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Chapter 14

Q. 14.4

Response of an Ion-Selective Electrode

When a fluoride electrode was immersed in standard solutions (maintained at a constant ionic strength of 0.1 M with NaNO_{3}), the following potentials (versus S.C.E.) were observed:

[F^{−}] (M) E(mV)
1.00 × 10^{−5} 100.0
1.00 × 10^{−4} 41.5
1.00 × 10^{−3} −17.0

Because the ionic strength is constant, the response should depend on the logarithm of the F^{−} concentration. Find [F^{−}] in an unknown that gave a potential of 0.0 mV.

Step-by-Step

Verified Solution

We fit the calibration data with Equation 14-12:

E = constant − β(0.059  16) \log \mathcal{A_{F^{−}}}(outside)        (14-12)

\underset{y}{E} = m \underbrace{\log[F^{- }]}_{x} + b

Plotting E versus \log [F^{−}] gives a straight line with a slope m = −58.5 mV and a y-intercept b = −192.5 mV. Setting E = 0.0 mV, we solve for [F^{−}]:

0.0 mV = (−58.5 mV) \log[F^{−}]  −  192.5  mV ⇒ [F^{−}] = 5.1 × 10^{−4} M

Test Yourself     Find [F^{−}] if E = 81.2 mV. Is the calibration curve valid for E = 110.7 mV?
(Answer: 2.1 × 10^{−4} M; no, because calibration points do not go above 100 mV)

14-4