For a particular redox reaction NO is oxidized to NO3^– and Cu^2+ is reduced to Cu. Complete and balance the equation for this reaction in basic solution:

NO + Cu^2+ --> NO3^- + Cu^+

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4OH- + NO + 3Cu2+ ----> NO3- + 3Cu+ + 2H2O

To complete and balance the equation for the redox reaction in basic solution, follow these steps:

Step 1: Write the unbalanced equation.
Start by writing the unbalanced equation for the reaction:
NO + Cu^2+ → NO3^- + Cu^+

Step 2: Balance the non-hydrogen and non-oxygen elements.
In this case, the only non-hydrogen and non-oxygen elements are nitrogen (N) and copper (Cu). To balance the nitrogen, add a coefficient of 2 in front of NO3^- on the right side of the equation:
NO + Cu^2+ → 2NO3^- + Cu^+

Step 3: Balance the hydrogen atoms.
Next, balance the hydrogen atoms by adding the appropriate number of OH^- ions to the side of the equation that lacks hydrogen. Since this is a basic solution, we can add OH^- ions:
NO + Cu^2+ + OH^- → 2NO3^- + Cu^+ + H2O

Step 4: Balance the oxygen atoms.
After adding OH^- ions, the equation now looks unbalanced with oxygen atoms. To balance the oxygen atoms, add H2O molecules to the side that lacks oxygen. In this case, the left side needs additional oxygen:
NO + Cu^2+ + OH^- → 2NO3^- + Cu^+ + H2O

Step 5: Balance the charge.
Finally, check the charge balance on each side of the equation. On the left side, we have NO and Cu^2+ with a total charge of +2. On the right side, we have 2NO3^- and Cu^+ with a total charge of -2. To balance the charges, add 2e^- (electrons) to the left side:
NO + Cu^2+ + OH^- + 2e^- → 2NO3^- + Cu^+ + H2O

Step 6: Check the overall balance.
To assure the equation is fully balanced, check all the atoms and charges once more. On both sides, there are the same number of each atom, and the charges are balanced. Therefore, the final balanced equation for the redox reaction in basic solution is:

3NO + 2Cu^2+ + 4OH^- → 2NO3^- + 3Cu^+ + 2H2O + 2e^-

NO + OH^- + 3Cu(OH)2 ==> 3CuOH + NO3^- + 2H2O