List the 1/2 equations in order least positive to most positive:
# " " "E"^@("V")#
#stackrel(color(white)(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx))(color(blue)(larr)#
#" "sf(Al^(3+)+3erightleftharpoonsAl" "-1.66)#
#" "sf(Cu^(2+)+2erightleftharpoonsCu" "+0.34)#
#stackrel(color(white)(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx))(color(red)(rarr)#
Note we use the #rightleftharpoons# symbol to show that the 1/2 cells can go in either direction depending on what they are coupled with.
The 1/2 cell with the most +ve #"E"^@# is the one which will take in the electrons.
From this we can see that the 2nd 1/2 cell will be driven left to right and the 1st 1/2 cell right to left in accordance with the arrows.
So the 2 half - reactions are:
#sf(AlrarrAl^(3+)+3e" "color(red)((1)))#
#sf(Cu^(2+)+2erarrCu" "color(red)((2)))#
To get the electrons to balance you can see that we need to multiply equation #color(red)((1))# by 2 and equation #sf(color(red)((2))# by 3 then add both sides together:
This gives
#sf(2Al+3Cu^(2+)+cancel(6e)rarr2Al^(3+)+cancel(6e)+3Cu)#
So you can see that aluminium should displace copper(II) ions from a solution of its salt.
