Chemical equations free elements

Having classified the elements according to their ground-state electron configurations, we can now look at the way chemists represent metals, metalloids, and nonmetals as free elements in chemical equations. Because metals do not exist in discrete molecular units, we always use their empirical formulas in chemical equations. The empirical formulas are the same as the symbols that represent the elements. For example, the empirical formula for iron is Fe, the same as the symbol for the element. 

Strategy To calculate the standard Gibbs free energy change of a reaction, we look up the standard free energies of formation of reactants and products in Appendix 2 and use these values in Equation 8.40. Remember that AGf for elements such as 02(g) and Mg(i) is zero because they are stable allotropes of their respective elements at 1 bar and 25°C. Check that the chemical equations are balanced so that you use the correct stoichiometric coefficients in Equation 8.40. Finally, aU stochiometric coefficients are unitless, so AG xn is expressed in units of kJ moP. ... 

If an element occurs as a free element on either side of the chemical equation, balance it last. Always balance free elements by adjusting the coefficient on the free element. 

For the purposes of this review, the key concept embedded in equation (1) is the chemical affinity term, which is expressed as 1 — Q/K. The chemical affinity of a system is related to the free energy of the reaction and is a measure of the degree of departure from equilibrium (i.e.,/(AG) = 1 — Q/K). The form of the chemical affinity term indicates that as the concentrations of dissolved elements build up in solution, the system approaches saturation in a rate-limiting solid and the overall dissolution reaction slows down, and, at equilibrium, the rate would be zero. In the case of glass dissolution, there are many circumstances, which are reviewed below, where the rate behaviour does not comply with these expectations. 

Table 16-1 compiles some data for S°, the molar entropy, and AGp the free energy of formation from the elements. All values in Table 16-1 are presented at 25°C and at standard states. Notice that the units of entropy and free energy are stated per mole, mol-1. This means that the moles used to balance a chemical reaction are included by the multiplication of the coefficient (mol in balanced equation) and the value from the table so that unit mol cancels. This is also the way in which we handled calculations involving AH values. 

The most of chemical reactions accompanied by electron transfer from an atom of one reagent (reducer) to an atom of another reagent (oxidizer). Each element can have some oxidation states. The standard oxidation-reduction potential between two oxidation states of element is bonded with standard thermodynamic free energy of the transition from one state to another by the following equation ... 

The other solution species are formed from this "basis" by a series of chemical reactions, and their concentrations can be expressed through the use of equilibrium constants, in terms of the concentration of the chosen "basis". The resulting set of nonlinear simultaneous equations consists of as many unknowns as there are elements and can be solved by conventional niamerical methods. The "free energy minimization" method utilizes only free energy criteria for chemical equilibria making no distinction among the constituent species and is essentially a constraint non-linear minimization problem. A number of search methods have... 

Moreover, the equation can only be accurate for small strains, since considerable change in the end-to-end distance of the cords would distort the Gaussian distribution of statistical chain elements. This happens more readily for a smaller value of It also implies that at increasing strain, the chemical bonds in the primary chain become increasingly distorted. Consequently, the increase in elastic free energy is due not merely to a decrease in conformational entropy but also to an increase in bond enthalpy. If the value of is quite small, even a small strain will cause an increase in enthalpy. (In a crystalline solid, only the increase in bond enthalpy contributes to the elastic modulus.)... 

Even if we do accept the simple Bohr theory of valence, there is still the difficulty of how to handle chemical valence when the aufbau principle breaks down for free atoms, or when the n and l of individual electrons are poorly defined. In some cases, instabilities of valence can be expected. Nonintegral valences are indeed observed for many elements of the long periods in the condensed phase. This aspect of chemical valence will be further discussed in chapter 11, where it will also be related to properties of the radial equation. 

In the above equations (19.60) to (19.64), G is the total Gibbs free energy of the system jdi is the chemical potential of species i ni is the number of moles of species i N is the total number of species in the system c is the total number of components (for present purposes considered as the elements) Be is the number of moles of each component (or element, e) in the system hei is the number of moles of component (or element) e contained in one mole of species t p refers to a separate electrolyte (ionic) solution phase, and (j> is the total number of these electrolyte phases Zp i refers to the valence or charge of the ith species in the pth phase and is the slack variable defined in (19.64). 

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