Questions: Calculate the mass of hydrazine (N2H4) that contains a trillion (1.000 x 10^12) hydrogen atoms. Be sure your answer has a unit symbol if necessary, and round it to 4 significant digits.

Solution Steps

First, we need to find the number of moles of hydrogen atoms in a trillion hydrogen atoms. The number of atoms in one mole is given by Avogadro's number, \(6.022 \times 10^{23}\) atoms/mol.

\[ \text{Moles of hydrogen atoms} = \frac{1.000 \times 10^{12} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} = 1.661 \times 10^{-12} \text{ mol} \]

Each molecule of hydrazine \(\mathrm{N}_2\mathrm{H}_4\) contains 4 hydrogen atoms. Therefore, the number of moles of hydrazine is one-fourth the number of moles of hydrogen atoms.

\[ \text{Moles of hydrazine} = \frac{1.661 \times 10^{-12} \text{ mol}}{4} = 4.1525 \times 10^{-13} \text{ mol} \]

The molar mass of hydrazine \(\mathrm{N}_2\mathrm{H}_4\) is calculated as follows:

• Nitrogen (N) has a molar mass of approximately 14.01 g/mol.
• Hydrogen (H) has a molar mass of approximately 1.008 g/mol.

\[ \text{Molar mass of } \mathrm{N}_2\mathrm{H}_4 = 2 \times 14.01 + 4 \times 1.008 = 32.05 \text{ g/mol} \]

Now, calculate the mass of hydrazine:

\[ \text{Mass of hydrazine} = 4.1525 \times 10^{-13} \text{ mol} \times 32.05 \text{ g/mol} = 1.331 \times 10^{-11} \text{ g} \]

Final Answer