Standard-State Enthalpy of Formation and Absolute Entropy Data Table
Phase changes are isothermal and reversible. When the substance undergoes a phase change, the contribution that the phase change makes to the entropy of the substance is equal to the change in enthalpy for the phase change divided by the temperature at which it occurs. One can also define the standard entropy of the formation of a substance as the difference between its standard entropy (S^o_Aleft(Tright)) and those of its pure constituents in their standard states at the same temperature. This definition is incorporated into Lewis and Randall`s statement of the Third Act. For example, the standard entropy of water formation at 400 K is the difference The standard enthalpy of formation (ΔH0f) of a compound is the change in enthalpy, which accompanies the formation of 1 mole of a compound from its elements with all substances in their standard states. The following table shows the standard forming enthalpy, free standard Gibbs formation energy, standard entropy, and molar heat capacity at constant pressure of several inorganic compounds. Given ({Delta }_fH^o)(left(Tright)) and ({Delta }_fS^oleft(Tright)) you get the standard Gibbs formation energy free immediately from ({Delta }_fG^oleft(Tright)={Delta }_fH^oleft(Tright)-T{Delta }_fS^oleft(Tright)). For each element at any temperature, we have ({Delta }_fH^o=0) and ({Delta }_fS^o=0); It follows that the standard Gibbs energy free of the formation of an element in its standard state is zero. Tables with thermodynamic data typically contain values for({Delta }_fH^o), ({Delta }_fG^o), and (S^o). (A standard set of entropies contains the same information as the corresponding set of entropies of formation. Formation entropies are rarely presented in tabular form.
If ({Delta }_fS^o) is required, it can be calculated either from ({Delta }_fH^o) and ({Delta }_fG^o) or from the absolute entropies of the substance and the elements from which it is formed.) Hesse Law: If you switch from a certain set of reactants to a certain amount of products, the change in enthalpy is the same whether the reaction takes place in a single step or in a series of steps. The term standard state is used to describe a reference state for substances and is an aid in thermodynamic calculations (such as enthalpy, entropy, and Gibbs free energy calculations). The superscript degree symbol (°) indicates that the fabrics are in their standard state. (ΔH°, ΔG°, S°…..) We write (S^o_Aleft(Tright) to display the absolute entropy of the substance (A) in its default state at temperature (T). (S^o_Aleft(Tright)) is the entropy of the substance in its standard state at absolute zero plus the increase in entropy that occurs when the substance reversibly changes to its standard state at (T). As long as the substance (A) forms a perfect crystal at absolute zero, (S^o_Aleft(Tright)) is the difference between its molar entropy at (T) and its molar entropy at absolute zero – calculated from heat capacity and phase change enthalpy data. Because of this definition, the standard entropy of forming an element in its default state is zero. We can calculate the default entropy change for each reaction, ({Delta }_rS^oleft(Tright)), either as the difference between the standard entropies of formation (the values ({Delta }_fS^oleft(Tright)) of reactants and products, or as the difference between their standard entropies (the values (S^o_Aleft(Tright)). Both calculations are successful because they begin and end with a common set of elements that all have the same temperature. If we calculate ({Delta }_rS^oleft(Tright)) with values of (S^o_Aleft(Tright)) for reagents and products, the reference temperature for the elements is absolute zero.
If we calculate ({Delta }_rS^oleft(Tright)) with values of ({Delta }_fS^oleft(Tright)) for reagents and products, the reference temperature is (T). At a given temperature, the entropy value thus obtained is called absolute entropy of the substance or its entropy of the third law. When the entropy value for one mole of the substance is calculated in its standard state, the resulting absolute entropy is called standard entropy. The default entropy is usually marked with the symbol (S^o). It is usually included in thermodynamic data compilations for chemical substances. Given the entropy of a substance at absolute zero, its entropy at any higher temperature can be calculated from the changes in entropy that occur when the substance is heated to the new temperature. At the lowest temperatures, this change in entropy is calculated by integrating ({C_P}/{T}) using the theoretical Debye relation (C_P=AT^3). (A) results from the value (C_P) at the lowest temperature for which an experimental value of (C_P) is available. In temperature ranges where experimental heat capacity data are available, the change in entropy is obtained by integration using these data.
In Section 11.2, we note that many tables with thermochemical properties contain “absolute enthalpy” data for chemicals. According to Lewis and Randall`s statement of the Third Law, the entropy of a substance that forms a perfect crystal is zero at absolute zero. Just as the ideal temperature scale of gas has a natural zero at the temperature at which the volume is extrapolated to zero, a perfect crystalline substance at the same temperature has a natural zero of entropy. We can choose a non-zero value for the absolute zero point of temperature. The centigrade scale is based on such a choice. However, for thermodynamic purposes, such a choice is much less convenient. Similarly, we could choose arbitrary values for the entropies of the elements at absolute zero temperature. The entropy of a crystalline substance perfect to absolute zero would then be the sum of the entropies of its components. (See issue 5.) However, choosing non-zero values is much less convenient.
If the substance (A) does not form a perfect crystal at absolute zero, the actual value of (S^o_Aleft(Tright)) exceeds the calculated value. Excess is the molar entropy of the imperfect crystal at absolute zero. We observe that the deviation in the measurable values at (T) of the entropies of the reactions containing (A) do not correspond to those calculated with the incorrect value of (S^o_Aleft(Tright)). For enthalpy, there is no method to determine absolute values, only changes in enthalpy (ΔH values) can be measured. Then, it is important to have a common and well-defined reference state. Since enthalpy is a state function, a change in enthalpy does not depend on the path between two states. Note! The standard state is NOT the same as the standard temperature and pressure (STP) for a gas and should not be confused with this term. Enthalpy is a state function defined by the internal energy (E), pressure (P) and volume (V) of a system: [-Delta S^oleft(H_2, mathrm{400}mathrm{ }mathrm{K}right)-{frac{1}{2}}Delta S^oleft(O_2,mathrm{400}mathrm{K}right)] At constant pressure: ΔH = qp (qp = heat to or from the constant pressure chemical system, q is also called heat of reaction) Endothermic reaction: ΔH positive (heat adsorbed by the system from the environment).
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