Question

Is the reaction `"2Al(s) + 3CuSO"_4"(aq)" → "Al"_2("SO"_4)_3"(aq)"+"3Cu(s)"` spontaneous?

Answer 1

The reaction is spontaneous....

Explanation:

We gots `2Al(s) + 3CuSO_4(aq) rarr Al_2(SO_4)_3(aq)+3Cu`...

And let us look at the standard reduction potentials....

`Al^(3+) + 3e^(-) rarr Al(s)` `; E^@=-1.66*V`

`Cu^(2+) + 2e^(-) rarr Cu(s)` `; E^@=+0.34*V`....

`E_"cell"^@={-(-1.66)+0.34}*V=+2.00*V`...and since `E_"cell"^@` is positive, `DeltaG^@=-nFE^@=??*kJ*mol^-1`, this reaction is spontaneous....

And if you take a solution of copper sulfate (which you should find in a lab), and place some aluminum foil in the solution, the foil will acquire a salmon pink coating of copper metal IN REAL TIME before disintegrating and going up into solution. The more active aluminum metal will displace copper ion from the solution...

Answer 2

Yes, the reaction is spontaneous.

Explanation:

The standard reduction potentials for each half-reaction are:

`ulbb("Standard Reduction Potentials"color(white)(ml)E^@//"V"`
`"Al"^"3+" + "3e"^"-" → "Al" color(white)(mmmmmmmmm mll)"-1.662"`
#"Cu"^"2+" + "2e"^"-" → "Cu"color(white)(mmmmmmmmmll )"+0.3419"#

Calculate the standard cell potential

`bb(color(white)(mmmmmmmmmmmmmmmm)ul(E^@//"V")`
`2×["Al" → "Al"^"3+" + "3e"^"-" → "Al"]color(white)(mmml)1.662`
`3×"["ul("Cu"^"2+" + "2e"^"-" → "Cu]"color(white)(mmmmml))color(white)(m)ul0.3419`
`color(white)(mml)"2Al + 3Cu"^"2+"→ "2Al"^"3+" + "3Cu"color(white)(m)2.004`

`"E^@ > 0`, so the reaction is spontaneous as written.