Assign oxidation number to atoms of only those elements which undergo oxidation number change in the following redox reactions, and then balance the equations.

${\mathrm{MnO}}_4^{-}+{\mathrm{CN}}^{-}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{MnO}}_2+{\mathrm{CNO}}^{-}+{\mathrm{OH}}^{-}$

Given:

$\begin{array}{rcl}{\mathrm{E}}_{{\mathrm{Ag}}^{+}/\mathrm{Ag}}^0& =& +0.80 \mathrm{V}\\ {\mathrm{E}}_{{\mathrm{Mg}}^{2+}/\mathrm{Mg}}^0& =& -2.37 \mathrm{V}\\ {\mathrm{E}}_{{\mathrm{Cu}}^{2+}/\mathrm{Cu}}^0& =& +0.34 \mathrm{V}\\ {\mathrm{E}}_{{\mathrm{Hg}}^{2+}/\mathrm{Hg}}^0& =& +0.79 \mathrm{V}\end{array}$

Which of the following is correct?

Two beakers, $\mathrm{A}$ and $\mathrm{B}$ each contain a nickel ion solution. A silver strip is dipped in beaker $\mathrm{A}$ and a copper strip is dipped in beaker $\mathrm{B}$.

Given that,

${\mathrm{E}}_{{\mathrm{Ni}}^{2+}/\mathrm{Ni}}^0=-0.25 \mathrm{V},$ ${\mathrm{E}}_{{\mathrm{Cu}}^{2+}/\mathrm{Cu}}^0=+0.34 \mathrm{V}$ and ${\mathrm{E}}_{{\mathrm{Ag}}^{2+}/\mathrm{Ag}}^0=0.80 \mathrm{V}$.

Based on the above information, which of the following is correct?

a) $$\begin{gathered} {\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-}\to {\mathrm{Fe}}^{2+}\left(\mathrm{aq}\right) \\ {\mathrm{E}}^0=+0.77 \mathrm{V} \end{gathered}$$

b) $$\begin{gathered} {\mathrm{Al}}^{3+}+3{\mathrm{e}}^{-}\to \mathrm{Al}\left(\mathrm{s}\right) \\ {\mathrm{E}}^0=-1.66 \mathrm{V} \end{gathered}$$

c) $$\begin{gathered} {\mathrm{Br}}_2+2{\mathrm{e}}^{-}\to 2{\mathrm{Br}}^{-}\left(\mathrm{aq}\right) \\ {\mathrm{E}}^0=+1.08 \mathrm{V} \end{gathered}$$

Based on the data given above, what is the correct order of reducing power?

What is the meaning of a positive sign for the half-cell potential? 

What is the meaning of a positive sign for cell potential?