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Consider submerging a plate of pure silver in a solution with $\mathrm{pH} = 1$. Does the redox reaction with hydrogen happen spontaneously?

The composition of the solution is not given.

My attempt:

  • I considered the standard potential for $\mathrm{pH} = 0$. Since the silver must be oxidised, the reaction happens at the anode.

$$ \begin{align} \ce{Ag+ + e- &-> Ag} &\qquad E^\circ &= \pu{0.80 V} \\ \ce{2 H+ + e- &-> H2} &\qquad E^\circ &= \pu{0.00 V} \end{align} $$

  • At this point, it is obvious that the reaction cannot be spontaneous since the potential for this cell is less than zero. In fact:

$$\Delta E = E_\mathrm{red} - E_\mathrm{ox} = \pu{-0.80 V}$$

  • From Nernst equation, the potential for the hydrogen at $\mathrm{pH}=1$ must be negative. Thus the reaction is all the more non spontaneous ($E = \pu{-0.059 V}$).

However, this seems to be wrong. I must be applying the $\Delta E$ wrong, because the solution for this problem states clearly that it is given by:

$$\Delta E = E_\mathrm{red} - E_\mathrm{ox} = \pu{-0.059 V} - (\pu{-0.80 V}) = \pu{0.741 V}$$

This is driving me crazy. Where does the minus sign come from?

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    $\begingroup$ I would love it if the downvoters explained. I think the question is clear, and my attempt to solve the problem is given. $\endgroup$ – Niki Di Giano Jan 20 '18 at 12:17
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    $\begingroup$ The question looks fine to me, I edited it a little. Sometimes one gets downvoted for no good reason. Feel free to check out this page, this page and this one on how to format your future posts better with MathJax and Markdown. $\endgroup$ – andselisk Jan 20 '18 at 14:31
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    $\begingroup$ Let me guess, you are using a mobile app? If so, refer to the web version of stack exchange (with a web browser) since the mobile app is severely handicapped and doesn't render many things properly. $\endgroup$ – andselisk Jan 20 '18 at 15:30
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    $\begingroup$ @andselisk yes, I am using the mobile app. That's too bad, I'll check it out from PC browser. Thanks again. $\endgroup$ – Niki Di Giano Jan 20 '18 at 15:33
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    $\begingroup$ No prob, I only use mobile app to get notifications. The Stack Overflow app is great, but they don't really care much about other sites on SX network since there is not much traffic in comparison. $\endgroup$ – andselisk Jan 20 '18 at 15:35
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The answer given in the solution was wrong. It has been corrected, and it eventually proved my point.

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