2. Consider the following reaction occurring in basic solution: Mn^2++H_(2)O_(2)arrow MnO_(2)+H_(2)O Determine the SUM of ALL coefficients when the equation is properly balanced. Include coefficients of one. a) 4 b) 5 c) 6 d) 7 e) 9

1. Write oxidation and reduction half-reactions <br /> Oxidation: $H_2O_2 \rightarrow O_2$ (O changes from -1 to 0) <br /> Reduction: $Mn^{2+} \rightarrow MnO_2$ (Mn changes from +2 to +4)<br /><br />2. Balance reduction half-reaction in basic medium <br /> $Mn^{2+} \rightarrow MnO_2$: <br />Add $2H_2O$ to right: $Mn^{2+} \rightarrow MnO_2 + 2H_2O$ <br />Balance O with $2OH^-$ on left: $Mn^{2+} + 2OH^- \rightarrow MnO_2 + 2H_2O$ <br />Balance H: Already balanced. <br />Balance charge: Add $2e^-$ to left: $Mn^{2+} + 2OH^- \rightarrow MnO_2 + 2H_2O + 2e^-$ → Actually electrons go to right: $Mn^{2+} + 2OH^- \rightarrow MnO_2 + 2H_2O + 2e^-$ (correct).<br /><br />3. Balance oxidation half-reaction in basic medium <br /> $H_2O_2 \rightarrow O_2$: <br />Add $2OH^-$ to left: $H_2O_2 \rightarrow O_2$ <br />Balance O: O balanced. <br />Balance H: Add $2H_2O$ to right: $H_2O_2 + 2OH^- \rightarrow O_2 + 2H_2O$ <br />Balance charge: Add $2e^-$ to right in basic solution: $H_2O_2 + 2OH^- \rightarrow O_2 + 2H_2O + 2e^-$<br /><br />4. Combine half-reactions <br /> Both produce $2e^-$, so add directly: <br />$Mn^{2+} + 2OH^- + H_2O_2 + 2OH^- \rightarrow MnO_2 + 2H_2O + O_2 + 2H_2O$ <br />Simplify OH^-: $Mn^{2+} + H_2O_2 + 4OH^- \rightarrow MnO_2 + O_2 + 4H_2O$<br /><br />5. Count coefficients <br /> Coefficients: $Mn^{2+}(1) + H_2O_2(1) + OH^-(4) + MnO_2(1) + O_2(1) + H_2O(4)$ → Sum = $1+1+4+1+1+4 = 12$ <br />(Wait—need to double check: The oxidation half was wrong for O₂ product; here in original reaction, final product is MnO₂ and H₂O only — revise)<br /><br />6. Correct for given reaction (no O₂ product) <br /> Basic solution likely: $Mn^{2+} + H_2O_2 \rightarrow MnO_2 + H_2O$ (H₂O₂ oxidizes Mn²⁺ without free O₂) <br />Balanced: $Mn^{2+} + H_2O_2 + 2OH^- \rightarrow MnO_2 + 2H_2O$ <br />Count coefficients: $1 + 1 + 2 + 1 + 2 = 7$