Dependence of the Cell Potential on Concentration

The process is spontaneous, as indicated both by the negative sign of AG° and by the positive sign of u- 

This reaction is used industrially to deposit copper metal from solutions containing dissolved copper ores. 

Using the data from Table 11.1, predict whether 1 M HNO3 will dissolve gold metal to form a 1 M Au solution. 

Solution The half-reaction for HNO3 acting as an oxidizing agent is 

The sum of these half-reactions gives the required reaction  

So far we have described cells under standard conditions. In this section we consider the dependence of the cell potential on concentration. For example, under standard conditions (all concentrations 1 M) the cell with the reaction 

The dependence of the cell potential on concentration results directly from the dependence of free energy on concentration. Recall from Chapter 10 that the equation 

Professor Walter Hermann von Nernst (1864-1941) was one of the pioneers in the development of electrochemical theory and is generally given credit for first stating the third law of thermodynamics. He won the Nobel Prize in chemistry in 1920 for his contributions to our understanding of thermodynamics. 

Equation (11.1), which gives the relationship between the cell potential and the concentrations of the cell components, is commonly called the Nernst equation after the German chemist Hermann Nernst. 

The Nernst equation is often given in terms of a log (base-10) form that is valid at 25°C  

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The standard values of free energy and also the redox potentials refer to standard concentrations of oxidized and reduced reactants, including the concentration (more precisely, the activity) of H = 1, pH = 0. The dependency of half-cell potentials on concentration is given by the following expression ... 

The dependence of a cell potential on the concentrations of the reactants and products may be derived from the known dependence of G upon concentration, (16-6). 

In ion-selective electrode potentiometry, the cell potential reflects the dependence of the membrane potential on the primary ion activity (concentration). According to the Teorell-Meyer-Sievers (TMS) theory, the sum of... 

In ISE potentiometry, the cell potential reflects the dependence of the membrane potential on the primary ion activity (concentration). According to the Teorell-Meyer-Sievers (TMS) theory, the membrane potential is the sum of three potential contributions namely the phase boundary potentials generated by ion-exchange processes at both interfaces, ((()i - c )n, i) and (([)n, 2 4>2). and the inter membrane diffusion potential, (c )ni i - <[)ni,2). If the membrane composition is constant and there are no concentration gradients within the membrane, then the membrane diffusion potential is zero and the membrane potential can be described by phase boundary potentials (see Figure 10.3b). This approach is also used to treat the response of ISE made with a range of membranes. 

The Nemst equation describes the dependence of the half-cell potential on concentration ... 

In practice, the dependence of the sensor signal on the concentration tp of certain components B in one of the electrode compartments, is of interest. It is useful to divide between the electrodes of the cell in order to ascertain how the signal function U (

defines electrode potentials and considers electrode potential equations which describe the dependence on temperature and composition quantities of the potential-forming substances. 

Thinking it Through The Nemst equation expresses the dependence of cell potential on concentration of the cell components. The equation itself may be given in the problem, or may be found in a general table of useful equations in other ACS exams. There may also be questions where you are expected to know the relationship, or derive it from changes in free energy. The value of Q is defined in the same manner as an equilibrium constant, but remember that these cell concentrations are not standard state concentrations.. For this problem, Q is evaluated by this expression. 

The cell potential of any voltaic cell is positive. The magnitude of the cell potential depends on the reactions that occur at the cathode and anode, the concentrations of reactants and products, and the temperature, which we will assume to be 25 C unless otherwise noted. In this section we focus on cells that are operated at 25 C under standard conditions. Recall from Table 19.2 that standard conditions include 1 M concentrations for reactants and products in solution and 1 atm pressure for gaseous reactants and products. The cell potential under standard conditions is called either the standard cell potential or standard emf and is denoted For the Zn-Cu voltaic cell... 

Amperometric sensors are small electrochemical cells consisting of two or three electrodes that are usually combined in a single body. A constant potential is applied, i.e., the sensor operates as a Faradaic cell, and a dependence of the measured current on the analyte concentration in the sample is obtained. As in ordinary amperometry, this requires a diffusion layer on the surface of the working electrode. This diffusion layer, in which the analyte concentration is depleted, arises because the analyte is consumed in the electrode reaction. In order for this depletion to occur, the electrode kinetics has to be faster than the... 

The majority of solid electrolyte sensors are based on proton conductors (Miura et al. 1989, Alberti and Casciola 2(X)1). Metal oxides that can potentially meet the requirements for application in solid electrolyte sensors are listed in Table 2.7. These proton condnctors typically do not have high porosity but rather can reach 96-99% of the theoretical density (Jacobs et al. 1993). Similar to oxygen sensors, solid-state electrochemical cells for hydrogen sensing are typically constructed by combining a membrane of solid electrolyte (proton conductor) with a pair of electrodes (electronic conductors) Most of the sensors that use solid electrolytes are operated potentiometrically. The voltage produced is from the concentration dependence of the chenucal potential, which at eqnihbrium is represented by the Nemst equation (Eq. 2.3). 

In fact, some care is needed with regard to this type of concentration cell, since the assumption implicit in the derivation of A2.4.126 that the potential in the solution is constant between the two electrodes, caimot be entirely correct. At the phase boundary between the two solutions, which is here a semi-pemieable membrane pemiitting the passage of water molecules but not ions between the two solutions, there will be a potential jump. This so-called liquid-junction potential will increase or decrease the measured EMF of the cell depending on its sign. Potential jumps at liquid-liquid junctions are in general rather small compared to nomial cell voltages, and can be minimized fiirther by suitable experimental modifications to the cell. 

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