Standard states of solute

Standard States of Solutes in Solution For a solute, particularly in situations where only dilute solutions can or will be considered, the usual procedure is to define the standard state in terms of a hypothetical solution that follows Henry s law at either a concentration of. y2 =1 or mi = 1. These standard states are known as Henry s law standard states. The standard state solutions are said to be hypothetical because real solutions at these high concentrations do not follow Henry s law. 

Here C is the concentration of component i in grams per liter, and t/ is the activity coefficient of component i on this concentration scale. The quantity m° is the standard state chemical potential of component i and is a function of temperature only. The standard state of solute component i is chosen so that In t/ — 1 as c, — 0. In Equation 4, R is the universal gas constant, 8.314 X 107 ergs/(deg mole), and T is the absolute temperature. The quantity In t/ is a function of the concentration of all q solutes thus... 

Statement (a) is true, but statement (b) is not. The standard state of solutes is normally defined as unit activity (1 Mfor all but the most careful work). In biological systems, the pH is frequently in the neutral range (i.e., H is close to 10" M) the modification is a matter of convenience. Water is the solvent, not a solute, and its standard state is the pure liquid. 

It has been pointed out by Adamson (34) and others (35,36) that the entropy-related chelate effect, as manifested in the stability constants, disappears when unit mole fraction replaces unit molality as the standard state of solutes in aqueous systems. On this basis the stability constants assumed for the model compounds in Table II (20) would have to be equivalent in magnitude regardless of the number of chelate rings formed. On the other hand the relative degrees of dissociation of the model compounds in Table II remain an experimental fact, with the larger concentration unit giving smaller numerical concentrations for the solutions illustrated, thus compensating for the disappearance of the chelate effect in the numerical values of the stability constants. 

We denote the standard state value of a property by the superscript on the symbol for the property, as in for the standard molar enthalpy of a substance and p for the standard pressure of 1 bar. For example, the standard state of hydrogen gas is the pure gas at 1 bar and the standard state of solid calcium carbonate is the pure solid at 1 bar, with either the calcite or aragonite form specified. The physical state needs to be specified because we can speak of the standard states of the sohd, liquid, and vapor forms of water, for instance, which are the pure sohd, the pure liquid, and the pure vapor, respectively, at 1 bar in each case. The standard states of solutions, which are never pure , need to be treated differently (Section 3.8). 

The standard states of Ag and of Ag (aq) have the conventional definitions, but there is an ambiguity in the definition of the standard state of e. Suppose that a reference electrode R is positioned above a solution of AgN03, which in turn is in contact with an Ag electrode. The Ag electrode and R are connected by a wire. Per Faraday, the processes are... 

The standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

The numerical values of AG and A5 depend upon the choice of standard states in solution kinetics the molar concentration scale is usually used. Notice (Eq. 5-43) that in transition state theory the temperature dependence of the rate constant is accounted for principally by the temperature dependence of an equilibrium constant. 

In order to compare the thermodynamic parameters of different reactions, it is convenient to define a standard state. For solutes in a solution, the standard state is normally unit activity (often simplified to 1 M concentration). Enthalpy, internal energy, and other thermodynamic quantities are often given or determined for standard-state conditions and are then denoted by a superscript degree sign ( ° ), as in API", AE°, and so on. 

But that is not all. For dilute solutions, the solvent concentration is high (55 mol kg ) for pure water, and does not vary significantly unless the solute is fairly concentrated. It is therefore common practice and fully justified to use unit mole fraction as the standard state for the solvent. The standard state of a close up pure solid in an electrochemical reaction is similarly treated as unit mole fraction (sometimes referred to as the pure component) this includes metals, solid oxides etc. 

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... 

An enthalpy of reaction also depends on the conditions (such as the pressure). All the tables in this book list data for reactions in which each reactant and product is in its standard state, its pure form at exactly 1 bar. The standard state of liquid water is pure water at 1 bar. The standard state of ice is pure ice at 1 bar. A solute in a liquid solution is in its standard state when its concentration is 1 mol-L". The standard value of a property X (that is, the value of X for the standard state of the substance) is denoted X°. 

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 numerical value of the activity clearly depends upon the standard state, and one often encounters other choices for the standard state for solutes. For example, just as we obtained Equations 29 and 30 from Equation 22, we could have obtained similar looking equations from Equations 23 or Equation 24. However, the derivation requires a mention of... 

Before closing this section we note that even in nonideal solutions we can use the standard state of Equation 16 for the solute. Since Equation 16 only holds for ideal solutions, one generalizes to obtain48... 

In our quantum mechanical solvation modeling,12 27 we take the standard state of the vapor to be a 1 molar ideal gas at 298° K and the standard state of the solute to be a hypothetical 1 molar Henry s law solute at the same... 

In the discussion of the Daniell cell, we indicated that this cell produces a voltage of 1.10 V. This voltage is really the difference in potential between the two half-cells. The cell potential (really the half-cell potentials) is dependent upon concentration and temperature, but initially we ll simply look at the half-cell potentials at the standard state of 298 K (25°C) and all components in their standard states (1M concentration of all solutions, 1 atm pressure for any gases and pure solid electrodes). Half-cell potentials appear in tables as the reduction potentials, that is, the potentials associated with the reduction reaction. We define the hydrogen half-reaction (2H+(aq) + 2e - H2(g)) as the standard and has been given a value of exactly 0.00 V. We measure all the other half-reactions relative to it some are positive and some are negative. Find the table of standard reduction potentials in your textbook. 

In the foregoing calculation of Asin//(1) and Asin//(3), we have used the tabulated values for the standard enthalpies of formation of ethanol and acetic acid aqueous solutions. This looks sensible (after the definitions given in section 2.3), because the standard states of ethanol and acetic acid solutions in water correspond to 1 mol of C2H5OH or CH3COOH in about... 

However, the equilibrium constant must still be considered as pure and dimensionless numbers (according to the classical relation —AG° = RT In Ks). All molar concentrations in the expression of Ks should thus be interpreted as molar concentrations relative to a standard state of 1 mol dm-3 i.e. they are the numerical values of the molar concentrations5 . If the solution is not dilute enough, the equilibrium constants can still be written with concentrations but they must be considered as apparent stability constants. 

Vera and co-workers (7,W,lj ) have extended the thermodynamic correlation and made two additions. First, they have developed a semi-empirical expression for the excess Gibbs energy in place of the simple empirical equations originally used (Equations 8 and 9). Also, while they use a standard state of the electrolyte of a saturated solution, they change the standard state of water back to the conventional one of pure water. 

Concentrations of aqueous electrolyte solutions are conventionally expressed using the aquamolality scale (L = moles salt per 55.508 mol solvent (l,000g for H20)). Some typical solubilities (298.15K) are listed in Table 5.13. Almost all salts are less soluble in D20 than in H20. For those salts whose solubility increases with temperature, which is the ordinary behaviour, the isotope effects decrease with temperature. Writing the standard state partial molar free energy of pure solid salt as Pxsalt) and its standard state in solution as p, (HorD) we have on comparing the saturated solutions in H20 and D20,... 

As seen from Eq. (130) an activity coefficient may deviate significantly from unity at higher salt concentrations. The activity coefficient can therefore also be used as a measure of the deviation of the salt solution from a thermodynamically ideal solution. If the chemical potential of a solute in a (pressure-dependent) standard state of infinite dilution is /x°, we find the standard partial molar volume from... 

In Equation (15.11), the choice of is entirely arbitrary. However, it is conventional to choose m2 =1 mol kg that is, the standard state of the solute is a hypothetical one molal state that is the point of extrapolation of Henry s law behavior to a molality of 1 mol kg In a figure analogous to Figure 15.1, but with ni2 along the horizontal axis, the standard state would be a point on the Henry s law dotted line directly above m2=l mol kg ... 

From the definitions of standard states for components of solutions, it is clear that AGm is a function only of the temperature, because the standard state of each reactant and product is defined at a specific fixed pressure. Thus, AGm is a constant for a particular reaction at a fixed temperature. Hence, we can write... 

Table 16.1 summarizes the information on the standard states of pure phases as well as those of solvents and solutes. 

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