To determine the number of atoms in a given mass of a substance, you need to use the concept of Avogadro's number and the molar mass of the substance.
The molar mass of methane (CH4) can be calculated by adding up the atomic masses of its constituent elements: carbon (C) and hydrogen (H).
Carbon (C) atomic mass = 12.01 g/mol Hydrogen (H) atomic mass = 1.01 g/mol
Molar mass of methane (CH4) = 12.01 g/mol (carbon) + 4 × 1.01 g/mol (hydrogen) = 16.05 g/mol
Now, using the molar mass of methane, you can calculate the number of moles in 32 grams of methane:
Number of moles = Mass (g) / Molar mass (g/mol) Number of moles = 32 g / 16.05 g/mol ≈ 1.99 mol
Avogadro's number states that 1 mole of any substance contains 6.022 × 10^23 entities, which can be atoms, molecules, or other particles. Therefore, in 1.99 moles of methane, there are:
Number of atoms = Number of moles × Avogadro's number Number of atoms = 1.99 mol × 6.022 × 10^23 atoms/mol ≈ 1.20 × 10^24 atoms
So, there are approximately 1.20 × 10^24 atoms in 32 grams of methane.