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Moved from a technical forum

**Summary:**Our chemistry teacher gave a sample problem regarding balancing a redox equation. I managed to proceed to a considerable distance, but I can't seem to understand how to get the final balanced equation. Please help me out.

The problem is;

**reaction of K**

_{2}Cr_{2}O_{7}with SO_{2}in the presence of H_{2}SO_{4}(aq) giving Cr^{3+}ions and SO_{4}^{2ˉ}ions as main products.I could complete the following steps :

Oxidation half reaction :

**SO**

_{2}------------------ > SO_{4}^{2ˉ}Reduction half reaction :

**Cr**

2H

6e

_{2}O_{7}^{2-}------------------- > Cr^{3+}2H

_{2}O + SO_{2}------------------ > SO_{4}^{2ˉ}+ 4H^{+}+ 2e^{-}6e

^{-}+ 14H^{+}+ Cr_{2}O_{7}^{2-}------------------- > 2Cr^{3+}+ 7H_{2}OThen I multiplied the "

**2H**" equation by three so that I can add the both equations by equalizing the electron amount.

_{2}O + SO_{2}------------------ > SO_{4}^{2ˉ}+ 4H^{+}+ 2e^{-}Then I added the both like this....

**6H**

_{2}O + 3SO_{2}+ 14H^{+}+ Cr_{2}O_{7}^{2-}------ > 3SO_{4}^{2ˉ}+ 12H^{+}+ 2Cr^{3+}+ 7H_{2}OThen simplified it into this :

**2H**

^{+}+ Cr_{2}O_{7}^{2-}+ 3SO_{2}-----> 2Cr^{3+}+ 3SO_{4}^{2ˉ}+ H_{2}OBut the ultimate balanced equation that I should get is,

**H**

_{2}SO_{4}(aq) + K_{2}Cr_{2}O_{7}(aq) + 3SO_{2}(g) ------ > Cr_{2}(SO_{4})_{3}(aq) + K_{2}SO_{4}(aq) + H_{2}O(aq)right?

How can I proceed to get the ultimate balanced equation? I can't understand how to do it. Please help me on this. Thank you very much in advance.