To calculate the mass of ammonia ([tex]$NH_3$[/tex]) that contains a trillion ([tex]$1.000 \times 10^{12}$[/tex]) hydrogen atoms, we can follow these steps:
1. Number of Hydrogen Atoms in Ammonia:
Each molecule of ammonia ([tex]$NH_3$[/tex]) contains 3 hydrogen atoms.
2. Avogadro's Number:
Avogadro's number, which is the number of atoms or molecules in one mole of a substance, is [tex]\(6.022 \times 10^{23}\)[/tex].
3. Molar Mass of Ammonia:
The molar mass of ammonia is calculated by summing the molar masses of its constituent atoms:
- Nitrogen (N): [tex]\(14.01 \, \text{g/mol}\)[/tex]
- Hydrogen (H): [tex]\(1.008 \, \text{g/mol}\)[/tex]
Therefore,
[tex]\[
\text{Molar mass of } NH_3 = 14.01 + 3 \times 1.008 = 17.034 \, \text{g/mol}
\][/tex]
4. Number of Moles of Hydrogen Atoms:
The number of moles of hydrogen atoms in a trillion hydrogen atoms is calculated by dividing by Avogadro's number:
[tex]\[
\text{Moles of hydrogen atoms} = \frac{1.000 \times 10^{12}}{6.022 \times 10^{23}} \approx 1.661 \times 10^{-12} \, \text{moles}
\][/tex]
5. Number of Moles of Ammonia:
Considering each molecule of ammonia contains 3 hydrogen atoms, the number of moles of ammonia containing [tex]$1.000 \times 10^{12}$[/tex] hydrogen atoms is:
[tex]\[
\text{Moles of ammonia} = \frac{1.661 \times 10^{-12}}{3} \approx 5.535 \times 10^{-13} \, \text{moles}
\][/tex]
6. Mass of Ammonia:
The mass of this amount of ammonia can be calculated by multiplying the number of moles of ammonia by its molar mass:
[tex]\[
\text{Mass of ammonia} = 5.535 \times 10^{-13} \, \text{moles} \times 17.034 \, \text{g/mol}
\][/tex]
[tex]\[
\text{Mass of ammonia} \approx 0.0 \, \text{g}
\][/tex]
After rounding the final answer to 4 significant digits, the mass of ammonia containing a trillion hydrogen atoms is:
[tex]\[ 0.0 \, \text{g} \][/tex]
So, the mass of ammonia ([tex]$NH_3$[/tex]) needed to contain a trillion ([tex]$1.000 \times 10^{12}$[/tex]) hydrogen atoms is effectively zero grams when rounded to four significant digits.
