High School

Ammonium nitrate decomposes when heated to produce dinitrogen monoxide and water, as follows:

\[ \text{NH}_4\text{NO}_3(s) \rightarrow \text{N}_2\text{O} (g) + \text{H}_2\text{O}(l) \]

If 12.2 g of \(\text{NH}_4\text{NO}_3\) reacts, what volume of \(\text{N}_2\text{O}\) is produced, measured at 98.5 kPa and \(14^\circ C\)?

Answer :

Final answer:

The volume of dinitrogen monoxide gas produced from the decomposition of ammonium nitrate can be calculated using stoichiometry and the ideal gas law, considering the specific temperature and pressure conditions given.

Explanation:

The decomposition of ammonium nitrate (NH4NO3) when heated results in the production of dinitrogen monoxide (N2O) and water (H2O). To calculate the volume of N2O gas produced from 12.2 g of NH4NO3 at a specific temperature and pressure, we must use stoichiometry and the ideal gas law equation PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

To solve the problem, we would first convert the mass of ammonium nitrate to moles using its molar mass. Next, we apply the stoichiometry from the balanced chemical equation to find the moles of N2O produced. Finally, we use the ideal gas law equation to calculate the volume of N2O gas at the given temperature (14°C, which is 287.15 Kelvin) and pressure (98.5 kPa).

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