Zn(s) + 2H^+(aq) → Zn^2+(0.1 M) + H2(g)(1 atm) 0.542 V

Zn(s) + 2H^+(aq) → Zn^2+(0.1 M) + H2(g)(1 atm) 0.542 V

 

 

The EMF of a cell corresponding to the reaction:

Zn(s) + 2H^+(aq) → Zn^2+(0.1 M) + H2(g)(1 atm) is 0.542 V at 25℃.

Calculate the pH of the solution at the hydrogen electrode.

E°(Zn^2+/Zn) = –0.76 V and E°(H^+/H2) = 0 V

 

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산화-환원 반응식

Zn(s) + 2H^+(aq) → Zn^2+(aq) + H2(g)

 

Q = [Zn^2+] / [H^+]^2

 

 

 

E°_cell = E°_red(환원전극) – E°_red(산화전극)

= (환원된 물질의 표준환원전위) – (산화된 물질의 표준환원전위)

( 참고 https://ywpop.tistory.com/4558 )

 

= (0) – (–0.76) = +0.76 V

 

 

 

E = E° – (0.0592 V / n) × logQ

( 참고 https://ywpop.tistory.com/2900 )

 

0.542 = 0.76 – (0.0592 / 2) × log(0.1 / x^2)

 

(0.0592 / 2) × log(0.1 / x^2) = 0.76 – 0.542 = 0.218

 

log(0.1 / x^2) = 0.218 / (0.0592 / 2)

 

0.1 / x^2 = 10^(0.218 / (0.0592 / 2))

 

x = (0.1 / 10^(0.218 / (0.0592 / 2)))^(1/2)

= 6.57×10^(-5) M = [H^+]

 

 

 

pH = –log(6.57×10^(-5))

= 4.18

 

 

 

답: pH = 4.18

 

 

 

 

[ 관련 예제 https://ywpop.tistory.com/22085 ] Zn(s) + 2H^+(aq) → Zn^2+(0.1 M) + H2(g)(1 atm) 0.28 V

 

 

 

[키워드] Zn-H2 cell 기준문서