Standard state of a liquid

We define the standard state of a liquid as ay = 1 and for gases as an ideal gas pressure of 1 bar, Pj = I- For ideal liquid solutions (activity coefficients of unity), we write ay = Cy so at chemical equilibrium... 

The symbols and nomenclature are essentially those which have been widely adopted in the American chemical literature however, for reasons given in the text, and in accordance vith a modern trend, the Gibbs symbol fjL and the shorter term chemical potential" are employed for the partial molar free energy. Because atmospheric pressure is postulated for the conventional standard state of a liquid, some confusion has resulted from the use of the same S3rmbol for the standard state as for the liquid at an arbitrary pressure. Hence, the former state is indicated in the text in... 

We are already used to the concept of standard state in respect of pure solids, liquids and gases. The standard state of a liquid or solid substance, whether pure or in a mixture, or for a solvent is taken as the state of the pure substance at 298 K and 1 bar pressure (1 bar = 1.00 x 10 Pa) the standard state of a gas is that of the pure gas at 298 K, 1 bar pressure and exhibiting ideal gas behaviour. 

The reference point for all enthalpy expressions is called the standard molar enthalpy of formation (AHf) which is defined as the heat change that results when 1 mole of a compound in its standard state is formed from its elements in their standard states. The standard state of a liquid or solid substance is its most thermodynamically stable pure form at 1 bar pressure. The standard state for gases is similar, except that standard state gases are assumed to obey the ideal gas law exactly. The standard state for solutes dissolved in solution will be discussed in Chapter 10. In the notation AHf, the superscript represents standard-state conditions (1 bar), and the subscript f stands for formation. Although the standard state does not specify a temperature, we will assume, unless otherwise stated, AH° values are measured at 25°C. 

The molar enthalpy of any substance depends on its state. The standard state of a liquid or solid substance is specified to be the pure substance at a fixed pressure of exactly 1 bar (100,000 Pa), which we denote by P°. The standard state for a gas is defined to be the corresponding ideal gas at pressure P°. The difference between the molar enthalpy of a real gas at 1 bar pressure and the corresponding ideal gas at 1 bar is numerically very small, but we will discuss this difference in a later chapter. If substance number i is in its standard state, its molar enthalpy is denoted by H (i). A standard-state reaction is one in which all substances are in their standard states before and after the reaction. The enthalpy change for a standard-state reaction is denoted by A 71°. The standard-state pressure was at one time defined to equal 1 atm (101,325 Pa). The difference in numerical values is small, and the formulas involving P° are the same with either choice. For highly accurate work, one must determine which standard pressure was used for an older set of data. 

The standard state of a substance in a condensed phase is the real liquid or solid at 1 atm and T. 

Standard State of a Solvent in a Mixture The usual choice of a standard state for a solvent in a solution is the pure solvent at a pressure of 1 bar, the same convention as for a pure solid or liquid. Thus,u... 

A note on good practice Recall that the standard state of a pure substance is its pure form at a pressure of 1 bar (Section 6.15). For a solute, the standard state is for a concentration of 1 mol-L 1. Pure solids and liquids may always be regarded as being in their standard states provided the pressure is close to 1 bar. 

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 standard state (and thus any standard thermodynamic property) of a pure solid refers to the pure substance in the solid phase under the pressure p of 1 bar (0.1 MPa). The standard state of a pure liquid refers to the pure substance in the liquid phase at p = 1 bar. When the substance is a pure gas, its standard state is that of an ideal gas at p = 1 bar (or, which is equivalent, that of a real gas at P = o). 

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

The standard state of a condensed phase is taken at 1.0 bar pressure. Show that the activity of incompressible condensed matter at pressure P is from Eq. (47), a = exp Vm(P — 1 )/RT. Apply this formula to find the activity of liquid octane, with density 0.7g/cm at 25°C and 100 atm pressure. How much does the chemical potential of liquid octane change between 1 and 100 atm ... 

As absolute values of free energies and potentials of substances are not known, we can only quote the differences between the values belonging to them in concrete cases and the values related to a certain, so called standard state. Values of other thermodynamic functions, such as internal energy, enthalpy, etc. are quoted in the same way. As the standard state of pure liquid or solid substances we consider their state in stable modification at 1 atm. pressure and at the temperature of the system. As the standard state for gas, either alono or in a mixture, the state of a pure gas in ideal state is taken at 1 atm. pressure and at the temperature of the system. 

Employing standard states of a single solute in a physical state of infinite dilution in the liquid stationary phase at the temperature and pressure of the system and a single solute in the perfect gas state at unit pressure and the temperature of the system for the solute in the stationary and in the gaseous phase, respectively, we obtain for the standard molar Gibbs function of sorption of solute i, AG°p(/) [19] ... 

In this example the standard heat of formation of H20 is available for its hypothetical standard state as a gas at 25°C. One might expect the value of the heat of formation of water to be listed for its actual state as a liquid at 1 bar or l(atm) and 25°C. As a matter of fact, values for both states are given because they are both frequently used. This is true for many compounds that normally exist as liquids at 25°C and the standard-state pressure. Cases do arise, however, in which a value is given only for the standard state as a liquid or as an ideal gas when what is needed is the other value. Suppose that this, were the case for the preceding example and that only the standard heat of formation of liquid H20 is known. We must now include an equation for the physical change that transforms water from its standard state as a liquid into its standard state as a gas. The enthalpy change for this physical process is the difference between the heats of formation of water in its two standard states ... 

Assuming that it is only van der Waals forces which are acting in the solute/ solvent system, and that the heat of mixing is responsible for all deviations from ideal behaviour, as well as the fact that the solute/solvent interaction energy is the geometric mean of solute/solute and solvent/solvent interactions, Hildebrand [228, 229] and Scatchard [230] were able to develop the following expression for the activity coefficient f of the nonelectrolyte solute i dissolved in a solvent s (mole fraction basis), referred to a standard state of pure liquid solute (not infinite dilution) ... 

The standard state of a substance is a reference state that allows us to obtain relative values of such thermodynamic quantities as free energy, activity, enthalpy, and entropy. All substances are assigned unit activity in their standard state. For gases, the standard state has the properties of an ideal gas, but at one atmosphere pressure. It is thus said to be a hypothetical state. For pure liquids and solvents, the standard states are real states and are the pure substances at a specified temperature and pressure. For solutes In dilute solution, the standard state is a hypothetical state that has the properties of an infinitely dilute solute, but at unit concentration (molarity, molality, or mole fraction). The standard state of a solid is a real state and is the pure solid in its most stable crystalline form. 

The standard state for a pure liquid or solid is taken to be the substance in that state of aggregation at a pressure of 1 bar. This same standard state is also used for liquid mixtures of those components that exist as a liquid at the conditions of the mixture. Such substances are sometimes referred to as liquids that may act as a solvent. For substances that exist only as a solid or a gas in the pure component state at the temperature of the mixture, sometimes referred to as substances that can act only as a solute, the situation is more complicated, and standard states based on Henry s law may be used. In this case the pressure is again fixed at 1 bar, and thermal properties such as the standard-state enthalpy and heat capacity are based on the properties of the substance in the solvent at infinite dilution, but the standard-state Gibbs energy and entropy are based on a hypothetical state.of unit concentration (either unit molality or unit mole fraction, depending on the form of Henry s law used), with the standard-state fugacity at these conditions extrapolated from infinite-dilution behavior in the solvent, as shown in Fig. 9.1-3a and b. Therefore just as for a gas where the ideal gas state at 1 bar is a hypothetical state, the standard state of a substance that can only behave as a solute is a hypothetical state. However, one important characteristic of the solute standard state is that the properties depend strongly upon the solvent. used. Therefore, the standard-state properties are a function of the temperature, the solute, and the solvent. This can lead to difficulties when a mixed solvent is used. 

The standard state of a pure liquid substance is that of the liquid under the standard state pressure. 

Since a change in the state of aggregation (melting or vaporization) involves an increase in entropy, this contribution must be included in the computation of the entropy of a liquid or of a gas. For the standard entropy of a liquid above the meltin point of the substance, we have ... 

Hess s law allows you to calculate unknown AH values using known reactions and their experimentally determined AH values. However, recording AH values for all known chemical reactions would be a huge and unending task. Instead, scientists record and use enthalpy changes for only one type of reaction—a reaction in which a compound is formed from its elements in their standard states. The standard state of a substance means the normal physical state of the substance at 1 atm and 298 K (25°C3. For example, in their standard states, iron is a solid, mercury is a liquid, and oxygen is a diatomic gas. 

The magnitude of any enthalpy change depends on the temperature, pressure, and state (gas, liquid, or solid crystaUine form) of the reactants and products. To compare enthalpies of different reactions, we must define a set of conditions, called a standard suite, at which most enthalpies are tabulated. The standard state of a substance is its pure form at atmospheric pressure (1 atm) and the temperature of interest, which we usually choose to be 298 K (25 °C). The standard enthalpy change of a reaction is defined as the enthalpy change when all reactants and products are in their standard states. We denote a standard enthalpy change as AH°, where the superscript ° indicates standard-state conditions. 

Standard Reference Material See certified reference material, standard solution A solution whose composition is known by virtue of the way that it was made from a reagent of known purity or by virtue of its reaction with a known quantity of a standard reagent, standard state The standard state of a solute is 1 M and the standard state of a gas is 1 bar. Pure solids and liquids are considered to be in their standard states. In equilibrium constants, dimensionless concentrations are expressed as a ratio of the concentration of each species to its concentration in its standard state. 

The thennodynamic standard state of a substance is its most stable pure form under standard pressure (one atmosphere) and at some specific temperature (25°C or 298 K unless otherwise specified). Examples of elements in their standard states at 25°C are hydrogen, gaseous diatomic molecules, H2(g) mercury, a silver-colored liquid metal, Hg(f) sodium, a silvery-white solid metal, Na(s) and carbon, a grayish-black solid called graphite, C(graphite). We use C(graphite) instead of C(s) to distinguish it from other solid forms of carbon, such as... 

The standard state of a pure liquid or solid is the unstressed liquid or solid at pressure p° and the temperature of interest. If the liquid or solid is stable under these conditions, this is a real (not hypothetical) state. 

Let X represent one of the thermodynamic potentials or the entropy of a phase. The standard molar transition quantities Avap3t° = A°(g) — Xm(l) and Asub ° = m(g) — Zm(s) are functions only of T. To evaluate Avap3t° or Asub t at a given temperature, we must calculate the change of Xm for a path that connects the standard state of the liquid or solid with that of the gas. The simplest choice of path is one of constant temperature T with the following steps ... 

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