Temperature-dependent chemistry

The temperature variation throughout Titan s atmosphere from a cold 92 K at the surface to the somewhat warmer 170 K of the stratosphere suggests a number of different chemistry regimes. The calculation of rates at different temperatures follows the detailed analysis in Section 5.4 and can be applied to the indicative temperatures as follows  

Essentially, all reactions that require the formation of a chemical bond with an activation energy of around 100 kJ mol-1 are frozen out at the surface of Titan but are considerably faster in the stratosphere, although still rather slow compared with the rates of reaction at 298 K. Chemistry in the atmosphere of Titan will proceed slowly for neutral reactions but faster for ion-molecule reactions and radical-neutral reactions, both of which have low activation barriers. The Arrhenius equation provides the temperature dependence of rates of reactions but we also need to consider the effect of cold temperatures on thermodynamics and in particular equilibrium. 

The extension of thermodynamic calculations to low temperatures requires knowledge of how the equilibrium composition of a mixture, which varies at different temperatures, can be derived from the standard relation between AG and the equilibrium constant (Equation 8.12) to give the van t Hoff equation for the variation of the equilibrium constant with temperature  

The equilibrium constant is fairly easy to measure as a function of temperature in the laboratory and this provides a way of determining ArH. The integrated form 

The equilibrium constant K2 for the reaction at 298 K is 1.05. Calculate the value of K, at 98 K and 170 K ArH for the reaction can be calculated from the data in Appendix C and is -106.47 kJmoU1. Substituting this into Equation 10.3 gives  

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Thus, observations and related theoretical modelling of the anticorrelation between temperature and ozone in the upper stratosphere provide a graphic illustration of the role of temperature-dependent chemistry in modulating ozone, as shown in Figure 6.2. 

Several instniments have been developed for measuring kinetics at temperatures below that of liquid nitrogen [81]. Liquid helium cooled drift tubes and ion traps have been employed, but this apparatus is of limited use since most gases freeze at temperatures below about 80 K. Molecules can be maintained in the gas phase at low temperatures in a free jet expansion. The CRESU apparatus (acronym for the French translation of reaction kinetics at supersonic conditions) uses a Laval nozzle expansion to obtain temperatures of 8-160 K. The merged ion beam and molecular beam apparatus are described above. These teclmiques have provided important infonnation on reactions pertinent to interstellar-cloud chemistry as well as the temperature dependence of reactions in a regime not otherwise accessible. In particular, infonnation on ion-molecule collision rates as a ftmction of temperature has proven valuable m refining theoretical calculations. 

Monkos, Karol 2000. Viscosity analysis of the temperature dependence of the solution conformation of ovalbumin. Biophysical Chemistry 85, 7-16. 

Finally, although both temperature-programmed desorption and reaction are indispensable techniques in catalysis and surface chemistry, they do have limitations. First, TPD experiments are not performed at equilibrium, since the temperature increases constantly. Secondly, the kinetic parameters change during TPD, due to changes in both temperature and coverage. Thirdly, temperature-dependent surface processes such as diffusion or surface reconstruction may accompany desorption and exert an influence. Hence, the technique should be used judiciously and the derived kinetic data should be treated with care ... 

Although decarbonylation of supported metal carbonyl clusters sometimes occurs almost without changes in the metal frames, the chemistry is complex and only partially understood. When decarbonylation takes place at elevated temperatures (depending on the support), migration and aggregation of the metal inevitably occur, and these processes are less well understood than the decarbonylation with near retention of the metal frame. 

The chemistry of iron(IV) in solid-state materials and minerals is restricted to that of oxides, since other systems such as iron(IV)-halides are not stable [186]. Iron(lV) oxides are easy to handle because they are usually stable in air, but they often have a substoichiometric composition, with oxygen vacancies contributing to varying degrees. Moreover, the samples may contain different amounts of iron(lll) in addition to the intended iron(IV) oxide, a complication which may obscure the Mossbauer data [185]. Even iron(V) was found in iron(IV) oxides due to temperature-dependent charge disproportionation [188, 189]. 

It is not the purpose of chemistry, but rather of statistical thermodynamics, to formulate a theory of the structure of water. Such a theory should be able to calculate the properties of water, especially with regard to their dependence on temperature. So far, no theory has been formulated whose equations do not contain adjustable parameters (up to eight in some theories). These include continuum and mixture theories. The continuum theory is based on the concept of a continuous change of the parameters of the water molecule with temperature. Recently, however, theories based on a model of a mixture have become more popular. It is assumed that liquid water is a mixture of structurally different species with various densities. With increasing temperature, there is a decrease in the number of low-density species, compensated by the usual thermal expansion of liquids, leading to the formation of the well-known maximum on the temperature dependence of the density of water (0.999973 g cm-3 at 3.98°C). 

Link, S. and El-Sayed, M.A. (1999) Size and temperature dependence of the plasmon absorption of colloidal gold nanopartides. Journal of Physical Chemistry B, 103 (21), 4212—4217. 

The planets nearest the Sun have a high-temperature surface while those further away have a low temperature. The temperature depends on the closeness to the Sun, but it also depends on the chemical composition and zone structures of the individual planets and their sizes. In this respect Earth is a somewhat peculiar planet, we do not know whether it is unique or not in that its core has remained very hot, mainly due to gravitic compression and radioactive decay of some unstable isotopes, and loss of core heat has been restricted by a poorly conducting mainly oxide mantle. This heat still contributes very considerably to the overall temperature of the Earth s surface. The hot core, some of it solid, is composed of metals, mainly iron, while the mantle is largely of molten oxidic rocks until the thin surface of solid rocks of many different compositions, such as silicates, sulfides and carbonates, occurs. This is usually called the crust, below the oceans, and forms the continents of today. Water and the atmosphere are reached in further outward succession. We shall describe the relevant chemistry in more detail later here, we are concerned first with the temperature gradient from the interior to the surface (Figure 1.2). The Earth s surface, i.e. the crust, the sea and the atmosphere, is of... 

FIGURE 4.2 Linewidth increase with temperature for an S = 1/2 system. The linewidth of a feature in the low-spin heme spectrum from cytochrome a in bovine heart cytochrome oxidase has been fit as a convolution of a constant component from inhomogeneous broadening and a temperature-dependent component from homogeneous broadening (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

Leckrone, K. J. and Hayes, J. M. (1997) Efficiency and temperature dependence of water removal hy memhrance dryers. Analytical Chemistry 69, 911 918. 

Calculations Equilibrium Dissolved gases Rates of reaction Chemical potential and AG with the extent of reaction Henry s Law and the pH of the oceans Temperature dependence of chemistry and the analysis of chemical networks in prebiotic environments... 

Atmospheric chemistry Temperature dependence dictates that all neutral chemistry is frozen out at the surface temperature of 92 K. What of radical-driven chemical networks Stratospheric chemistry at 170 K... 

The temperature dependence of the molar magnetic susceptibility (x) of an assembly of paramagnetic spins without interaction is characterized by the Curie behavior with x = C/T where C = /Vy2( 2.S (.S + l)/3k. It is a very common situation in the organometallic chemistry of radical species when the spin density is essentially localized on the metal atom. Since, in most cases, this atom is surrounded by various innocent ligands, intermolecular interactions are very weak and in most cases are reflected by a small contribution described by a Curie-Weiss behavior, with x = C/(T 0) where 0 is the Curie-Weiss temperature. A positive value for 0 reflects ferromagnetic interactions while a negative value — the most common situation — reflects an antiferromagnetic interaction. 

Dalai TK, Krishnaswami S, Sarin MM (2002) Major ion chemistry in the headwaters of the Yamuna river system chemical weathering, its temperature dependence and C02 consumption in the Himalaya. Geochim Cosmochim Acta 66(19) 3397-3416... 

The possible intervention of classical, competitive reactions in the low temperature solution chemistry of benzylchlorocarbene (10a) requires careful investigation. There are reasons to suspect azine (48) formation Goodman reported minor yields of azine in analogous MeCCl experiments,60 and Liu et al. found 40% of 48 in the photolysis of neat diazirine 9a.65 Perhaps azine formation is also significant at low temperature in hydrocarbon solvents. If so, the intervention of bimolecular azine formation, in competition with the unimolecular carbene 1,2-H shift, could lead to a nonlinear temperature dependence for the disappearance of 10a. Arrhenius curvature could then be explained without invoking QMT. 

Fig. 13 Temperature dependence of / eff both in the cooling and warming modes for [Fe(isoxazole)6](BF4)2 ([72] - reproduced with permission of the Royal Society of Chemistry)...

One-step chemistry is often employed as an idealized model for combustion chemistry. The primary difference with the results presented above is the strong temperature dependence of the reaction rate constant k T). For constant-property flows, the temperature can be related to the mixture fraction and reaction-progress variable by a linear expression of the form... 

The structural chemistry of the organotin halides is dominated by their Lewis acid properties and their propensity to form five- and six-coordinate complexes. Self-association may give oligomers or polymers in the solid state, which usually dissociate in solution. The structure of tricyclohexyltin chloride in the crystal is temperature-dependent. At 108 K, it has the form of a rod-like polymer with distorted trigonal-bipyramidal tin and Sn-Cl separations of 245.6(7) and 300.77(7) pm, but at 298 K, the structure is best regarded as consisting of near-tetrahedral discrete molecules.3... 

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