Page 329 - Modern Analytical Chemistry

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312 Modern Analytical Chemistry

standard deviations from 0.15% to 4.7%. The smallest volume of sample that was
Diffusional
microburet successfully titrated was 20 mL.
More recently, a method has been described in which the acid–base titration is
11
conducted within a single drop of solution. The titrant is added using a microbu-
Agar gel
membrane ret fashioned from a glass capillary micropipet (Figure 9.23). The microburet has a
1–2 mm tip filled with an agar gel membrane. The tip of the microburet is placed
within a drop of the sample solution, which is suspended in heptane, and the titrant
is allowed to diffuse into the sample. The titration is followed visually using a col-
ored indicator, and the time needed to reach the end point is measured. The rate of
Sample Heptane the titrant’s diffusion from the microburet must be determined by calibration.
(a) Once calibrated, the end point time can be converted to an end point volume. Sam-
ples usually consisted of picoliter volumes (10 –12 L), with the smallest sample being
0.7 pL. The precision of the titrations was usually about 2%.
Titrations conducted with microliter or picoliter sample volumes require a
smaller absolute amount of analyte. For example, diffusional titrations have been
successfully conducted on as little as 29 femtomoles (10 –15 mol) of nitric acid. Nev-
ertheless, the analyte must still be present in the sample at a major or minor level
for the titration to be performed accurately and precisely.

Accuracy When working with macro–major and macro–minor samples,
acid–base titrations can be accomplished with relative errors of 0.1–0.2%. The prin-
(b)
cipal limitation to accuracy is the difference between the end point and the equiva-
Figure 9.23 lence point.
(a) Experimental set-up for a diffusional
microtitration; (b) close-up showing the tip
of the diffusional microburet in contact with Precision The relative precision of an acid–base titration depends primarily on the
the drop of sample. precision with which the end point volume can be measured and the precision of
the end point signal. Under optimum conditions, an acid–base titration can be ac-
complished with a relative precision of 0.1–0.2%. The relative precision can be im-
proved by using the largest volume buret that is feasible and ensuring that most of
its capacity is used to reach the end point. Smaller volume burets are used when the
cost of reagents or waste disposal is of concern or when the titration must be com-
pleted quickly to avoid competing chemical reactions. Automatic titrators are par-
ticularly useful for titrations requiring small volumes of titrant, since the precision
with which the volume can be measured is significantly better (typically about
±0.05% of the buret’s volume).
The precision of the end point signal depends on the method used to locate the
end point and the shape of the titration curve. With a visual indicator, the precision
of the end point signal is usually between ±0.03 mL and 0.10 mL. End points deter-
mined by direct monitoring often can be determined with a greater precision.

Sensitivity For an acid–base titration we can write the following general analytical
equation
Volume of titrant = k ´moles of analyte

where k, the sensitivity, is determined by the stoichiometric relationship between
analyte and titrant. Note that this equation assumes that a blank has been analyzed
to correct the signal for the volume of titrant reacting with the reagents.
Consider, for example, the determination of sulfurous acid, H 2 SO 3 , by titrating
with NaOH to the first equivalence point. Using the conservation of protons, we write
Moles NaOH = moles H 2 SO 3