Which one of the following has the same number of atoms as are in 6g of H₂O?

CONCEPT:

Number of Atoms in a Given Mass

• The number of atoms in a given mass of a substance can be calculated using Avogadro's number, which is 6.022 x 10²³ atoms per mole.
• The molar mass of a substance is used to convert the mass of the substance to moles.
• Once the number of moles is known, it can be multiplied by Avogadro's number to find the number of atoms.

EXPLANATION:

• First, we calculate the number of moles in 6g of H₂O:
  • Molar mass of H₂O = 2(1) + 16 = 18 g/mol
  • Number of moles of H₂O = mass / molar mass = 6 g / 18 g/mol = 1/3 mol
• The number of atoms in 1/3 mol of H₂O:
  • Each molecule of H₂O has 3 atoms (2 hydrogen + 1 oxygen)
  • Total number of atoms = 1/3 mol x 6.022 x 10²³ molecules/mol x 3 atoms/molecule = 6.022 x 10²³ atoms
    •  0.4g He
      • Molar mass of He = 4 g/mol
      • Number of moles of He = 0.4 g / 4 g/mol = 0.1 mol
      • Number of atoms = 0.1 mol x 6.022 x 10²³ atoms/mol = 6.022 x 10²² atoms
    •  22g CO₂
      • Molar mass of CO₂ = 12 + 2(16) = 44 g/mol
      • Number of moles of CO₂ = 22 g / 44 g/mol = 0.5 mol
      • Number of molecules = 0.5 mol x 6.022 x 10²³ molecules/mol = 3.011 x 10²³ molecules
      • Each molecule of CO₂ has 3 atoms (1 carbon + 2 oxygen)
      • Number of atoms = 3.011 x 10²³ molecules x 3 atoms/molecule = 9.033 x 10²³ atoms
    •  1g H₂
      • Molar mass of H₂ = 2 g/mol
      • Number of moles of H₂ = 1 g / 2 g/mol = 0.5 mol
      • Number of molecules = 0.5 mol x 6.022 x 10²³ molecules/mol = 3.011 x 10²³ molecules
      • Each molecule of H₂ has 2 atoms (2 hydrogen)
      • Number of atoms = 3.011 x 10²³ molecules x 2 atoms/molecule = 6.022 x 10²³ atoms
    •  12g CO
      • Molar mass of CO = 12 + 16 = 28 g/mol
      • Number of moles of CO = 12 g / 28 g/mol = 0.4286 mol
      • Number of molecules = 0.4286 mol x 6.022 x 10²³ molecules/mol = 2.579 x 10²³ molecules
      • Each molecule of CO has 2 atoms (1 carbon + 1 oxygen)
      • Number of atoms = 2.579 x 10²³ molecules x 2 atoms/molecule = 5.158 x 10²³ atoms

Therefore, the correct answer is option 3, which is 1g H₂.