Carbon standard entropies

Use data in Table 7.3 or Appendix 2A to calculate the standard entropy change for each of the following reactions at 25°C. For each reaction, interpret the sign and magnitude of the reaction entropy, (a) The synthesis of carbon disulfide from natural gas (methane) CH4(g) + 4 S(s, rhombic) - CS2(1) +... 

A i reaction (CaO) + S (C02) - S (CaCO ) The entropy of each solid is its standard entropy, S °, but the entropy of the gas must be corrected for the deviation of pressure from standard conditions. Equation gives the molar entropy of carbon dioxide as a ftmction of its partial pressure S (CO2) — S ° (CO2) - i In p(pc02) Now substitute the corrected entropy of CO2 into the equation for A ... 

PROBLEM 17.5 Calculate the standard entropy of reaction at 25°C for the decomposition of calcium carbonate ... 

Measurements of deviation of the standard adsorption entropy at graphitized carbon black have been carried out for thietane and other heterocyclic molecules. The theoretical standard entropy for the thietane molecule shows a greater deviation from the experimental value in comparison to others, which seems to indicate that for thietane a simple model of an adsorbed molecule with 2° of freedom is not accurate <1997ZP1333>. 

The sum of the standard entropies of gaseous water and carbon monoxide is larger than the sum of the standard entropies of gaseous hydrogen and carbon dioxide. So, the AS for this reaction should be positive. 

A least square plot of log Ccsc as a function of number of carbon atoms in the alkyl chain is given in Fig. 4.13. obtained from the slope of this line is —0.95kT and is comparable to the free energy of micellization measured for similar surfactants in solution (Fig. 4.14). Heat and standard entropy changes associated with the adsorption process can be calculated by considering the adsorption of the long-chain molecules, X, as follows (Somasundaran and Fuerstenau, 1972). 

EXAMPLE I Calculate the standard entropy change for the reaction of a mole of carbon monoxide with oxygen to produce carbon dioxide at 25°C. 

The temperature functions of the heat capacities of hydrothermally synthesised calcite type carbonates MnC03, FeC03, C0CO3, and NiC03 were investigated between 70 and 300 K. The respective standard entropies were calculated by the integration of IT versus T curves. 

For a given reaction, AG° and AH° would need to be calculated from standard formation values (graphite, oxygen, and carbon dioxide) first, before plugging into the equation. Also, AS° would need to be calculated from standard entropy values. 

This paper deals with the principles, advantages and limitations of measurement of sorption equilibria under isosteric conditions. It further assesses the sorption-isosteric method (SIM) as an effective tool for providing complete sets of sorption-thermodynamic functions, viz., enthalpy, standard entropy and standard Gibbs free energy of sorption, for nanoporous solids, i.e., micro- and mesoporous ones, as functions of sorption-phase concentration, n, over its entire range, and to approach such data for mixtures. The usefulness of SIM is exemplified by sorption systems that comprise atmospheric gases on zeolites and carbon dioxide, CO2, on carbonaceous sorbents, as well as several of their mixtures. 

Relative Standard Entropies Allotropes As mentioned previously, some elements can exist in two or more forms—called allotropes— in the same state of matter. For example, the allotropes of carbon include diamond and graphite— both solid forms of carbon. Since the arrangement of atoms within these forms is different, their standard molar entropies are different ... 

The standard entropy values S° of many common substances at 298 K and 1 aim are listed in Appendix 4. From these values you will see that the entropy of a substance does indeed increase in going from solid to liquid to gas. One especially interesting feature of this table is the very low S° value for diamond. The structure of diamond is highly ordered, with each carbon strongly bound to a tetrahedral arrangement of four other carbon atoms (see Section 10.5, Fig. 10.22). This type of structure allows very little disorder and has a very low entropy, even at 298 K. (iraphite has a slightly higher entropy because its layered structure allows for a little more disorder. 

Molar entropies increase as the size and complexity of the molecule increases. Compare, for example, the standard molar entropies of the three two-carbon hydrocarbons ... 

FIGURE 3.31. Reaction of alkyl chlorides with NO as a function of steric hindrance at carbon. Central line reactant state Left-hand lines ET transition and product states. Right-hand lines 5 2 transition and product states. Numbers above and below the lines are the standard free energies (in eV) numbers in parentheses are the entropies in meV/K. The numbers on the structures are bond lengths in A. From MP2/6-31G //UHF/6-31G and COSMO (solvation) calculations. 

References (20, 22, 23, 24, 29, and 74) comprise the series of Technical Notes 270 from the Chemical Thermodynamics Data Center at the National Bureau of Standards. These give selected values of enthalpies and Gibbs energies of formation and of entropies and heat capacities of pure compounds and of aqueous species in their standard states at 25 °C. They include all inorganic compounds of one and two carbon atoms per molecule. 

The standard partial molal volumes (V ), heat capacities (C >), and entropies (S ) of aqueous /i-polymers, together with their standard partial molal enthalpies AHj) and Gibbs free energies of formation from the elements AGf), are linear functions of the number of moles of carbon atoms in the alkyl chains (figure 8.28). 

The experimental entropies of adsorption were calculated after obtaining the free energies of adsorption at 0 = /% from the gas pressure in equilibrium with half the amount of adsorbate required to form the monolayer. The same principles were used to obtain the figure for the entropy of adsorption of O2 on unreduced steel. The values for carbon tetrachloride were taken directly from Foster s paper (4). The results for adsorption in chabazite were obtained from the work of Barrer and Ibbitson (15) with the slight modification needed to allow for the different standard states in the two phases used by them. The figures in the last column... 

Without performing any calculations, predict whether an increase or a decrease in entropy occurs for each of the following processes (a) combustion of methane (b) standard state formation of carbon dioxide (c) the coiling of two strands of DNA to form a double helix. 

Values of AG°f at 25°C for some common substances are listed in Table 17.3, and additional values are given in Appendix B. Note that AG°f for an element in its most stable form at 25°C is defined to be zero. Thus, solid graphite has AG°f = 0 kj/mol, but diamond, a less stable form of solid carbon at 25°C, has AG°f = 2.9kJ/mol. As with standard enthalpies of formation, AH°f, a zero value of AG°f for elements in their most stable form establishes a thermochemical "sea level," or reference point, with respect to which the standard free energies of other substances are measured. We can t measure the absolute value of a substance s free energy (as we can the entropy), but that s not a problem because we are interested only in free-energy differences between reactants and products. 

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