Answer :
To convert 5.00 liters of [tex]\( \text{NH}_3 \)[/tex] at standard temperature and pressure (STP) to grams, we can follow these steps:
1. Understand the concept: At STP, any ideal gas occupies 22.414 liters per mole. This is known as the molar volume.
2. Identify the molar mass of [tex]\( \text{NH}_3 \)[/tex]: The molar mass of ammonia ([tex]\( \text{NH}_3 \)[/tex]) is approximately 17.031 grams per mole. This value is based on the atomic masses of nitrogen (N) and hydrogen (H) from the periodic table, where nitrogen is about 14.007 g/mol and hydrogen is 1.008 g/mol.
3. Calculate the number of moles of [tex]\( \text{NH}_3 \)[/tex]: To find out how many moles of [tex]\( \text{NH}_3 \)[/tex] are in 5.00 liters, use the formula:
[tex]\[
\text{Moles of } \text{NH}_3 = \frac{\text{Volume of } \text{NH}_3 \text{ at STP}}{\text{Molar volume at STP}}
\][/tex]
Plug in the values:
[tex]\[
\text{Moles of } \text{NH}_3 = \frac{5.00 \, \text{liters}}{22.414 \, \text{liters/mole}} \approx 0.223 \, \text{moles}
\][/tex]
4. Calculate the mass of [tex]\( \text{NH}_3 \)[/tex]: Now that we know the number of moles, we can find the mass by multiplying the number of moles by the molar mass:
[tex]\[
\text{Mass of } \text{NH}_3 = \text{Moles of } \text{NH}_3 \times \text{Molar mass of } \text{NH}_3
\][/tex]
Substituting the values:
[tex]\[
\text{Mass of } \text{NH}_3 = 0.223 \, \text{moles} \times 17.031 \, \text{g/mole} \approx 3.80 \, \text{grams}
\][/tex]
Thus, 5.00 liters of [tex]\( \text{NH}_3 \)[/tex] at STP is approximately 3.80 grams.
1. Understand the concept: At STP, any ideal gas occupies 22.414 liters per mole. This is known as the molar volume.
2. Identify the molar mass of [tex]\( \text{NH}_3 \)[/tex]: The molar mass of ammonia ([tex]\( \text{NH}_3 \)[/tex]) is approximately 17.031 grams per mole. This value is based on the atomic masses of nitrogen (N) and hydrogen (H) from the periodic table, where nitrogen is about 14.007 g/mol and hydrogen is 1.008 g/mol.
3. Calculate the number of moles of [tex]\( \text{NH}_3 \)[/tex]: To find out how many moles of [tex]\( \text{NH}_3 \)[/tex] are in 5.00 liters, use the formula:
[tex]\[
\text{Moles of } \text{NH}_3 = \frac{\text{Volume of } \text{NH}_3 \text{ at STP}}{\text{Molar volume at STP}}
\][/tex]
Plug in the values:
[tex]\[
\text{Moles of } \text{NH}_3 = \frac{5.00 \, \text{liters}}{22.414 \, \text{liters/mole}} \approx 0.223 \, \text{moles}
\][/tex]
4. Calculate the mass of [tex]\( \text{NH}_3 \)[/tex]: Now that we know the number of moles, we can find the mass by multiplying the number of moles by the molar mass:
[tex]\[
\text{Mass of } \text{NH}_3 = \text{Moles of } \text{NH}_3 \times \text{Molar mass of } \text{NH}_3
\][/tex]
Substituting the values:
[tex]\[
\text{Mass of } \text{NH}_3 = 0.223 \, \text{moles} \times 17.031 \, \text{g/mole} \approx 3.80 \, \text{grams}
\][/tex]
Thus, 5.00 liters of [tex]\( \text{NH}_3 \)[/tex] at STP is approximately 3.80 grams.
