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Unformatted text preview: Vout as a function of the pH of the solution. GHK equation: +
+
−
RT PK ⋅ [H ]− + PNa ⋅ [ Na ]− + PCl ⋅ [Cl ]+
Vout =
ln
F
PK ⋅ [H + ]+ + PNa ⋅ [ Na + ]+ + PCl ⋅ [Cl − ]− = (60 mV ) ⋅ log10
= (60 mV ) ⋅ log10
pH1 ~ pH7: € 1000 ⋅ [H + ]− + 0.001 ⋅ 0.1
1000 ⋅ 0.1 + 0.001 ⋅ [Cl − ]−
1000 ⋅ [H + ]− + 0.0001
100 + 0.001 ⋅ [Cl − ]− Vout ≅ (60 mV ) ⋅ log10 1000 ⋅ [H + ]−
100
pH7 ~ pH14 € € Vout ≅ (60 mV ) ⋅ log10 ( = ( 60 mV ) ⋅ log10 10 ⋅ [H + ]− = (60 mV ) ⋅ (1 − pH )
0.0001
= −360 mV 100 ) b. For a sample that contains only a solution of NaCl, derive Vout as a function of the Na+ concentration. GHK equation: +
+
−
RT PK ⋅ [H ]− + PNa ⋅ [ Na ]− + PCl ⋅ [Cl ]+
Vout =
ln
F
PK ⋅ [H + ]+ + PNa ⋅ [ Na + ]+ + PCl ⋅ [Cl − ]− = (60 mV ) ⋅ log10 1 ⋅ [ Na + ]− + 0.001 ⋅ 0.1 [ Na ]
+ = (60 mV ) ⋅ log10
[NaCl] > 0.1 mmol/L 100 + 0.001 ⋅ [Cl − ]−
− + 0.0001 100 + 0.001 ⋅ [Cl − ]− [ Na ]
+ ( ) = (60 mV ) ⋅ log10 [ Na + ]− − 2
[NaCl] < 0.1 mmol/L Vout ≅ (60 mV ) ⋅ log10 € The equation is not a function of [Na+] € Vout ≅ (60 mV ) ⋅ log10 − 100 0.0001
= −360 mV...
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 Winter '08
 PeterChen

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