How can oxidation numbers be used to balance chemical equations?

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SUMMARY

The discussion focuses on using oxidation numbers to balance the chemical equation $$aN_2H_4+bH_2O_2=cHNO_3+dH_2O$$. Participants emphasize the importance of understanding the changes in oxidation states, specifically that oxygen transitions from -1 to -2 and nitrogen from -2 to +5. The balancing of hydrogen atoms remains unchanged, which simplifies the process. The key takeaway is that total oxidation number conservation aids in solving the equations for the unknowns b, c, and d in terms of a.

PREREQUISITES
  • Understanding of oxidation numbers in chemical reactions
  • Familiarity with balancing chemical equations
  • Basic algebra for solving equations with multiple variables
  • Knowledge of chemical species involved: hydrazine (N2H4), hydrogen peroxide (H2O2), nitric acid (HNO3), and water (H2O)
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  • Study the principles of oxidation states and their role in redox reactions
  • Learn techniques for balancing complex chemical equations
  • Explore algebraic methods for solving systems of equations in chemistry
  • Review examples of balancing reactions involving hydrazine and hydrogen peroxide
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Chemistry students, educators, and anyone interested in mastering the balancing of chemical equations using oxidation numbers.

Witcher
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Homework Statement
I have been on letter A problem for hours now and can’t seem to balance the equation.
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It is a combustion reaction i think because both sides have oxygen and hydrogen
I attached my attempt and the question from the book, as you can see i kept failing because my hydrogens wouldn't balance and neither would my oxygens.
 

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I can't read the pictures: they are rotated 90 degrees to the right. Please put hem upright, or better: type them out.
 
A is not a combustion reaction though.
 
You can do example (a) algebraically. Write the balanced equation as $$aN_2H_4+bH_2O_2=cHNO_3+dH_2O$$Based on this, what is the balance on nitrogen atoms? What is the balance on H atoms? What is the balance on O atoms? Solve these 3 equations in 4 unknowns for b, c, and d in terms of a. What do you get?
 
This one may be simpler if you go by oxidation numbers, noting that total oxidation number is conserved.
Hint: oxygen goes from -1 to -2 (in both products); nitrogen goes from -2 to +5; H doesn't change.
 

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