Thermodynamics standard state

You may wonder why the equilibrium constant, 11, has no units. The reason is that each term in the reaction quotient represents the ratio of the measured pressure of the gas to the thermodynamic standard state of one atmosphere. Thus the quotient (f3No2)2/f>N2o4 in Experiment 1 becomes... 

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. 

The thermodynamic standard state of a substance is its most stable state under standard pressure (1 atm) and at some specific temperature (usually 25°C). Thermodynamic refers to the observation, measurement and prediction of energy changes that accompany physical changes or chemical reaction. Standard refers to the set conditions of 1 atm pressure and 25°C. The state of a substance is its phase gas, liquid or solid. Substance is any kind of matter all specimens of which have the same chemical composition and physical properties. 

The conventional thermodynamic standard state values of the Gibbs energy of formation and standard enthalpy of formation of elements in their standard states are A(G — 0 and ArH = 0. Conventional values of the standard molar Gibbs energy of formation and standard molar enthalpy of formation of the hydrated proton are ArC (H +, aq) = 0 and Ar// (H +, aq) = 0. In addition, the standard molar entropy of the hydrated proton is taken as zero 5 (H+, aq) = 0. This convention produces negative standard entropies for some ions. 

Two issues associated with thermodynamic standard states bear some further attention. The first is associated with the enthalpy of ions. Ion heats of formation may be defined based on the heats of ionization of neutral molecules (or electron attachments thereto). For example, one might consider a reaction like... 

Following this, the thermodynamic arguments needed for determining CMC are discussed (Section 8.5). Here, we describe two approaches, namely, the mass action model (based on treating micellization as a chemical reaction ) and the phase equilibrium model (which treats micellization as a phase separation phenomenon). The entropy change due to micellization and the concept of hydrophobic effect are also described, along with the definition of thermodynamic standard states. 

In this section we consider the thermodynamics of micellization from two points of view the law of mass action and phase equilibrium. This will reveal the equivalency of the two approaches and the conditions under which this equivalence applies. In addition, we define the thermodynamic standard state, which must be understood if derived parameters are to be meaningful. 

In addition to specifying the physical state of reactants and products when reporting an enthalpy change, it s also necessary to specify the pressure and temperature. To ensure that all measurements are reported in the same way so that different reactions can be compared, a set of conditions called the thermodynamic standard state has been defined. 

Values of Kc are generally reported without units because the concentrations in the equilibrium constant expression are considered to be concentration ratios in which the molarity of each substance is divided by its molarity (1 M) in the thermodynamic standard state (Section 8.6). Because the units cancel, the concentration ratios and the values of Kc are dimensionless. For experiment 1 in Table 13.1, for example,... 

The standard enthalpy of formation of a compound, AHf, is defined as the increment in enthalpy associated with the reaction of forming a given compound from its elements, with each substance in its thermodynamic standard state at the given temperature.2 The thermodynamic cycle for the enthalpy of formation of methane (CH4) from the standard states of carbon and hydrogen (graphite and hydrogen molecules) is shown in Figure 1. 

The Third Law of Thermodynamics postulates that the entropy of a perfect crystal is zero at 0 K. Given the heat capacity and the enthalpies of phase changes, Eq. (12-3) allows the calculation of the standard absolute entropy of a substance, S° = AS for the increase in temperature from 0 K to 298 K. Some absolute entropies for substances in thermodynamic standard states are listed in Table 12-1. 

The lattice energy U of an ionic compound is defined as the energy required to convert one mole of crystalline solid into its component cations and anions in their thermodynamic standard states (non-interacting gaseous ions at standard temperature and pressure). It can be calculated using either the Born-Land6 equation... 

A standard thermodynamic value occurs with all components at 25 °C and 100 kPa. This thermodynamic standard state is slightly different from the standard temperature and pressure (STP) often used for gas law problems ( 0 °C and 1 atm=101.325 kPa). Standard properties of common chemicals are listed in tables. 

J. H. Rytting, S. S. Davis and T. Higuchi. Suggested thermodynamic standard state for comparing dmg molecules in stmcture-actMty studies. /. Pharm. Sci., 61, 816-8 (1972)... 

Standard state has two easily distinguishable meanings in the book. When the conventional thermodynamic standard state is meant (105 Pa = 1 bar, ideal gas), it is not denoted here by any superscript (ArG, A vapH, Asub>S, etc.) In the meantime, the thermodynamic consideration of the adsorption phenomena requires accepting less common standard states these will be specified in Sect. 5.1.1 and denoted by the superscript ° , like in S°, A csS° and K°. 

Standard state (of a substance) See Thermodynamic standard state of a substance. 

Thermodynamic standard state of a substance The most stable state of the substance at one atmosphere pressure and at some specific temperature (25°C unless otherwise specified). 

A cell in which all reactants and products are in their thermodynamic standard states (1 M for dissolved species and 1 atm partial pressure for gases) is called a standard cell. 

The superscript in indicates thermodynamic standard-state conditions. 

Standard electrode potentials, designated refer to standard-state conditions. These standard-state conditions are one molar solutions for ions, one atmosphere pressure for gases, and all solids and liquids in their standard states at 25°C. (Remember that we refer to thermodynamic standard-state conditions, and not standard temperature and pressure as in gas law calculations.) As any of the standard cells described earlier operates, and concentrations or pressures of reactants change, the observed cell voltage drops. Similarly, cells constructed with solution concentrations different from one molar, or gas pressures different from one atmosphere, cause the corresponding potentials to deviate from standard electrode potentials. 

Construction of the free energy profile (Figure 6.7) for the whole reaction required a choice of thermodynamic standard state, since bimolecular and unimolecular rate constants were being compared. This was taken as 40 pM, the physiological concentration of the triose phosphates. 

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