Question

Calculate the mass of hydrazine (N2H4) that contains a billion (1.000 x 10^9) hydrogen atoms.

Be sure your answer has a unit symbol if necessary, and round it to 4 significant digits.

Answer 1

To find the mass of hydrazine with 1 billion hydrogen atoms, calculate the number of moles of hydrogen, convert that to moles of N2H4, and then use the molar mass of hydrazine to find the mass in grams, resulting in 1.330 x 10^-14 g.

Step-by-step explanation:

To calculate the mass of hydrazine, N2H4, containing 1 billion hydrogen atoms, we first need to determine the number of moles of hydrogen atoms present. Knowing that one mole of hydrogen contains Avogadro's number of atoms (approximately 6.022 x 1023), we can use dimensional analysis to find the number of moles corresponding to 1.000 x 109 hydrogen atoms.

Number of moles of H = (1.000 x 109 atoms) / (6.022 x 1023 atoms/mol) = 1.660 x 10-15 mol H

We know that there are 4 hydrogen atoms in one molecule of hydrazine, therefore:

Number of moles of N2H4 = (1.660 x 10-15 mol H) / (4 atoms of H per molecule of N2H4) = 4.150 x 10-16 mol N2H4

Next, we find the molar mass of hydrazine. From the periodic table, nitrogen has a molar mass of approximately 14.01 g/mol and hydrogen has a molar mass of 1.01 g/mol:

Molar mass of N2H4 = (2 x 14.01 g/mol) + (4 x 1.01 g/mol) = 32.04 g/mol

Finally, we calculate the mass by multiplying the moles of N2H4 by its molar mass:

Mass of N2H4 = 4.150 x 10-16 mol x 32.04 g/mol = 1.330 x 10-14 g

Therefore, the mass of hydrazine that contains 1 billion hydrogen atoms is 1.330 x 10-14 g, or when rounded to 4 significant digits, 1.330 x 10-14 g.

Answer 2

1.3285 × 10⁻¹⁴ g of hydrazine

Step-by-step explanation:

if 32 g of hydrizine (1 mole) contains 4 × 6.022 × 10²³ hydrogen atoms

then X g of hydrizine contains 1 × 10⁹ hydrogen atoms

X = (32 × 1 × 10⁹) / (4 × 6.022 × 10²³)

X = 1.3285 × 10⁻¹⁴ g of hydrazine