Question

The pH of a solution was found by measuring the emf of a cell composed of a standard silver electrode and a hydrogen electrode of unknown hydrogen ion concentration. If the emf was 1.01v when the pressure of hydrogen was 1.00atm, what was the pH at 25^oC?

Answer 1

anode reaction: oxidation takes place

H2(g) -------------------------> 2H+ (aq) + 2e-   ,   E⁰_H+/H2 = 0.00 V

cathode reaction : reduction takes palce

2 Ag+(aq) + 2e- -----------------------------> 2 Ag(s) , E⁰_Ag+/Ag = +0.80 V

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net reaction: H2(g) + 2 Ag+(aq) -------------------------> 2H+ (aq) + Ag(s)

E⁰_cell= E⁰_cathode- E⁰_anode

E⁰_cell= E⁰_Ag+/Ag - E⁰_H+/H2

          = 0.80 - (0.00)

          = 0.80V

nernest equation

Ecell = E⁰_cell -2.303RT/nF* log { [H+]^2 /[Ag+]^2 P_H2 }

Here R= universal gas constant

T = absolute temperature =25(0C)= 298k

F= faraday = 96500 Coloumb/mol

     n   = no of moles of electrons are transfered =2

P_H2 = 1 atm

[Ag+] = 1 M

Ecell = E⁰_cell -(0.059 /n)* log{ [H+]^2 /[Ag+] P_H2 }

1.01   = 0.80 - (0.059 /2) * log{ [H+]^2 /1 x 1 }

7.106 = - log{ [H+]^2

-log[H+] = 7.106/2

     pH      = 3.55 ----------------------------(answer)