In acid:
3H2O + C2H5OH ==> 2CO2 + 12e + 12H^+
Cr2O7^2- + 6e + 14H^+ ==> 2Cr^3+ + 7H2O
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Multiply eqn 1 by 1 and eqn 2 by 2, add them. You will need to adjust H^+ and H2O since both will appear on both sides. The electrons will cancel.
In basic:
C2H5OH + 12OH^- ==> 2CO2 + 12e + 9H2O
Cr2O7^2- + 6e + 7H2O ==> 2Cr^3+ + 14OH^-
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Multiply eqn 1 by 1 and eqn 2 by 2 and add them. Adjust the eqn for OH^- and H2O as in the other equation. The electrons will cancel.
Balance the chemical equation in both acidic and basic medium cr2 O7^2- + C2H5OH gives Cr3+CO2
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