CONDUCTOMETRIC METHODS

32.1 INTRODUCTION
* the measurements of the electrical conductance of solutions fall in the electroanalytic category    of ionics
     in contrast to the electrodics techniques involve the measurement of interfacial properties         as redox changes occur at an indicator or working electrode
* conductance is a nonspecific property of electrolytes that has been useful in measurements of    concentrations of ionic species
    in elucidating the extent to which ionogenic substances dissociate in solvents, and in the        development of electrolyte solution theory
* the applications of conductometric methods extend from systems of small conductance and   very low concentration( a saturated solution of AgCl at 25) to those of high conductance and   concentration( the fused salt mixture NaCl-KCl at 800)
   when a single strong electrolyte is present in dilute solution (in a pure solvent) its       concentration can commonly be found directly from a conductance observation
    at concentrations above 10
-3M, conductance may still be used to measure the concentration        if a calibration curve is first determined
* in the usual sample, several electrolytes(some of which are impurities) are present
   the contribution of an individual analyte to the conductance of such a solution cannot be       deduced in any simple, exact way
     even in this situation, however, the concentration of an ionic analyte single species may             be determinable conductometrically if it is the only species varying in concentration
      for example, this situation ideally holds for the elution of species in ion chromatography
         many analytes may be measured by conductometric titration
* with ordinary care, a precision of about 1% is possible in a conductometric determination
   with precision equipment and control of variables it may be extended downward to 0.1%
 
32.2 CONDUCTANCE RELATIONSHIPS
* conductance is the reciprocal of resistance
  a measured resistance depends on the spacing and area of a pair of electrodes and the      volume of solution between them
    if a sample of regular shape is placed between a pair of parallel electrodes, the resistance        measured increases linearly with sample length l and decreases linearly with        cross-sectional area A
* by defining the
specific resistance as the resistance of a cube of sample 1 cm on edge
   remove the dependence on shape and size
   in terms of , the measured resistance R of a sample is given by the expression R = l/A
     since R is in ohms, must have units   cm
                                Table 5.1
* the reciprocal of , the specific conductance (in ), is defined by the equation
                             = l / = l /AR                      (32.1)
   for measurements on solutions the ratio l/A is fixed by the spacing and size of electrodes in       the conductance cell (see Section 32.4)
* in dealing with dissolved electrolytes, it is convenient to define also an equivalent conductance   as the conductance associated with one Faraday of charge
   the conductivity of a slab of solution 1cm thick and of sufficient breadth and length to hold       the volume of solution that contains one equivalent of the electrolyte
   the equivalent conductance   is related to specific conductance by the formal expression
                  = 1000 / C                       (32.2)
     C is the normality of the solution
   since both positive and negative ions will share in carrying the current, we can write in       terms of the equivalent ionic conductances
+ and
        
++- = 1000 / C
   only at infinite dilution are the ionic conductances known precisely
                                      Table 32.1  Table 26.1
                                              Figure 5.1
* how should we relate conductances to the discussion of mass-transport processes?
   conductance is the experimental measure of the transport process called migration
* when we apply a potential difference across a pair of electrodes, ions first move to set up   electrical double layers at the electrode surface
   if the potential is sufficiently large, the oxidation or reduction of electroactive species also       begins
   as ions are removed by reaction, additional ions move toward the electrodes
                                         Figure 32.1  Figure 26-1
* the current through a unit cube of solution may now be expressed in terms of mobilities
   assume for simplicity that a single electrolyte has completely dissociated
     for the positive ions let N
+ be their number per cubic centimeter, u+ be their mobility, and          z+ be their charge
     for the negative ions will be denoted by N
-, u-, and z-
   the total charge arriving at the negative electrode per unit area per second is then        N
+u+z+eE
   to convert to cell current, we must include charge arriving at the positive electrode and        multiply by electrode area A
   the equation obtained is
               i = (N
+u+z+ + N-u-z-)eEA                (32.3)
* by use of Ohm's law and Eq.(32.1), we can formulate the specific conductance from Eq.(32.3)
                     = (n
+u+z+ + n-u-z-)e            (32.4)

Concentration Dependence
* at very low concentration, ions behave essentially independently
   any given ion moves in a medium where other ions are so distant that they fail to influence       its velocity or physical behavior
   but from concentrations of the order of 10
-6 upward ions approach each other sufficiently       often that interionic forces are important
     in addition many kinds of ions begin to associate
   where such a process occurs, conductance decreases proportionally
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* some interactions of ions and solvent

Mobility
* the mobility u of an ion is its velocity v under an electric field strength E of 1 Vcm
-1
               v = uE
   a force z
ieE acts upon each ion,
     where z
i is the charge on the ion and e the electron charge
   as a result of this force, an ion accelerates very rapidly until its motion is just offset by th       frictional resistance of the solution
     mobility is a measure of its steady-state motion
   so rapidly is a limiting velocity attained by ions that in audio-frequency conductance       measurements ions may be assumed to travel at a constant velocity, even though the field is       reversing a great many times per second
* the limiting velocity or mobility of an ionic species is determined by the viscosity of the    solvent, the solvated size of the ion, the concentration of the solution, and the    potential gradient
   for ions whose radius is about 0.5nm(5) or greater, Stokes's law describes approximately       the relation between the force on the ion F, bulk viscosity , and mobility u
                         u = F/6r                (32.5)
     where r is the radius of the ion
  equation (32.5) is of limited validity, but does apply to spherical ions moving in a solvent      whose molecules are considerably smaller than the ions
* most ions are of the same general size as solvent molecules
   they share in the general thermal agitation and have at best a randomly directed type of       progress
   the instantaneous velocity of any ion in a liquid is of the order of 10
4cms-1, but its mean free       path is so short that its average velocity toward an electrode is no more than 10-3 to 10-4        cms-1 when the electrical field strength is of the order of 1 Vcm-1

Electrophoretic Effect
* in an electrolytic solution, any ion is surrounded by a sheath of solvent molecules, each held   with reasonably strong ion-dipole forces
   when an ion moves, its solvation sheath tends to accompany it
    there is a continuing interchange between "bound" and "free" solvent in the sheath
* since ions of opposite charge move toward different electrodes, a given ion experiences a drag   as solvent "bound" to ions of opposite charge moves past
   for example, any negative ion moves through solvent that is not stationary but is actually       flowing in the opposite direction since it loosely accompanies positive ions

Relaxation Effect
* another important property of an electrolyte solution that affects ion migration arises from the    tendency toward electroneutrality
   any ion may be regarded as surrounded by an atmosphere of ions whose net charge is equal       to its charge but opposite in sign
   for an ion of charge +1, the essentially spherical atmosphere will include both positive and       negative ions but will have an overall charge of -1
   the dimensions of an
ion atmosphere can be shown to be inversely proportional to the ionic       strength of the solution
   at high dilution the radius of the atmosphere is large, in concentrated solutions it may be       only a few times the radius of the central ion
* when an ion moves, it tends to leave its atmosphere and a finite time will be required for the   thermal and electrical forces to reestablish the randomly arranged atmosphere
  each ion is therefore subjected to a transient restoring force exerted by its old atmosphere      as it decays
   the opposing force tending to return the central ion to its original location is small at best       and because of its time-dependent behavior is termed a relaxation effect
    this force also tends to diminish conductance

* according to the general electrostatic theory of electrolytes developed by Fuoss and Onsager   we can represent conductance as a function of concentration C by the following equation
               =
0 - SC1/2 + EC log C + JC             (32.6)
   where
0 is the equivalent conductance at infinite dilution, S is the Onsager coefficient of the       limiting conductance law, E is a constant, and J is a factor dependent on ion size
    appropriate modifications to Eq. (32.6) can be made to cover association of electrolytes
   the equation has been shown to hold generally up to concentrations of about 0.1N

32.3 ALTERNATING-CURRENT MEASUREMENTS
* because conductance involves the transfer of mass, both solution and electrodes are altered   during a measurement
   when a dc voltage is imposed across a conductance cell there result two immediate,       undesirable effects
   the electrodes polarize slightly as
    (a) the solution layer near the electrodes tends to become depleted in any species being          oxidized or reduced
    (b) the electrode surfaces are altered by the products of electrolysis
   the effects are not serious if the current is kept small (<10
-7A), but attention must       customarily be given to them
    if a larger current flows, a dc conductance measurement may well be invalid
* when an
audio frequency voltage is applied, the changes described are largely minimized         because of the frequency reversal of electrolysis, the ionic movement and electrolysis            that take place during one half of a cycle can be completely or nearly completely            destroyed during the second half of each cycle
    concentrations are maintained essentially constant even though a current exists
* the conductance of the solution and the current density at the electrode for a given applied   voltage are key variables in arriving at an optimum frequency
   if solutions of extremely low conductivity( <10
-7) are being studied or the current           density is very low, even dc measurements can be accurate
       if the conductance is slightly larger, 60Hz line current may allow precise measurements
         usually, however, a frequency of about 1000 Hz is preferable
   where great precision is required, we find the conductance at several frequencies in the       audio range and extrapolate to infinite frequency
* larger conductance values are usually found at radio frequencies (10
5107Hz)
   the change is a direct consequence of the increased importance of circuit capacitances and       inductances
    at radio frequencies, the interpretation must thus be broadened to include the bulk        capacitance of the cell as well as the resistance of the solution
      in Section 32.7
* a further aid in the elimination of surface polarization effects is the use of platinized platinum    electrodes
   finely divided platinum has been deposited in a thin, adherent layer by electrolysis
   as a result of the greatly increased surface area, the reunion of liberated hydrogen and           oxygen appears to be catalyzed
        the polarization from this source is thus minimized
      the large surface area also eliminates concentration polarization

32.4 CONDUCTANCE CELLS
* the usual envelopes for cells with electrodes are made of hard glass
  where ruggedness is required, other inert, stable dielectrics such as hard rubber and some of      the plastics are also in common use
    the electrodes are generally square pieces of stiff platinum foil aligned parallel to each        other
    the electrodes be rigidly supported at the desired spacing
                                            Figure 32.2  Figure 1

Leads
* special attention is always given to the arrangement of the leads to the electrodes, except   where an accuracy of from 2 to 5% is adequate
  if leads are bare and are brought out close together through the solution, stray electrolytic      and capacitive current will pass between them
   accordingly, it is good practice to use insulated lead wires and bring them out of the       electrode chamber in opposite directions
* note that all obstructed spaces where mixing will not occur readily have been eliminated in the   cells of types (a) and (b)

Cell Constant
* the resistance of a solution between the electrodes of a cell is a function not only of solution   specific conductance but also of the volume of conducting solution between the electrodes
  for a pair of parallel electrodes of area A and spacing l, may be obtained by rewriting Eq.      (32.1) as R = l/Ak  
   in practice we determine the ratio l/A, termed the
cell constant, for each cell by measuring       its resistance when filled with a conductance standard
   solutions of potassium chloride of known concentration are primary standards, their       conductances having been accurately determined in cells of known electrode geometry
                                               Table 26-2
* for accurate conductance work over a range of concentration it is desirable to use cell of different cell constant
  in aqueous work cell constants from about 0.1 to 10 are needed
      in nonaqueous media other ranges are called for
  the reason is that a bridge of conventional design(Section 32.5) is capable of greatest      accuracy if the cell resistance falls in the range from 1 to 30 k

Thermostating
* control of temperature is indispensible if reliable conductance measurements are sought
  the specific conductance of electrolytes increases on the average about 2% per degree      Celsius
    to reduce the error from this source to 1% therefore requires regulation to 0.5
    to reduce the error to 0.01% requires regulation to 0.005
* a constant-temperature bath filled with a light transformer oil is often used to achieve the   desired regulation
   water is seldom used as the fluid because of accompanying undesirable capacitance effects       between cell and ground

32.5 THE AC WHEATSTONE BRIDGE
* this bridge is the basic instrument for determining conductance
   the dc version of the Wheatstone bridge was treated in Section 3.4
     background is now assumed familiar
                                  Figure 32.3  Figure 5.3
                                                 Figure 2
* the condition of balance of the dc bridge is that the potential at points C and D must be equal,   yielding the equation
                       R
1/R2 = R3/R4               (32.7)
    conductance is then obtained by taking the reciprocal of R
3
   this condition holds for balance of the ac bridge to within 0.1%
* some variation is to be expected since the ac bridge is properly an
impedance bridge
   sources of error in the ac bridge will be considered below

Range of Measurement
* the range of resistance measurable may be deduced from Eq. (32.7)
   if R
1 = R2, unknown resistance R3 can be measured by the bridges shown in Fig. 32.3 when       its value falls within the range 0<R3R4

    since this span is short, ways to extend it are important
     one method is to vary the ratio R
1/R2 as well as R4
      bridges offering several set ratios of R
1/R2 from 0.01 to 100 are common
* range is traded off for accuracy in these bridges
   they are accurate at best to about 1%
* alternatively, range can be extended in conductance measurements by the strategem of use of   cells of different cell constant
   this approach permits use of equal values for R
1 and R2, which is necessary to the       construction of precision conductance bridges
* If R
1 and R2 have equal values and have been carefully constructed of stable,   low-temperature-coefficient alloy, we can assume their resistances will change in like amount   with time and temperature and keep the ratio invariant

Sources of Error
* contact resistance in switches and in leads to the cells, a major potential source of error, can    be minimized by keeping every contact possible in series with the power supply(V) or detector
* consider certain sources of error peculiar to the use of ac
   the resistors that comprise the bridge arms possess distributed inductance and capacitance
      regard the cell itself as a combination of capacitances and resistances
   a considerable number of possible stray current paths in an ac bridge
     any part of the bridge has some capacitance with respect to ground and offers a leakage             path
        by virtue of the inductance of the resistance coils, there exists the possibility of inductive             pickup of stray ac currents from power lines or from the oscillator that supplies the             bridge power
* the contribution of error from these sources may be reduced considerably by proper   resistance, shielding, and physical arrangement
  the resistors should be noninductively wound
    the bifilar winding, in which the length of wire required to obtain the desired resistance is        doubled back on itself and then wound on the form, is widely used to minimize inductance
  it is advantageous to have enough residual capacitance so that the capacitive reactance will      nearly cancel the inductive reactance at the operating frequency
    the cell capacitance C
3 can be compensated by placing a variable capacitor C4 in the bridge        parallel with resistance R4
                                              Figure 32.3b
* for examination of the more difficult problem of eliminating stray leakage paths the reader may   consult references 6-8

Power Sources
* some industrial and field conductivity instruments operate on 60Hz ac stepped down from a   power line
  much better accuracy is generally secured by operation at audio frequencies in the range of      from 500 to 4000 Hz
    in this case, a sine-wave ac signal generator is usually employed
  its output should ideally be of a single frequency(a pure sine wave) and should be variable in      amplitude from zero to several volts
* if the harmonic content is minimized, a more precise balance can be obtained, for the problem   of phase shifts will be simplified
* a variable voltage output allows flexibility of operation

Phase Relationships
* for a true bridge balance, the ac waves must be in phase at points C and D  
  this condition requires either no phase change in either arm or the same phase change in      each
    only the latter is a possible solution to the requirement
  the capacitance and inductance of the resistors and cell can be minimized but not eliminated
* if accuracies of the order of 1% are satisfactory we may ignore the phase difference, providing   the bridge resistors have been wound with reasonable care
  for most nonresearch measurements and conductometric titrations, the phase difference          can be neglected
     work in which the precision must be 0.1% or better calls for a careful examination of the         phase dependence of the arms
  it is customary to simplify the problem by using matched resistors for the ratio arms R
1 and      R2 so that not only are the resistances equal, but the phase behavior is identical
  there remains the question of whether the phase difference introduced by the cell in arm 3      will be equal to that caused by the parallel R
4-C4 combination
   a thorough discussion is beyond the scope of this book, but a limiting case can be considered
    if the R
4-C4 combination introduces a phase shift of less than about 10 minutes of arc, R4         can be taken as equal to the cell resistance R3 within 0.1%

Bridge Amplifiers
* an amplifier designed to give a logarithmic response offers a definite advantage
   for it will produce the greatest response where the signal is smallest, near the point of       balance
* some protection against overload must also be provided and is not difficult to incorporate
* amplifiers inevitably have considerable capacitance to ground
  since the possibility of picking up stray signals is therefore large,
     electrostatic shielding of the amplifier is essential, and
     transformer coupling between bridge and amplifier or between stages of the amplifier         should be avoided
   where transformers must be used,
       they should be small and carefully shielded magnetically
       it will also relieve the situation considerably if the bridge points C and D can be operated           at zero potential by means of a Wagner ground or a similar device
                                Figure 32.4  Figure 24.10
* many commercial bridges use 60 Hz line voltage in lieu of an audio frequency of 500-1000 Hz   such as the oscillator would supply
   the null detector may be an electron ray tube (magic eye), oscilloscope, or other suitable       device to register the level of ac voltage across the bridge

Conductometric Titrator
* where only changes in conductance and not absolute values are of
  interest, a Wheatstone bridge is not mandatory
  Ohm's law, V = iR, suggests that changes in the resistance of a cell might be measured by      determining changes in i when a constant voltage V is imposed, i = V/R
   it is easy to instrument this approach using operational amplifiers
                                           Figure 32.5
   in the circuit, operational amplifier A serves as a current amplifier and provides an output       voltage proportional to i
* the instrument in Fig 32.5 is especially suitable for conductometric titrations, for which we   need only relative values of conductance
  it is also usual to provide for attenuation in the inverting amplifier by adjustments of the ratio      of feedback to input resistance(R
f/Rcell) that determines the gain of this device
* we should estimate in advance the maximum value of conductance expected during a titration   and use it as a basis for setting the attenuation to the level to be employed throughout the   titration

32.6 CONDUCTOMETRIC TITRATIONS
                                                  Figure 23-3
* in solution, chemical reactions that involve electrolytes are accompanied by a conductance   change
  if the change is sufficient, we may often determine the end point of the reaction simply by      monitoring the conductance
* we can best understand the origin of the variation by inspection of a representative ionic   reaction:
                   A
+B-  +  C+D-    AD  +  C+B-
               unknown     titrant
   where CD is taken as the titrant and AD, one of the products, to be a weakly ionized species
   up to the end point,
      the equivalents of C+ ion in the solution at any time are essentially equal to the          equivalents of A
+ that have been used up to form species AD
      the concentration of B
- ions does not change
      the conductance attributable to C
+ ions increases gradually
        during titration while that of A
+ ions decreases
   after the end point
     further addition of titrant sends the conductance upward in proportion to the volume added,         since the concentration of C
+ and D+ ions in the solution grows steadily
                                             Table 5.5
                          Figure 32.6  Figure 24.13  Figure 5.5  
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example 32.1  the titration of 0.01 M HCl by 0.1 M NaOH gives the V-shaped conductance curve in Fig. 32.6
  as long as rapidly moving hydrogen ions are being replaced by much more slowly moving      sodium ions, the conductance falls
  after the reaction is complete, further addition of NaOH adds both sodium ions and      fast-moving hydroxyl ions and conductance rises sharply and linearly
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* in a manual titration we take conductance values periodically after addition of titrant and mixing
  amounts of titrant should be roughly calculated on the basis of estimated end point and the      need to obtain four or more points on each branch of the conductometric titration curve well      away from the end-point region
* we eliminate any appreciable dilution error resulting from the increase in solution values at   each point by multiplying the observed conductance by the ratio (V + V
0)/V0,
     where V
0 is the original solution volume and V is the volume of titrant added
* we then plot the data and draw the best straight line through each set of points
   we should take the point of intersection as the end point
                                                     Figure 32.6
* with an operational amplifier system like that in Fig. 32.5, we obtain a titration curve   automatically, provided we add titrant slowly and secure complete reaction at all times
   note there is no provision to correct for dilution as the curve is recorded
   linear parts of the curve should be extrapolated to their intersection to locate the end point
* conductance data near the end point are less valuable
   since in this region there is little excess of any common ion and eactions may not be       complete
    for example, near the end point a weak acid or a weak base is more fully dissociated than       at other times
       if a slightly soluble precipitate forms in a titration, it will be more soluble near the end        point
   any incomplete reaction leads to curvature in the plot
* since we can determine an end point by reliance on data far from the end-point region, we can   follow conductometrically many reactions that are too incomplete for their end point to be   located potentiometrically
   for example, phenol, boric acid, and other quite weak acids can be successfully titrated in       aqueous solution conductometrically but not potentiometrically
* we can also apply the conductometic method to very dilute solutions and to some nonaqueous   solutions with good precision if we use sufficiently sensitive bridges and good thermostating
   against these advantages we must set a number of limitations considered later
* in any analysis it is valuable to be able to interpret the form of the characteristic curve    obtained
  this way we can gain both insight into the behavior of a system and assurance that a reaction      is progressing
  since at the concentration levels that usually prevail conductance varies nearly linearly with      concentration, it is not difficult to predict behavior in conductometric titrations
    to predict a titration curve we also need a listing of relative ionic conductances
                                                  Table 32.1
  though the data are valid at infinite dilution, they provide a basis for comparison even at      ordinary concentrations
    the contribution of each ionic species is presumed independent of other
   Figure 32.6b shows the result of applying this kind of analysis to the titration system of                                                     Figure 32.6a
                                                    Figure 32.7
* with bridges like those in Figs. 32.4 and 32.5, we may expect a precision of 1% or better under favorable circumstances
  where additional refinement in titration and thermostating is possible and we can arrange the      use of a high-precision bridge like the Jones bridge manufactured by Leeds and Northrup,      reliability can sometimes be of the order of 0.1%

Limitations and Sources of Error
* we may group the salient "chemical" limitations and sources of error of the conductometric   method as follows :
  an indistinguishable difference in slope of intersecting lines,
  curvature in one or more conductance lines beyond end-point region,
  volume increase during titration, and
  temperature change

* in these comments we assume that a bridge or other instrumentation yielding results accurate    to 1% is used
  with better thermostating and more precise instrumentation we may, of course, increase the      acceptable range of conductance titrations
* the accuracy of locating the end point of a reaction depends significantly on how greatly    intersecting conductance curves differ in slope  
  in this connection, compare the curves in Fig 32.6a and 32.7a
    accuracy is certain to be smaller in the latter case
  indeed, if the change in slope is quite small an ionic reaction cannot be followed      conductometrically
   usually this difficulty is inherent in a system and may arise for any of several reasons
   it may be the result of a high concentration of a foreign electrolyte
    most redox reactions are ill adapted to conductometric monitoring
     often such solutions must be strongly acidic (as in dichromate and permanganate         oxidations), basic, or contain added salt (as in many iodometric procedures)
    in a highly conducting solution a small change in conductance attributable to the desired        reaction is difficult to detect precisely
   small differences in slope may arise because the sample is dilute
   there may be little change in slope because the sample is a very weak electrolyte
    Figure 32.7a gives an illustration of this situation
     in all such cases, unless instrumentation capable of better than 1% precision is available, a         conductometric titration will not be feasible
  the second source of chemical error, incompleteness of reaction or the occurrence of side      reactions, needs only brief comment
     if a product of the reaction undergoes substantial hydrolysis, ionization, dissolution, or         indeed almost any side reaction, there will be pronounced curvature in the conductance         curve and little possibility of determining the end point reliably
    often the disturbing effects may be suppressed

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example 32.2
* in aqueous systems it is common to add ethanol to reduce ionization or to lower the solubility   of a precipitate
  when we can no longer locate the linear portion of a curve easily, we can sometimes apply a      mathematical method of end-point calculation

Mixtures of Acids or Bases
* often, we may analyze a mixture of a strong and a weak acid (or a strong and a weak base) by   conductometric titration
    the method is especially attractive when simple photometric and potentiometric methods do        not give satisfactory results
   so long as one acid is strong and pK
a values differ by at least 5, the portion of the       conductance curve attributable to each acid is definite
   to interpret the graph, we should view the titration as a combination of the separate       titrations of HCl and acetic acid

Precipitation Titrations
* before deciding to follow a precipitation reaction conductometrically, we must study the growth   of the crystals that would be involved and their tendency toward adsorption
  even though there is a sufficient change in conductance during the reaction, the slowness of      precipitation, coprecipitation, appreciable solubility, and adsorption effects can greatly      increase the uncertainty in the results
* there are very favorable instances for the application of precipitation titration, for example, in    determining some of the alkaline earths, by using sulfates
  a particularly good illustration is the titration of solutions containing barium ions, using      standard sulfuric acid solutions
  the titration curve obtained resembles that in Fig. 32.7a
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32.7 OTHER APPLICATIONS
*
direct conductance determinations of concentration are most often carried out when there is   only a single electrolyte
  the determination is possible because, as noted for conductometric titrations, an      approximately linear relation is observed between specific conductance and concentration      from 10
-5 to 10-1M
* provision for offsetting the effect of temperature becomes important in industrial   determinations, where the temperature of a process stream may vary widely
* with a weak electrolyte allowance must be made for the effect of one or more equilibria

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example 32.3. conductance is widely used to monitor water purity in laboratory and industrial boiler water supplies. Pure water has a specific resistance of about 10 M. Can conductance measurements also be applied successfully to estimation of salt levels in water?
   for estimation of salt concentrations only an acceptable working curve is needed, a plot of       specific conductance for a calibrated, thermostated cell for the analyte system
    in oceanography salinity (really a total concentration of salts) can be registered on a scaled        conductance meter

example 32.4. we can study the rate of the following reaction by monitoring the concentration of BH+ and CH3CH2NO2- conductometrically:
                          CH
3CH2NO2 + B = CH3CHNO2- + BH+
  here B is a neutral organic base
   note that the only ionic species present are those formed during the reaction
   in calculating the results, we assume the ions that are produced do not hydrolyze or       associate at the concentration level used

example 32.5. when a conductance detector is used in ion chromatography what choices must be made about variables such as conductance cell constants, dc or ac measurement, mobile phase conductivity, and solution temperature?
 * as long as the chromatographic column resolves the ions in a sample, detection of species    requires only that conductance is higher when they elute than it is for the mobile phase alone
 * to preserve the resolution effected by the column the conductance cell should have a minute    volume (about 2 L)
    to ensure low detection limits the cell should also have a large electrode area
 * mobile phase conductivity can be electronically suppressed to achieve a stable chromatograph     baseline
    with that stability minimum changes in conductance of 1040parts in 10
5 can be detected
    conductance is commonly measured at 410 kHz
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* when conductance is used to determine concentrations at trace levels, special care is required
   since the measurement is not selective, we must either first remove foreign conductors or       make a correction
    in some instances, limiting ionic conductances can be used to calculate the concentration
    more often we prepare a calibration curve in advance

High-Frequency Methods: Oscillometry
* conductance measurements are also obtained at high audio and radio frequencies(about   10
 107Hz)
  because substantially different instrumentation is required for rf measurements, these      methods are usually collected under the name
oscillometry
* the advantage gained in oscillometry is that no metal electrodes need be in contact with the    solution under investigation
   for the measurements it is sufficient to place the glass cell or section of tubing holding the       sample solution between the plates of a capacitor (or within the coil of an inductor) that is
      a part of the resonant circuit of an oscillator
* in instruments that handle separate samples, the oscillator itself serves as a detector
   since the frequency of its output depends on the conductance and dielectric constant of the       solution
   the capacitor type of arrangement is the more sensitive of the two means of coupling the       solution to the oscillator circuit
* for
continuous monitoring of the flow of a solution two loops or coils of wire are wrapped    around the tube or pipe carrying the conducting solution far enough apart so that the   conducting solution is the only current loop connecting them
  then the rf signal in the primary coil induces a signal in the second coil that is a measure of      the conductance and capacitance of the solution in the tube and can be amplified and      registered directly
  a more precise arrangement is use of a circuit that provides for a null-balance readout
   oscillometry is useful in monitoring an electrolyte stream mainly when contact with metal       electrodes is undesirable
* it is possible to carry out some nonaqueous titrations by oscillometer with surprising sensitivity   if one component has a markedly different dielectric constant
  cells should be used that provide adequate shielding and are insensitive to fluid level when      filled beyond a given point
   for example, water is often determined in organic fluids by this method,
     binary liquid pairs such as ethanol(=24.3)-nitrobenzene(= 34.8) or benzene(=2.27)-         chlorobenzene(=5.62) can be analyzed with precision