One half cell in a voltaic cell is constructed by dipping a silver rod in an $AgNO_3$ solution of unknown concentration, and the other half cell is a $Zn$ rod dipped in a $1 \text{ M}$ solution of $ZnSO_4$. $A$ voltage of $1.60 \text{ V}$ is measured at $298 \text{ K}$ for this cell. What is the concentration of $Ag^+$ ions in terms of $\log x$ (where $x = [Ag^+]$)? Given: $E^\ominus_{Zn^{2+}/Zn} = -0.76 \text{ V}$, $E^\ominus_{Ag^+/Ag} = +0.80 \text{ V}$, and $\frac{2.303RT}{F} = 0.059 \text{ V}$.

  • A
    $\frac{2}{3.9}$
  • B
    $\frac{4}{5.9}$
  • C
    $\frac{2.9}{2}$
  • D
    $\frac{5.9}{4}$

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By how much will the potential of the half-cell $Cu^{2+}/Cu$ change if the solution is diluted to $100$ times at $298 \ K$?

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