Answer:
[1]
The balanced chemical equation for the reaction is:
2NH₂ + H₂O₂ → N₂H₄ + 2H₂O
The molar mass of NH₂ is 16 g/mol (2 × 1.008 + 2 × 14.01), and the molar mass of H₂O₂ is 34 g/mol (2 × 1.008 + 2 × 16.00). The molar mass of N₂H₄ is 32 g/mol (2 × 14.01 + 2 × 1.008), and the molar mass of H₂O is 18 g/mol.
The total mass of the reactants is:
2 × 16 g/mol NH₂ + 34 g/mol H₂O₂ = 66 g/mol
The total mass of the products is:
32 g/mol N₂H₄ + 2 × 18 g/mol H₂O = 68 g/mol
The atom economy is the mass of the desired product divided by the total mass of the reactants, expressed as a percentage:
Atom economy = (mass of desired product / total mass of reactants) × 100%
Atom economy = (32 g/mol N₂H₄ / 66 g/mol) × 100%
Atom economy = 48.5%
To calculate the mass of calcium that contains the same number of atoms as there are molecules in 9.1 g of SO₂, we need to first find the number of molecules of SO₂ in 9.1 g of the compound.
[2]
The molar mass of SO₂ is 64 g/mol (32.06 + 2 × 16.00). The number of moles of SO₂ in 9.1 g of the compound is therefore:
n = mass / molar mass = 9.1 g / 64 g/mol = 0.142 mol
One mole of any substance contains the same number of particles (atoms, molecules, or ions) as the number of atoms in 12 g of carbon-12, which is approximately 6.02 × 10²³ particles (Avogadro's number). Therefore, the number of molecules of SO₂ in 9.1 g of the compound is:
number of molecules = n × Avogadro's number = 0.142 mol × 6.02 × 10²³/mol = 8.56 × 10²² molecules
To find the mass of calcium that contains the same number of atoms as there are molecules in 9.1 g of SO₂, we need to calculate the number of atoms in 8.56 × 10²² molecules of SO₂. The balanced chemical equation for the formation of SO₂ is:
S + O₂ → SO₂
One molecule of SO₂ contains one sulfur atom and two oxygen atoms. Therefore, 8.56 × 10²² molecules of SO₂ contain:
8.56 × 10²² molecules SO₂ × 1 sulfur atom / molecule = 8.56 × 10²² sulfur atoms
8.56 × 10²² molecules SO₂ × 2 oxygen atoms / molecule = 1.71 × 10²³ oxygen atoms
To obtain the same number of atoms of calcium, we need to divide the number of atoms of sulfur by the number of atoms of calcium in the following balanced chemical equation:
Ca + S → CaS
One calcium atom reacts with one sulfur atom to form one molecule of CaS. Therefore, the number of calcium atoms required is:
8.56 × 10²² sulfur atoms / 1 sulfur atom per Ca atom = 8.56 ×