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Determining the directiom of spontaneity...

Determining the directiom of spontaneity from electrode pot`Na^(+)(aq.) + e^(-) rarr Na(s) E^(@) = -2.71 V`entials : Predict from Table 3.1, whether `Pb^(2+)(aq.)` can oxidize `Al(s)` or `Cu(s)` under standard conditions. Calculate `E^(ɵ)` for each reaction at `25^(@)C`.
Strategy: To predict whether a redox reaction is spontaneous, remember that an oxidizing agent can oxidize any reducing agent that lies below it in the table but can't oxidize one that lies above it.
Alternatively, write the expected reaction. Find the oxidizing agents in the equations, one is on the left side and the other on the right side. Locate these oxidizing agents in a table of electrode potentials (the oxidizing agent is on the left side of the reduction half-reaction). The stronger oxidizing agent is the one involved in the half-reaction with the more positive standard electrode potential.

Text Solution

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`Pb^(2+)(aq.)` is above `Al(s)` in the table but below `(Cu)(s)`. Therefore, `Pb^(2+)(aq.)` can oxidize `Al(s)` but can't oxidize `Cu(s)`. To confirm these predictions, we can calculate `E^(@)` values for the overall reactions.
`{:(3xx[Pb^(2+)(aq.)2e^(-)hArr Pb(s)]" "E^(@)=-0.13V),(2xx[Al(s)hArr Al^(3+)(aq.)+3e]" "E^(@)=1.66V),(bar(3Pb^(2+)(aq.)+2Al(s)hArr3Pb(s)+2Al^(3+)(aq.)E^(@)=1.53V)):}`
For the oxidation of `Al` by `Pb^(2+), E^(@)` is positive and therefore the reaction is spontaneous : Note that we have multiplied the `Pb^(2+)//Pb` half-reaction by a factor of `3` and the `Al//Al^(3+)` half reaction by a factor of `2` so that the elecrons will cancel. but we do not multiply the `E^(@)` values by these factors because electrode potential is an intensive property.
`{:(Pb^(2+)(aq.)+2e^(-)hArr Pb(s)" "E^(@)=-0.13V),(Cu(s)hArr Cu^(+)(aq.)+2e^(-)" "E^(@)=-0.34V),(bar(Pb^(2+)(aq.)+Cu(s)hArrPb(s)+Cu^(+)(aq.)E^(@)=-0.47V)):}`
For the oxidation of `Cu` by `Pb^(2+), E^(@)` is negative (-0.47 V), and therefore the reaction is non-spontaneous.
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