Given the standard reduction potentials in acidic medium: NO ₃^- NO ; E ^ = 0.80 V HNO ₂ NO ; E ^ = 1.10 V The standard cell potential ( E ^ _ cell ) for the disproportionation reaction 3 HNO ₂ NO ₃^- + 2 NO + H ^+ + H ₂ O is:

Step-by-step solution

First, determine the oxidation states of nitrogen in each species: NO ₃^- : +5 HNO ₂ : +3 NO : +2 The overall reduction of NO ₃^- to NO involves a 3-electron transfer ( n = 3 ) with E ^ = 0.80 V . This process can be split into two steps: NO ₃^- HNO ₂ ( n₁ = 2 ) and HNO ₂ NO ( n₂ = 1 , E ₂^ = 1.10 V ). Using G ^ additivity: n E ^ = n₁ E ₁^ + n₂ E ₂^ 3(0.80) = 2( E ₁^ ) + 1(1.10) 2.40 = 2 E ₁^ + 1.10 2 E ₁^ = 1.30 E ₁^ = 0.65 V So, the standard reduction potential for NO ₃^- / HNO ₂ is 0.65 V . For the disproportion