Homework 3 Solutions

1001 180 mv 100 the range of reliable measurement

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Unformatted text preview: 100 c. Now consider that the solution contains 100 mmol/L of NaCl, in addition to HCl in variable € concentrations. Derive and sketch Vout as function of pH. Accordingly, what is the range of pH that we can reliably measure with this H+ ­selective electrode? GHK equation: + + − RT PK ⋅ [H ]− + PNa ⋅ [ Na ]− + PCl ⋅ [Cl ]+ Vout = ln F PK ⋅ [H + ]+ + PNa ⋅ [ Na + ]+ + PCl ⋅ [Cl − ]− = (60 mV ) ⋅ log10 = (60 mV ) ⋅ log10 1000 ⋅ [H + ]− + 1 ⋅ 0.1 + 0.001 ⋅ 0.1 ( 1000 ⋅ 0.1 + 0.001 ⋅ 0.1 + [Cl − ]− ) 1000 ⋅ [H + ]− + 0.1001 ( 100 + 0.001 ⋅ 0.1 + [Cl − ]− )  ­ pH1 ~ pH4 € Vout ≅ (60 mV ) ⋅ log10 1000 ⋅ [H + ]− 100 = (60 mV ) ⋅ (1 − pH )  ­ pH4 ~ pH14 € € Vout ≅ (60 mV ) ⋅ log10 ( = ( 60 mV ) ⋅ log10 10 ⋅ [H + ]− 0.1001 = −180 mV 100  ­ The range of reliable measurement pH1 ~ pH3 ­5 (depends on error tolerance) ) Part c. Just for your reference: Part a. Problem 2: Consider an ion ­sensitive field ­effect transistor (ISFET) as described in Figure 10.17 (Webster 4th Ed.). For this problem you may assume that ion concentrations on either side of the membrane do not change during measurement, and that the voltage VGS on the gate relative to the source, determined in equilibrium by the ion Nernst potential across the membrane, is below the threshold voltage VTH of the...
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