Carbon standard state

Carbon can exist as graphite or diamond under standard conditions. It can, however, have only one standard state. Carbons standard state is graphite. 

For a free energy of fonnation, the preferred standard state of the element should be the thennodynamically stable (lowest chemical potential) fonn of it e.g. at room temperature, graphite for carbon, the orthorhombic crystal for sulfiir. 

There are many ways to express the energy of a molecule. Most common to organic chemists is as a heat of formation, AHf. This is the heat of a hypothetical chemical reaction that creates a molecule from so-called standard states of each of its constituent elements. For example, AHf for methane would be the energy required to create CH4 from graphite and H2, the standard states of carbon and hydrogen, respectively. 

In the reaction shown above, the volume of the reaction products (2 mol CO) is seen to be much greater than that of the reactants (2 mol of solid carbon plus 1 mol of oxygen). The effect of pressure on the free energy of formation of an oxide associated with an increase in the number of gas molecules which is representative of the type of reaction in the present illustration is shown in Figure 4.2 (A). Applying the criterion of volume increase per mole accompanying reaction at standard state to the case of metal oxidation such as... 

At 900 °F the equilibrium constant for this reaction is 5.62 when the standard states for all species are taken as unit fugacity. If the reaction is carried out at 75 atm, what molal ratio of steam to carbon monoxide is required to produce a product mixture in which 90% of the inlet CO is converted to C02 ... 

The equilibrium constants are based on a standard state of unit fugacity for the gaseous species and on a standard state corresponding to the pure solid for carbon. 

Fig. 12.4. Vapor-to-water transfer data for saturated hydrocarbons as a function of accessible surface area, from [131]. Standard states are 1M ideal gas and solution phases. Linear alkanes (small dots) are labeled by the number of carbons. Cyclic compounds (large dots) are a = cyclooctane, b = cycloheptane, c = cyclopentane, d = cyclohexane, e = methylcyclopentane, f = methylcyclohexane, g = cA-l,2-dimethylcyclohexane. Branched compounds (circles) are h = isobutane, i = neopentane, j = isopentane, k = neohexane, 1 = isohexane, m = 3-methylpentane, n = 2,4-dimethylpentane, o = isooctane, p = 2,2,5-tri-metbylhexane. Adapted with permission from [74], Copyright 1994, American Chemical Society...

As a result of the mobility of the electrons in n orbitals, graphite is a conductor of electricity. It is also the form of carbon used as the thermodynamic standard state. On the other hand, diamond contains carbon atoms that are bonded to four others, so all of the electrons are used in localized bonding, and it is a nonconductor that has the structure shown in Figure 13.12. 

Example 2.3 Consider the formation of benzene and carbon dioxide from their elemental substances. Find the heat required per unit mole at the standard state 25 °C, 1 atm. 

Heating graphite at the same time as compressing it under enormous pressure will yield diamond. The energy needed to convert 1 mol of graphite to diamond is 2.4 kJmol-1. We say the enthalpy of formation AHt for the diamond is +2.4 kJ mol-1 because graphite is the standard state of carbon. 

For completeness, we stipulate that the elements must exist in their standard states. This sub-clause is necessary, because whereas most elements exist in a single form at s.t.p. (in which case their enthalpy of formation is zero), some elements, such as carbon... 

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 superscript to the heat of formation symbol A// represents the standard state, and the subscript number represents the base or reference temperature. From the example for the Law of Heat Summation, it is apparent that the heat of formation of carbon monoxide from Eq. (1.8) is... 

However, since the standard state of carbon is the condensed state, carbon graphite, the only partial pressure it exerts is its vapor pressure (pw), a known thermodynamic property that is also a function of temperature. Thus, the preceding formation expression is written as... 

Some elements exist in more than one form under standard conditions. For example, carbon can exist as either graphite or diamond, as shown in Figure 5.16. Graphite is defined as the standard state of carbon. Therefore, the standard enthalpy of formation of graphite carbon is 0 kj/mol. The standard enthalpy of formation of diamond is 1.9 kj/mol. Another example is oxygen, 02(g). Oxygen also exists in the form of ozone,... 

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... 

B) The formation of hydrogen sulfide from hydrogen gas and sulfur conforms to the definition of both standard enthalpy of reaction and standard enthalpy of formation since the heat change that is measured is for the formation of one mole of compound from the elements in their standard state. In Choice (D), diamond is not the stable aUotrope of carbon—it is graphite. 

Figure 8. Comparison of observed and calculated values for AGt° (molar standard state) for the transfer of salts from water to propylene carbonate. The electrostatic contribution was estimated from Equation 69 with n = 4 (Li+, Na+, K + ), n = 8 (Cl, 04B ), and the following solvated radii in A 3.6 (Li +), 3.9 (Na +), 4.2 (K +), 4.3 (Cl and 6.9 (AB )...

Standard states. The standard or reference state of each of the elemental substances is taken to be that physical state (or one of them, if there are two or more) in which the element naturally exists at a pressure, or a fugacity, of one atmosphere and at a temperature of 18°. The isotopic composition of each element in its standard state is understood to be the naturally existing one. For the element carbon, we have selected its form as diamond, C (c, diamond), as the standard state because no other form of solid carbon is at present a reproducible and invariable one. 

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. 

The free energy change, when all the reactants and products are in their standard states (1 M oxaloacetate dianion and pyruvate anion, 10-7 m hydrogen ion, and 1 atm C02), is —7.4 kcal/mole. The negative value of AG° means that the reaction proceeds spontaneously under these conditions. However, some of the concentrations are not very realistic. At pH 7, carbon dioxide is present partly in the form of the bicarbonate anion, rather than as gaseous C02. To take this into account, we can add the standard free energy change... 

PROBLEM 17.6 By determining the sign of AStotai, show whether the decomposition of calcium carbonate is spontaneous under standard-state conditions at 25°C. 

The standard free energy of formation of a substance measures its thermodynamic stability with respect to its constituent elements. Substances that have a negative value of AG°f, such as carbon dioxide and water, are stable and do not decompose to their constituent elements under standard-state conditions. Substances that have a positive value of AG°f, such as ethylene and nitrogen dioxide, are thermodynamically unstable with respect to their constituent elements. Once prepared, though, such substances can exist for long periods of time if the rate of their decomposition is slow. 

C (c, diamond). We have selected diamond as the standard state for carbon because, with respect to heat content, it is the only truly reproducible form of solid carbon. 

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