Homework 3 Solutions

0001 360 mv 100 b for a sample that contains only

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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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