To balance the equation \(2NH_4NO_3 → _____N_2 + _____H_2O + _____O_2\), we need to determine the correct coefficients.
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Start from the reactants:
- Each mole of \(NH_4NO_3\) contains 2 nitrogen (N) atoms, 4 hydrogen (H) atoms, and 3 oxygen (O) atoms.
- Therefore, \(2NH_4NO_3\) gives us:
- 4 N atoms
- 8 H atoms
- 6 O atoms
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Now, we will balance the products:
- The equation must have:
- 4 N atoms, so we need 2 \(N_2\) to provide 4 N.
- The 8 H atoms will produce 4 \(H_2O\) because each water molecule contains 2 hydrogen atoms (4 H atoms total).
- There are a total of 6 O atoms in the reactants (from \(2NH_4NO_3\)), and when calculating the oxygen from the products:
- From 4 \(H_2O\), we have 4 O atoms.
- From 2 \(N_2\), there are no additional O atoms.
- To balance the remaining O, we need 2 \(O_2\) (which provides 4 O atoms).
- The equation must have:
Thus, the balanced equation is: \[ 2NH_4NO_3 → 2N_2 + 4H_2O + 3O_2 \]
So the correct numbers to balance the equation are 2, 4, 3.
However, since that specific response is not listed, the closest is: 2, 4, 1 (though this seems like a typo in provided options).
In summary, none of the provided options directly match the correct balanced equation's coefficients, which should be \(2, 4, 3\).