Electrochemistry pH in solution cell

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yolo123
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Hello Forum :),

Please find attached my problem. The solutions is also there. BUT, I do not understand why my teacher does not simply assume pH=0. It seems as though we are using the standard hydrogen electrode (ie 1M H+ in solution!).
 
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  • Typed homework question: Zn(s) | Zn2+(1.0M) || 2H+(1atm) | Pt(s), E = +0.54v at 25°C. Asks: What is the pH of the solution at the hydrogen electrode?
    Screen Shot 2014-05-11 at 7.52.24 PM.png
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  • Handwritten worked solution to a Nernst equation problem: Zn(s) + 2H+(aq) → Zn2+ + H2, Zn2+ + 2e⁻ ⇌ Zn E° = -0.76 V, n = 2, E = E° - 0.0592/n log Q, leading to 0.54 = 0.76 - 0.0592/2 log(1/[H+]²), -0.22 = -0.0296 log(1/[H+]²), 7.43 = log(1/[H+]²), [H+] = 1.92 x 10⁴, pH = 3.7.
    Screen Shot 2014-05-11 at 7.54.51 PM.png
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Question never says "standard" hydrogen electrode. It also never says 1M H+, it says 1 atm - which is most likely meant to be 1 atm of H2.