Free radicals, molecules with unpaired electrons, play a large role in most reactions of alkanes. Free radical halogenation reactions occur with halogens, leading to the production of haloalkanes. The hydrogen atoms of the alkane are progressively replaced by halogen atoms. The reaction of alkanes and fluorine is highly exothermic and can lead to an explosion. These reactions are an important industrial route to halogenated hydrocarbons. There are three steps: |
Alkane | 639 | Chemical properties | Experiments have shown that all halogenation produces a mixture of all possible isomers, indicating that all hydrogen atoms are susceptible to reaction. The mixture produced, however, is not statistical: Secondary and tertiary hydrogen atoms are preferentially replaced due to the greater stability of secondary and tertiary free-radicals. An example can be seen in the monobromination of propane: |
Alkane | 639 | Chemical properties | In the Reed reaction, sulfur dioxide and chlorineconvert hydrocarbons to sulfonyl chlorides under the influence of light. |
Alkane | 639 | Chemical properties | Under some conditions, alkanes will undergo Nitration. |
Alkane | 639 | Chemical properties | Certain transition metal complexes promote non-radical reactions with alkanes, resulting in so C–H bond activation reactions. |
Alkane | 639 | Chemical properties | Cracking breaks larger molecules into smaller ones. This reaction requires heat and catalysts. The thermal cracking process follows a homolytic mechanism with formation of free radicals. The catalytic cracking process involves the presence of acid catalysts (usually solid acids such as silica-alumina and zeolites), which promote a heterolytic (asymmetric) breakage of bonds yielding pairs of ions of opposite charges, usually a carbocation. Carbon-localized free radicals and cations are both highly unstable and undergo processes of chain rearrangement, C–C scission in position beta (i.e., cracking) and intra- and intermolecular hydrogen transfer or hydride transfer. In both types of processes, the corresponding reactive intermediates (radicals, ions) are permanently regenerated, and thus they proceed by a self-propagating chain mechanism. The chain of reactions is eventually terminated by radical or ion recombination. |
Alkane | 639 | Chemical properties | Dragan and his colleague were the first to report about isomerization in alkanes. Isomerization and reformation are processes in which straight-chain alkanes are heated in the presence of a platinum catalyst. In isomerization, the alkanes become branched-chain isomers. In other words, it does not lose any carbons or hydrogens, keeping the same molecular weight. In reformation, the alkanes become cycloalkanes or aromatic hydrocarbons, giving off hydrogen as a by-product. Both of these processes raise the octane number of the substance. Butane is the most common alkane that is put under the process of isomerization, as it makes many branched alkanes with high octane numbers. |
Alkane | 639 | Chemical properties | In steam reforming, alkanes react with steam in the presence of a nickel catalyst to give hydrogen and carbon monoxide. |
Alkane | 639 | Occurrence | Alkanes form a small portion of the atmospheres of the outer gas planets such as Jupiter (0.1% methane, 2 ppm ethane), Saturn (0.2% methane, 5 ppm ethane), Uranus (1.99% methane, 2.5 ppm ethane) and Neptune (1.5% methane, 1.5 ppm ethane). Titan (1.6% methane), a satellite of Saturn, was examined by the Huygens probe, which indicated that Titan's atmosphere periodically rains liquid methane onto the moon's surface. Also on Titan, the Cassini mission has imaged seasonal methane/ethane lakes near the polar regions of Titan. Methane and ethane have also been detected in the tail of the comet Hyakutake. Chemical analysis showed that the abundances of ethane and methane were roughly equal, which is thought to imply that its ices formed in interstellar space, away from the Sun, which would have evaporated these volatile molecules. Alkanes have also been detected in meteorites such as carbonaceous chondrites. |
Alkane | 639 | Occurrence | Traces of methane gas (about 0.0002% or 1745 ppb) occur in the Earth's atmosphere, produced primarily by methanogenic microorganisms, such as Archaea in the gut of ruminants. |
Alkane | 639 | Occurrence | The most important commercial sources for alkanes are natural gas and oil. Natural gas contains primarily methane and ethane, with some propane and butane: oil is a mixture of liquid alkanes and other hydrocarbons. These hydrocarbons were formed when marine animals and plants (zooplankton and phytoplankton) died and sank to the bottom of ancient seas and were covered with sediments in an anoxic environment and converted over many millions of years at high temperatures and high pressure to their current form. Natural gas resulted thereby for example from the following reaction: |
Alkane | 639 | Occurrence | These hydrocarbon deposits, collected in porous rocks trapped beneath impermeable cap rocks, comprise commercial oil fields. They have formed over millions of years and once exhausted cannot be readily replaced. The depletion of these hydrocarbons reserves is the basis for what is known as the energy crisis. |
Alkane | 639 | Occurrence | Alkanes have a low solubility in water, so the content in the oceans is negligible; however, at high pressures and low temperatures (such as at the bottom of the oceans), methane can co-crystallize with water to form a solid methane clathrate (methane hydrate). Although this cannot be commercially exploited at the present time, the amount of combustible energy of the known methane clathrate fields exceeds the energy content of all the natural gas and oil deposits put together. Methane extracted from methane clathrate is, therefore, a candidate for future fuels. |
Alkane | 639 | Occurrence | Aside from petroleum and natural gas, alkanes occur significantly in nature only as methane, which is produced by some archaea by the process of methanogenesis. These organisms are found in the gut of termites and cows. The methane is produced from carbon dioxide or other organic compounds. Energy is released by the oxidation of hydrogen: |
Alkane | 639 | Occurrence | It is probable that our current deposits of natural gas were formed in a similar way. |
Alkane | 639 | Occurrence | |
Appellate procedure in the United States | 640 | United States appellate procedure involves the rules and regulations for filing appeals in state courts and federal courts. The nature of an appeal can vary greatly depending on the type of case and the rules of the court in the jurisdiction where the case was prosecuted. There are many types of standard of review for appeals, such as de novo and abuse of discretion. However, most appeals begin when a party files a petition for review to a higher court for the purpose of overturning the lower court's decision. |
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Appellate procedure in the United States | 640 | An appellate court is a court that hears cases on appeal from another court. Depending on the particular legal rules that apply to each circumstance, a party to a court case who is unhappy with the result might be able to challenge that result in an appellate court on specific grounds. These grounds typically could include errors of law, fact, procedure or due process. In different jurisdictions, appellate courts are also called appeals courts, courts of appeals, superior courts, or supreme courts. |
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Appellate procedure in the United States | 640 | The specific procedures for appealing, including even whether there is a right of appeal from a particular type of decision, can vary greatly from state to state. The right to file an appeal can also vary from state to state; for example, the New Jersey Constitution vests judicial power in a Supreme Court, a Superior Court, and other courts of limited jurisdiction, with an appellate court being part of the Superior Court. |
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Appellate procedure in the United States | 640 | Access to appellant status | A party who files an appeal is called an "appellant", "plaintiff in error", "petitioner" or "pursuer", and a party on the other side is called an "appellee", "defendant in error", "respondent". A "cross-appeal" is an appeal brought by the respondent. For example, suppose at trial the judge found for the plaintiff and ordered the defendant to pay $50,000. If the defendant files an appeal arguing that he should not have to pay any money, then the plaintiff might file a cross-appeal arguing that the defendant should have to pay $200,000 instead of $50,000. |
Appellate procedure in the United States | 640 | Access to appellant status | The appellant is the party who, having lost part or all their claim in a lower court decision, is appealing to a higher court to have their case reconsidered. This is usually done on the basis that the lower court judge erred in the application of law, but it may also be possible to appeal on the basis of court misconduct, or that a finding of fact was entirely unreasonable to make on the evidence. |
Appellate procedure in the United States | 640 | Access to appellant status | The appellant in the new case can be either the plaintiff (or claimant), defendant, third-party intervenor, or respondent (appellee) from the lower case, depending on who was the losing party. The winning party from the lower court, however, is now the respondent. In unusual cases the appellant can be the victor in the court below, but still appeal. |
Appellate procedure in the United States | 640 | Access to appellant status | An appellee is the party to an appeal in which the lower court judgment was in its favor. The appellee is required to respond to the petition, oral arguments, and legal briefs of the appellant. In general, the appellee takes the procedural posture that the lower court's decision should be affirmed. |
Appellate procedure in the United States | 640 | Ability to appeal | An appeal "as of right" is one that is guaranteed by statute or some underlying constitutional or legal principle. The appellate court cannot refuse to listen to the appeal. An appeal "by leave" or "permission" requires the appellant to obtain leave to appeal; in such a situation either or both of the lower court and the court may have the discretion to grant or refuse the appellant's demand to appeal the lower court's decision. In the Supreme Court, review in most cases is available only if the Court exercises its discretion and grants a writ of certiorari. |
Appellate procedure in the United States | 640 | Ability to appeal | In tort, equity, or other civil matters either party to a previous case may file an appeal. In criminal matters, however, the state or prosecution generally has no appeal "as of right". And due to the double jeopardy principle, the state or prosecution may never appeal a jury or bench verdict of acquittal. But in some jurisdictions, the state or prosecution may appeal "as of right" from a trial court's dismissal of an indictment in whole or in part or from a trial court's granting of a defendant's suppression motion. Likewise, in some jurisdictions, the state or prosecution may appeal an issue of law "by leave" from the trial court or the appellate court. The ability of the prosecution to appeal a decision in favor of a defendant varies significantly internationally. All parties must present grounds to appeal, or it will not be heard. |
Appellate procedure in the United States | 640 | Ability to appeal | By convention in some law reports, the appellant is named first. This can mean that where it is the defendant who appeals, the name of the case in the law reports reverses (in some cases twice) as the appeals work their way up the court hierarchy. This is not always true, however. In the federal courts, the parties' names always stay in the same order as the lower court when an appeal is taken to the circuit courts of appeals, and are re-ordered only if the appeal reaches the Supreme Court. |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | Many jurisdictions recognize two types of appeals, particularly in the criminal context. The first is the traditional "direct" appeal in which the appellant files an appeal with the next higher court of review. The second is the collateral appeal or post-conviction petition, in which the petitioner-appellant files the appeal in a court of first instance—usually the court that tried the case. |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | The key distinguishing factor between direct and collateral appeals is that the former occurs in state courts, and the latter in federal courts. |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | Relief in post-conviction is rare and is most often found in capital or violent felony cases. The typical scenario involves an incarcerated defendant locating DNA evidence demonstrating the defendant's actual innocence. |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | "Appellate review" is the general term for the process by which courts with appellate jurisdiction take jurisdiction of matters decided by lower courts. It is distinguished from judicial review, which refers to the court's overriding constitutional or statutory right to determine if a legislative act or administrative decision is defective for jurisdictional or other reasons (which may vary by jurisdiction). |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | In most jurisdictions the normal and preferred way of seeking appellate review is by filing an appeal of the final judgment. Generally, an appeal of the judgment will also allow appeal of all other orders or rulings made by the trial court in the course of the case. This is because such orders cannot be appealed "as of right". However, certain critical interlocutory court orders, such as the denial of a request for an interim injunction, or an order holding a person in contempt of court, can be appealed immediately although the case may otherwise not have been fully disposed of. |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | There are two distinct forms of appellate review, "direct" and "collateral". For example, a criminal defendant may be convicted in state court, and lose on "direct appeal" to higher state appellate courts, and if unsuccessful, mount a "collateral" action such as filing for a writ of habeas corpus in the federal courts. Generally speaking, "[d]irect appeal statutes afford defendants the opportunity to challenge the merits of a judgment and allege errors of law or fact. ... [Collateral review], on the other hand, provide[s] an independent and civil inquiry into the validity of a conviction and sentence, and as such are generally limited to challenges to constitutional, jurisdictional, or other fundamental violations that occurred at trial." "Graham v. Borgen", 483 F 3d. 475 (7th Cir. 2007) (no. 04–4103) (slip op. at 7) (citation omitted). |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | In Anglo-American common law courts, appellate review of lower court decisions may also be obtained by filing a petition for review by prerogative writ in certain cases. There is no corresponding right to a writ in any pure or continental civil law legal systems, though some mixed systems such as Quebec recognize these prerogative writs. |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | After exhausting the first appeal as of right, defendants usually petition the highest state court to review the decision. This appeal is known as a direct appeal. The highest state court, generally known as the Supreme Court, exercises discretion over whether it will review the case. On direct appeal, a prisoner challenges the grounds of the conviction based on an error that occurred at trial or some other stage in the adjudicative process. |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | An appellant's claim(s) must usually be preserved at trial. This means that the defendant had to object to the error when it occurred in the trial. Because constitutional claims are of great magnitude, appellate courts might be more lenient to review the claim even if it was not preserved. For example, Connecticut applies the following standard to review unpreserved claims: 1.the record is adequate to review the alleged claim of error; 2. the claim is of constitutional magnitude alleging the violation of a fundamental right; 3. the alleged constitutional violation clearly exists and clearly deprived the defendant of a fair trial; 4. if subject to harmless error analysis, the state has failed to demonstrate harmlessness of the alleged constitutional violation beyond a reasonable doubt. |
Appellate procedure in the United States | 640 | Direct or collateral: Appealing criminal convictions | All States have a post-conviction relief process. Similar to federal post-conviction relief, an appellant can petition the court to correct alleged fundamental errors that were not corrected on direct review. Typical claims might include ineffective assistance of counsel and actual innocence based on new evidence. These proceedings are normally separate from the direct appeal, however some states allow for collateral relief to be sought on direct appeal. After direct appeal, the conviction is considered final. An appeal from the post conviction court proceeds just as a direct appeal. That is, it goes to the intermediate appellate court, followed by the highest court. If the petition is granted the appellant could be released from incarceration, the sentence could be modified, or a new trial could be ordered. |
Appellate procedure in the United States | 640 | Notice of appeal | A "notice of appeal" is a form or document that in many cases is required to begin an appeal. The form is completed by the appellant or by the appellant's legal representative. The nature of this form can vary greatly from country to country and from court to court within a country. |
Appellate procedure in the United States | 640 | Notice of appeal | The specific rules of the legal system will dictate exactly how the appeal is officially begun. For example, the appellant might have to file the notice of appeal with the appellate court, or with the court from which the appeal is taken, or both. |
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