# Given that the sulfate(IV) ion, SO_2^(-2), is converted to the sulfate(VI) ion, SO_4^(-2), in the presence of water, deduce the balanced equation for the redox reaction between Cr_2O_7^(-2) (aq) and SO_3^(-2)?

Nov 17, 2016

$C {r}_{2} {O}_{7}^{2 -} + 3 S {O}_{3}^{2 -} + 8 {H}^{+} \rightarrow 2 C {r}^{3 +} + 3 S {O}_{4}^{2 -} + 4 {H}_{2} O$

#### Explanation:

$\text{Oxidation half equation:}$

$S {O}_{3}^{2 -} + {H}_{2} O \rightarrow S {O}_{4}^{2 -} + 2 {H}^{+} + 2 {e}^{-}$ $\left(i\right)$

$\text{Reduction half equation:}$

$C {r}_{2} {O}_{7}^{2 -} + 14 {H}^{+} + 6 {e}^{-} \rightarrow 2 C {r}^{3 +} + 2 {H}^{+} + 7 {H}_{2} O$ $\left(i i\right)$

Both equations are balanced with respect to mass and charge; as indeed they must be if they reflect chemical reality. So we simply cross-mulitply to eliminate the electrons, $3 \times \left(i\right) + \left(i i\right) :$

$C {r}_{2} {O}_{7}^{2 -} + 3 S {O}_{3}^{2 -} + 8 {H}^{+} \rightarrow 2 C {r}^{3 +} + 3 S {O}_{4}^{2 -} + 4 {H}_{2} O$

Given that the sulfate and sulfite ions are colourless, what would be the macroscopic colour change observed in this reaction?