Dependence of emf on Concentration

I Nernst also formulated the third law of thermodynamics, for which he received the 1 Nobel Prize in 1920. 

The emf of a cell depends on the concentrations of ions and on gas pressures. For that reason, cell emfs provide a way to measure ion concentrations. The pH meter, for example, depends on the variation of cell emf with hydrogen-ion concentration. You can relate cell emfs for various concentrations of ions and various gas pressures to standard electrode potentials by means of an equation first derived by the German chemist WalthCT Nanst (1864—1941).  

Recall that the Iree-energy change, AG, is related to the standard Iree-energy change, AG°, by the following equation (Section 19.6)  

Here Q is the thermodynamic reaction quotient. The reaction quotient has the form of the eqirihbrium constant, except that the concentrations and gas pressures are those that exist in a reaction mixture at a given instant. You can apply this equation to a 

This resnlt rearranges to give the Nernst equation, an equation relating the cell emf to its standard emf and the reaction quotient. 

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Taking another example to illustrate the dependency of emf on concentration (temperature effect is not considered, as in the previous example), reference may be drawn to the familiar Cu-Zn cell a shown in standard notation as ... 

The cell, Pt(s) H2(g) 1 atm HCl unit activity AgN03(aq) Ag(s) has the following dependence of emf on concentration at 25°C. Use a graphical procedure to find. Why is it necessary to have highly accurate emf data What is the value of AG for this cell Comment on the fact that emf studies can fiimish such a quantity. How could other thermodynamic quantities be found for this cell reaction ... 

The dependence of emf on the activities or concentrations of the products and reactants of a cell reaction follows directly from a consideration of the relationship between emf and free energy change. For the cell reaction... 

Fig. 6.11 Dependence of EMF of (a) [Au,NaNO/NASICOM/Pt] and (b) [Au.NaNOj-LijCOj/NASICOM/Pt] cells on the concentration of NO and NO (T = 150°C) (Reprinted with permission from Yamazoe and Miura (1998). Copyright 1998 Kluwer Academic)...

To establish how the emf of a cell depends on concentration, we first note that the emf is proportional to the reaction Gibbs free energy (Eq. 2). We already know how AGr varies with composition ... 

FIG. 6 Dependence of the square root of the SHG intensity ( I(2a>)) for membrane 2 without KTpCIPB (a) with KTpCIPB (b) on K+ ion concentrations in the adjacent aqueous solution containing KCl (O) and KSCN ( ), respectively. Inset The corresponding observed EMF to KCl and KSCN. The concentrations of ionophore 2 and KTpCIPB were 3.0 X 10 M and 1.0 x 10 M, respectively for both SHG and EMF measurements. The data points present averages for three sets of measurements. Error bars show standard deviations. (From Ref. 15.)... 

Fig. 8 The dependence of the electromotive force (EMF) ofCd(ll) ion-selective electrode on logarithm of Cd(ll) concentration in M NaNOs at pH 7. Solid lines, calculated response curves on the basis of Eq. (7) in Ref 399.

The dependence of cell emf on the concentrations of reactants and products of the cell reaction is of fundamental importance in the understanding and design of certain practical battery systems. As a cell undergoes discharge, reactants are steadily converted to products until one of the reactants species is completely exhausted. Consider the cell reaction A + B -> C + D, where A-D are all solution species. For this system,... 

Selenium electrodes were obtained by electroplating selenium onto various substrates from a 10.45 M solution of potassium selenite. They were measured against a calomel electrode and the substrate did not affect the potentials. The emf of the selenium-calomel cell was measured with test solutions of potassium selenite of concentrations 0.1, 1, 2, 4, 6, 8, and 10.45 M. The solutions also contained 1 M KOH. The dependence of the emf on pH was studied in another series of experiments. 

Reversible reduction and oxidation processes are always thus connected Suppose that the actual conditions m the cell itself are such that a reduction is going on, yielding an evm f. of E Then if an external emf E be applied m the opposite direction, the reduction process will stop, and on making the externally applied emf just greater than the direct emf, an oxidation will take place The above formula bnngs out the dependence of the oxidising force upon the concentration of the various components which are taking part in the reaction... 

A new method for using photo-electromotive force (Photo-EMF) in the detection of gas and for controlling sensitivity is proposed (Vashpanov et al., 2011). Photo-EMF on the heterojunction between the PSi thin layer and the crystalline silicon wafer depends on the concentration of ammonia in the measurement chamber. A light-transparent contact to the porous Si was formed. Photo-EMF sensitivity corresponding to the ammonia concentration in the range from 10 ppm to 1000 ppm can be controlled by the intensity of the source of illumination. 

In the voltaic cells we have looked at thus far, the reactive species at the anode has been different from the reactive species at the cathode. Cell emf depends on concentration, however, so a voltaic cell can be constructed using the same species in both half-cells as long as the concentrations are different. A cell based solely on the emf generated because of a difference in a concentration is called a concentration cell. 

After the work of Nemst on electrode potentials in 1889 (Chapter 13), it became apparent that EMF measurements could be used in analytical work. The first potentiometric titration was performed in 1893 by Robert Behrend (1856-1926). He titrated a solution of mercury(i) nitrate with potassium chloride, thus precipitating mercury(i) chloride. The titration vessel contained a mercury electrode, and was separated by a porous membrane from another container of mercury(l) nitrate with a mercury electrode. The EMF of the resulting cell depended on the concentration of the mercury ions in the titration vessel, and showed a pronounced change in the region of the end-point. 

The value of Km depends both on the activity um and on the particular combination of analyte ion and interfering ion. Recently Bakker [48] suggested another equation which described the EMF versus concentration behavior of an ISE with a higher accuracy. The selectivity coefficients are determined here without conditioning the electrode with the measured ion, which yields constant selectivity coefficients. The new equation describes the situation when a monovalent analyte ion r is interfered by a divalent ion especially well, and vice versa ... 

The potentiometric response of a polymer sensor is shown in Fig. 3.12b, and, as is typical for poten-tiometric sensors, can be detected over many orders of magnitude in concentration. The EMF dependence on the logarithm of the hydrogen partial pressure is very close to linear but is non-Nems-tian. A nonlinear least-squares fit (NLLSF) of the data yielded a slope of 166 mV, well above the value predicted by the Nemst equation. If the data for 0.01% hydrogen is discarded, the value of the resultant... 

An electrode potential depends on concentrations of the electrode substances, according to the Nemst equation. Because of this relationship, cell emfs can be used to measure ion concentrations. This is the basic principle of a pH meter, a device that measures the hydrogen-ion concentration. 

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