Ion standard state

The chemical potential of an ion in water is given by:

where a, the activity of the species, is the product of its activity coefficient y and the concentration c , in moles per liter of solution, or M, the molarity1.

is the chemical potential of the ion in its standard state, and therein lies the difficulty. The standard state of a component in a nonaqueous solution is the pure substance (see Sect. 10.4). However, this cannot be applied to aqueous ions because a pure-ion state does not exist. Instead, the standard state is chosen as the ion in an infinitely-dilute solution, or, equivalently, at concentrations where Henry's law applies. This is the region where the activity is proportional to the concentration, or the activity coefficient is independent of concentration. This condition has a solid physical basis. Ions in a dilute solution are surrounded by water molecules and are not appreciably affected by other ions in the solution. The dilute-solution regime is chosen as the standard state and here the ion's activity coefficient is arbitrarily set equal to unity. In this regime, the chemical potential becomes:

This equation implies a hypothetical 1 M ideal-solution standard state, which is equivalent to the real solution with an activity of unity. The former state is hypothetical because at a concentration of 1 M, the ionic species may be beyond the Henry's law region, where y ^ 1. This standard state is best illustrated by the concentration cell for the H+/H2 couple shown at the top of Fig. 10.6.3 The right-hand half-cell contains a fixed acid concentration c(H) in the Henry's-law region (which is the reason for the designation c(H)).

The half-cell reaction in both sides of the cell is given by Eq (10.20). The concentration in the left-hand cell is varied and the cell EMF s is measured. With the chemical potential of the left-hand half-cell described by Eq (10.25) and (10.26), and that in the right-hand half-cell by Eq (10.27), the chemical potential difference is:

The middle part of Fig. 10.6 is an illustrative plot of the measured cell potential as a function of H+ concentration in the left-hand half-cell, which is expressed as the first term in the brackets of Eq (10.29). The difference between the solid curve and the dashed line is due to the second term in the brackets, and so permits measurement of yi.

The cell potential is related to A^ by Eq (10.24) with z = 2:

2 Most treatments of electrochemistry [2,3] use molality, which is the concentration unit expressed as moles of species i per kg of water. Molarity and molality differ by less than V2 %.

3 A concentration cell is one in which the two half-cells contain the same solutes but at different concentrations.

Fig. 10.6 An H+/H2 concentration cell (top); variation of cell EMF with the H+ concentration in the left-hand half cell (middle); Activity-concentration plot derived from the cell potential measurements (bottom).

That -s is greater than the continuation of the Henry's law line indicates that the activity coefficient chosen for this example is greater than unity.

The values of y as a function of c so obtained yield the activity-concentration plot shown at the bottom of Fig. 10.6. The intersection of the two dotted lines in this graph represents the hypothetical 1- M standard state of H+ in water. To establish unit H+ activity, however, the actual acid concentration must be c*, not 1 M. The purpose of the above analysis was to show how a unique reference half-cell, the standard hydrogen electrode, or SHE, is constructed.

The SHE is a solution with unit H+ activity and supplied with H2 gas at 1 atm pressure. This unique half-cell is the reference with which all other half-cells are paired in order to describe the thermodynamics of aqueous electrochemistry.

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  • jonna
    Does activity coefficient is unity in the standard state of that ionic species?
    2 years ago

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