Question

Identify the correct coefficients to balance the redox reaction with the lowest possible integer coefficients.

_Ag1+ + _AI -->
_Al3+ + _Ag

Answer 1

`\rm 3\; Ag^(1+) + 1\; Al \to 1\; Al^(3+) + 3\; Ag`.

Step-by-step explanation:

Electrons are conserved in a chemical equation.

The superscript of
`\rm Ag^(1+)` indicates that each of these ions carries a charge of
`+1`. That corresponds to the shortage of one electron for each
`\rm Ag^(+)` ion.

Similarly, the superscript
`+3` on each
`\rm Al^(3+)` ion indicates a shortage of three electrons per such ion.

Assume that the coefficient of
`\rm Ag^(+)` (among the reactants) is
`x`, and that the coefficient of
`\rm Al^(3+)` (among the reactants) is
`y`.

`\rm \mathnormal{x}\; Ag^(1+) + ?\; Al \to \mathnormal{y}\; Al^(3+) + ?\; Ag`.

There would thus be
`x` silver (
`\rm Ag`) atoms and
`y` aluminum (
`\rm Al`) atoms on either side of the equation. Hence, the coefficient for
`\rm Al\!` and
`\rm Ag\!` would be
`y\!` and
`x\!`, respectively.

`\rm \mathnormal{x}\; Ag^(1+) + \mathnormal{y}\; Al \to \mathnormal{y}\; Al^(3+) + \mathnormal{x}\; Ag`.

The
`x`
`\rm Ag^(1+)` ions on the left-hand side of the equation would correspond to the shortage of
`x` electrons. On the other hand, the
`y`
`Al^(3+)` ions on the right-hand side of this equation would correspond to the shortage of
`3\, y` electrons.

Just like atoms, electrons are also conserved in a chemical reaction. Therefore, if the left-hand side has a shortage of
`x` electrons, the right-hand side should also be
`x\!` electrons short of being neutral. On the other hand, it is already shown that the right-hand side would have a shortage of
`3\, y` electrons. These two expressions should have the same value. Therefore,
`x = 3\, y`.

The smallest integer
`x` and
`y` that could satisfy this relation are
`x = 3` and
`y = 1`. The equation becomes:

`\rm 3\; Ag^(1+) + 1\; Al \to 1\; Al^(3+) + 3\; Ag`.