# Question bb687

Oct 21, 2016

$\text{SO"_3^"2-" + 2"Cu"^"2+" +2"OH"^"⁻" → "SO"_4^"2-" + 2"Cu"^+ + "H"_2"O}$

#### Explanation:

I usually balance an equation like this in acid and then convert to base at the end.

You can find the detailed procedure here.

1. Half-reactions

$\text{SO"_3^"2-" → "SO"_4^"2-}$
${\text{Cu"^"2+" → "Cu}}^{+}$

2. Balance all atoms other than $\text{H}$ and $\text{O}$

$\textcolor{red}{1} \text{SO"_3^"2-" → color(red)(1)"SO"_4^"2-}$
$\textcolor{b l u e}{1} {\text{Cu"^"2+" → color(blue)(1)"Cu}}^{+}$

3. Balance O

$\textcolor{red}{1} \text{SO"_3^"2-" + color(olive)(1)"H"_2"O" → color(red)(1)"SO"_4^"2-}$
$\textcolor{b l u e}{1} {\text{Cu"^"2+" → color(blue)(1)"Cu}}^{+}$

4. Balance $\text{H}$

$\textcolor{red}{1} {\text{SO"_3^"2-" + color(olive)(1)"H"_2"O" → color(red)(1)"SO"_4^"2-" +color(olive)(2)"H}}^{+}$
$\textcolor{b l u e}{1} {\text{Cu"^"2+" → color(blue)(1)"Cu}}^{+}$

5. Balance electrons

$\textcolor{red}{1} \text{SO"_3^"2-" + color(olive)(1)"H"_2"O" → color(red)(1)"SO"_4^"2-" +color(olive)(2)"H"^+ + color(orange)(2)"e"^"-}$
$\textcolor{b l u e}{1} {\text{Cu"^"2+" + color(orange)(1)e^"-" → color(blue)(1)"Cu}}^{+}$

6. Equalize electrons transferred

color(brown)(1) × [color(red)(1)"SO"_3^"2-" + color(olive)(1)"H"_2"O" → color(red)(1)"SO"_4^"2-" +color(olive)(2)"H"^+ + color(orange)(2)"e"^"-"
color(brown)(2) × [color(blue)(1)"Cu"^"2+" + color(orange)(1)e^"-" → color(blue)(1)"Cu"^+]

color(brown)(1) × [color(red)(1)"SO"_3^"2-" + color(olive)(1)"H"_2"O" → color(red)(1)"SO"_4^"2-" +color(olive)(2)"H"^+ color(red)(cancel(color(black)(color(orange)(2)"e"^"-"')))
color(brown)(2) × [color(blue)(2)"Cu"^"2+" + color(red)(cancel(color(black)(color(orange)(1)e^"-"))) → color(blue)(2)"Cu"^+]
stackrel(————————————————————)(color(red)(1)"SO"_3^"2-" + color(blue)(2)"Cu"^"2+" + color(olive)(1)"H"_2"O" → color(red)(1)"SO"_4^"2-" + color(blue)(2)"Cu"^+ +color(olive)(2)"H"^+)

8. Convert to base

color(red)(1)"SO"_3^"2-" + color(blue)(2)"Cu"^"2+" + color(red)(cancel(color(black)(color(olive)(1)"H"_2"O"))) → color(red)(1)"SO"_4^"2-" + color(blue)(2)"Cu"^+ +color(red)(cancel(color(black)(color(olive)(2)"H"^+)))
color(red)(cancel(color(black)(color(olive)(2)"H"^+))) + 2"OH"^"⁻" → stackrelcolor(blue)(1)(color(red)(cancel(color(black)(color(olive)(2)))))"H"_2"O"
stackrel(————————————————————)(color(red)(1)"SO"_3^"2-" + color(blue)(2)"Cu"^"2+" +2"OH"^"⁻" → color(red)(1)"SO"_4^"2-" + color(blue)(2)"Cu"^+ + color(olive)(1)"H"_2"O")#

The balanced equation is

$\text{SO"_3^"2-" + 2"Cu"^"2+" +2"OH"^"⁻" → "SO"_4^"2-" + 2"Cu"^+ + "H"_2"O}$