Answer:
16.00 L
Explanation:
We are given the chemical reaction:
[tex]\rm N_2 + 3 \: H_2 \to 2\: NH_3[/tex]
and the amount of nitrogen gas reacted:
[tex]m_{\text{N2}} = 10.00\text{ g}[/tex]
We are being asked to calculate the volume of ammonia (the product) that will be formed from the given amount of nitrogen.
First, we can convert the mass of nitrogen to moles, then use the reaction's stoichiometric ratios to solve for how many moles of ammonia will be produced.
[tex]n = \dfrac{10.00\text{ g N}_2}{1}\times\dfrac{1 \text{ mole N}_2}{2(14.01)\text{ g N}_2} \times \dfrac{2\text{ mole NH}_3}{1\text{ mole N}_2}[/tex]
[tex]n \approx 0.71378 \text{ mole NH}_3[/tex]
Then, we can plug this amount of ammonia gas into the ideal gas law to solve for the amount of volume it will occupy at standard temperature and pressure (STP):
[tex]PV = nRT[/tex]
where:
- [tex]P[/tex] = pressure
- [tex]V[/tex] = volume
- [tex]n[/tex] = moles of gas
- [tex]R[/tex] = universal gas constant
- [tex]T[/tex] = temperature in Kelvin
According to the College Board, STP is defined as:
[tex]P = 1\text{ atm}[/tex], [tex]T = 273.15\text{ K}[/tex]
and the gas constant is:
[tex]R = 0.08206\ \dfrac{\text{ L}\cdot\text{atm}}{\text{mole} \cdot \text{K}}[/tex]
Solving the ideal gas law for volume gives us:
[tex]V = \dfrac{nRT}{P}[/tex]
Now, we can plug in the known values to solve for [tex]V[/tex]:
[tex]V = \dfrac{(0.71378\text{ mole})\,(0.08206 \text{ L}\cdot\text{atm} \, / \, [\text{mole} \cdot \text{K}])\,(273.15\text{ K})}{1\text{ atm}}[/tex]
[tex]\boxed{V = 16.00 \text{ L}}[/tex]
So, the volume of ammonia produced by the given reaction is 16.00 Liters.