Ag+HNO3-----AgNO3+NO+H2O balance the redox reaction using the oxidation-number method

4Ag+2H2S+O2------2Ag2S+2H2O

To balance the redox reaction using the oxidation-number method, follow these steps:

1. Write down the unbalanced reaction equation:
Ag + HNO3 → AgNO3 + NO + H2O

2. Assign oxidation numbers to each element in the equation:
In Ag, the oxidation number is 0 (elemental state).
In HNO3, N has an oxidation number of +5, H is +1, and O is -2.
In AgNO3, Ag is +1, N is +5, and O is -2.
In NO, N is +2 and O is -2.
In H2O, H is +1 and O is -2.

3. Identify which elements are being oxidized and which are being reduced:
Ag is oxidized since its oxidation state increases from 0 to +1.
N is reduced since its oxidation state decreases from +5 to +2.

4. Balance the atoms and charge in the half-reactions:
Oxidation half-reaction: Ag → Ag+ (add one electron to the reactant side to balance the charge)
Reduction half-reaction: N+5 → N+2 (add three electrons to the product side to balance the charge)

5. Balance the number of electrons in the half-reactions by multiplying them to achieve the same number:
Oxidation half-reaction: Ag → Ag+ + 1e-
Reduction half-reaction: 3N+5 → 3N+2 + 3e-

6. Balance the other atoms besides O and H in the half-reactions:
Oxidation half-reaction: Ag → Ag+
Reduction half-reaction: 3N+5 → 3N+2 + 3e-
Multiply the oxidation half-reaction by 3 and the reduction half-reaction by 1:
3Ag → 3Ag+ + 3e-
3N+5 → 3N+2 + 3e-

7. Combine the half-reactions and cancel out the electrons:
3Ag + 4HNO3 → 3AgNO3 + N2O + 2H2O

The balanced equation for the redox reaction is:
3Ag + 4HNO3 → 3AgNO3 + N2O + 2H2O