To balance the chemical equation \( \text{HNO}_3 + \text{NaHCO}_3 \rightarrow \text{NaNO}_3 + \text{H}_2\text{O} + \text{CO}_2 \), we need to make sure that the number of each type of atom is the same on both sides of the equation.
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Write down the unbalanced equation: \[ \text{HNO}_3 + \text{NaHCO}_3 \rightarrow \text{NaNO}_3 + \text{H}_2\text{O} + \text{CO}_2 \]
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Count the atoms on each side:
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Reactants:
- H: 1 (from HNO3) + 1 (from NaHCO3) = 2
- N: 1 (from HNO3) + 1 (from NaHCO3) = 2
- O: 3 (from HNO3) + 3 (from NaHCO3) = 6
- Na: 1 (from NaHCO3) = 1
- C: 1 (from NaHCO3) = 1
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Products:
- H: 2 (from H2O)
- N: 1 (from NaNO3)
- O: 3 (from NaNO3) + 1 (from H2O) + 2 (from CO2) = 6
- Na: 1 (from NaNO3)
- C: 1 (from CO2)
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Adjust coefficients to balance the equation:
The initial counts suggest that each side is balanced for sodium (Na), carbon (C), oxygen (O), and hydrogen (H), but nitrogen (N) must be reconsidered.
Adjusting N requires that we have matching amounts in reactants and products:
The balanced equation now reads: \[ 1 \text{ HNO}_3 + 1 \text{ NaHCO}_3 \rightarrow 1 \text{ NaNO}_3 + 1 \text{ H}_2\text{O} + 1 \text{ CO}_2 \]
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Final coefficients: \[ 1 \text{ HNO}_3 + 1 \text{ NaHCO}_3 \rightarrow 1 \text{ NaNO}_3 + 1 \text{ H}_2\text{O} + 1 \text{ CO}_2 \]
So, the coefficients are: 1, 1, 1, 1, 1, respectively for each compound in the equation. Thus, the fully balanced equation is: \[ \text{HNO}_3 + \text{NaHCO}_3 \rightarrow \text{NaNO}_3 + \text{H}_2\text{O} + \text{CO}_2 \]