To solve the problem of calculating the total volume of gas produced from the complete decomposition of 1 mole of Ammonium Nitrate (NH4NO3) at standard temperature and pressure (STP), we need to follow these steps:
1. Write the balanced chemical equation for the decomposition:
[tex]\[
\text{NH}_4\text{NO}_3(s) \rightarrow \text{N}_2(g) + 2 \text{H}_2\text{O}(g) + \frac{1}{2} \text{O}_2(g)
\][/tex]
2. Determine the moles of each gas produced:
- 1 mole of NH4NO3 produces:
- 1 mole of N2 (nitrogen gas)
- 2 moles of H2O (water vapor)
- 0.5 moles of O2 (oxygen gas)
3. Calculate the total moles of gas produced:
[tex]\[
\text{Total moles of gas} = \text{moles of N}_2 + \text{moles of H}_2\text{O} + \text{moles of O}_2
\][/tex]
[tex]\[
\text{Total moles of gas} = 1 + 2 + 0.5 = 3.5 \text{ moles}
\][/tex]
4. Recall the volume of one mole of an ideal gas at STP:
- At standard temperature and pressure, 1 mole of any ideal gas occupies 22.4 liters.
5. Calculate the total volume of gas produced:
[tex]\[
\text{Total volume of gas} = \text{Total moles of gas} \times \text{Volume per mole}
\][/tex]
[tex]\[
\text{Total volume of gas} = 3.5 \text{ moles} \times 22.4 \text{ liters/mole}
\][/tex]
[tex]\[
\text{Total volume of gas} = 78.4 \text{ liters}
\][/tex]
Therefore, the total volume of gas produced from the complete reaction of 1 mole of Ammonium Nitrate in a car's air bag at standard temperature and pressure is 78.4 liters.
