Section 3 Measuring Electrical Current

Figure 7-5 shows an apparatus in which an electric current can be passed through water. As remarked in Section 3-1.2, the electric current causes a decomposition of water. As work is done (electrical work), hydrogen gas and oxygen gas are produced. Measurements of the electric current and voltage show that 68.3 kcal of electrical work, W, must be done to decompose one mole of water. The equation for the reaction is... 

To illustrate these considerations, and to introduce a detector in which measured x-ray intensity is given by an electric current, we shall use experimental results obtained on the simple laboratory photometer described in Section 3.5. The general approach is broadly applicable in absorptiometry with polychromatic beams. 

Conductivity is a very important parameter for any conductor. It is intimately related to other physical properties of the conductor, such as thermal conductivity (in the case of metals) and viscosity (in the case of liquid solutions). The strength of the electric current I in conductors is measured in amperes, and depends on the conductor, on the electrostatic field strengtfi E in tfie conductor, and on the conductor s cross section S perpendicular to the direction of current flow. As a convenient parameter that is independent of conductor dimensions, the current density is used, which is the fraction of current associated with the unit area of the conductor s cross section i = I/S (units A/cnF). 

In addition to their use as reference electrodes in routine potentiometric measurements, electrodes of the second kind with a saturated KC1 (or, in some cases, with sodium chloride or, preferentially, formate) solution as electrolyte have important applications as potential probes. If an electric current passes through the electrolyte solution or the two electrolyte solutions are separated by an electrochemical membrane (see Section 6.1), then it becomes important to determine the electrical potential difference between two points in the solution (e.g. between the solution on both sides of the membrane). Two silver chloride or saturated calomel electrodes are placed in the test system so that the tips of the liquid bridges lie at the required points in the system. The value of the electrical potential difference between the two points is equal to that between the two probes. Similar potential probes on a microscale are used in electrophysiology (the tips of the salt bridges are usually several micrometres in size). They are termed micropipettes (Fig. 3.8D.)... 

If no side reactions occur at the electrode that would participate in the overall current flow, then the Faraday law can be used not only to measure the charge passed (i.e. in coulometres see Section 5.5.4) but also to define the units of electric current and even to determine Avogadro s constant. 

At sufficiently high anodic potentials, only the anodic reaction (1) wiU proceed at the experimental electrode. Then on the counter electrode the reactions (2) or (3) causing CMT measurements will proceed at the same electrical rate. These CMT measurements should coincide with the value of current measured electrically. The only restriction in this case (other than those discussed in Section II.2) is that dissolved metal ions must not be plated onto the counter electrode in a cathodic reaction in parallel with (2) or (3). 

If we choose a set of standard conditions (cf. Section 2.3) and one convenient half-cell to serve as a reference for all others, then a set of standard half-cell EMFs or standard electrode potentials E° (Appendix D)1-9 can be measured while drawing a negligible electrical current, that is, with the cell working reversibly so that the equations of reversible thermodynamics... 

Resistivity, p, measures how well a substance retards the flow of electric current when an electric field is applied J = Elp, where J is current density (current flowing through a unit cross section of the material, A/m2) and E is electric field (V/m). Units of resistivity are V m/A or fl m, because... 

Voltammetric methods in these methods, a potential is applied to the working electrode using a three-electrode setup (see section 1.6). The electrical current, resulting from charge transfer over the electrode-electrolyte interface, is measured and reveals information about the analyte that takes part in the charge transfer reaction. The potential applied can be constant (chronoamperometry, section2.5), varied linearly (cyclic voltammetry, section 2.3) or varied in other ways (Chapter 2). 

As described in section 2.4.2, an impedance experiment involves the application of an electrical signal (E or O) and the measurement of an electrical current or a potential. Consider that a potentiostatic experiment (application of a potential) with three types of input signals can be used for determination of the impedance49. 

In the previous section we considered the conditions under which mechanical resonances would occur in a TSM resonator. In considering only the mechanical properties of the crystal, however, we neglected consideration of how these resonances would actually be excited or detected. The device uses a piezoelectric substrate material in which the electric field generated between electrodes couples to mechanical displacement. This allows electrical excitation and detection of mechanical resonances. In constructing a practical sensor, changes in resonant frequency of the device are measured electrically. The electrical characteristics of the resonator can be described in terms of an equivalent-circuit model that describes the impedance (ratio of applied voltage to current) or admittance (reciprocal of impedance) over a range of frequencies near resonance. 

In voltaic cells, it is possible to carry out the oxidation and reduction halfreactions in different places when suitable provision is made for transporting the electrons over a wire from one half-reaction to the other and to transport ions from each half-reaction to the other in order to preserve electrical neutrality. The chemical reaction produces an electric current in the process. Voltaic cells, also called galvanic cells, are introduced in Section 17.1. The tendency for oxidizing agents and reducing agents to react with each other is measured by their standard cell potentials, presented in Section 17.2. In Section 17.3, the Nernst equation is introduced to allow calculation of potentials of cells that are not in their standard states. 

Scientists measure many different quantities—length, volume, mass (weight), electric current, voltage, resistance, temperature, pressure, force, magnetic field intensity, radioactivity, and many others. The metric system and its recent extension, Systeme International d Unites (SI), were devised to make measurements and calculations as simple as possible. In this section, length, area, volume, and mass will be introduced. Temperature will be introduced in Sec. 2.7 and used extensively in Chap. 12. The quantities to be discussed here are presented in Table 2-1. Their units, abbreviations of the quantities and units, and the legal standards for the quantities are also included. 

Two other types of analytical methods are based on mass. In gravimetric titrimetry, which is described in Section 13D, the mass of a reagent, of known concentration, required to react completely with the analyte provides the information needed to determine the analyte concentration. Atomic mass spectrometry uses a ma.ss. spectrometer to separate the gaseous ions formed from the elements making up a sample of matter. The concentration of the resulting ions is then determined by measuring the electrical current produced when they fall on the suiface of an ion detector. This technique is described briefly in Chapter 28. 

The electrical resistivity of a substance measures its resistance to an electrical current (equation 5.3) for a wire of uniform cross-section, the resistivity (p) is given units of ohm metre (flm). 

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