Which of the following is the correctly balanced chemical equation for the decomposition of dinitrogen trioxide (N2O3) into nitrogen gas and oxygen gas?

• A. N2O3 → N2 + O2
• B. 2 N2O3 → N2 + 2 O2
• C. 2 N2O3 → 2 N2 + 3 O2
• D. N2O3 → 2 N2 + 3 O2

Answer: (C)

Verified step by step guidance

1. Write down the unbalanced chemical equation for the decomposition of dinitrogen trioxide: \(\mathrm{N_2O_3 \rightarrow N_2 + O_2}\).
2. Count the number of atoms of each element on both sides of the equation. On the left, there are 2 nitrogen (N) atoms and 3 oxygen (O) atoms per molecule of \(\mathrm{N_2O_3}\). On the right, count the atoms based on the coefficients in front of \(\mathrm{N_2}\) and \(\mathrm{O_2}\).
3. Assign coefficients to balance nitrogen atoms first. Since each \(\mathrm{N_2}\) molecule contains 2 nitrogen atoms, balance nitrogen by ensuring the total nitrogen atoms on both sides are equal.
4. Next, balance oxygen atoms by adjusting the coefficient in front of \(\mathrm{O_2}\). Each \(\mathrm{O_2}\) molecule contains 2 oxygen atoms, so choose a coefficient that balances the total oxygen atoms from the left side.
5. Verify that both nitrogen and oxygen atoms are balanced with the chosen coefficients. The balanced equation will have integer coefficients that satisfy the conservation of mass.