To determine the number of atoms in a given mass of a substance, we need to use the concept of moles and Avogadro's number. Avogadro's number states that one mole of any substance contains approximately 6.022 x 10^23 particles (atoms, molecules, ions, etc.).
First, we need to calculate the number of moles of methane in 32 grams. The molar mass of methane (CH₄) is approximately 16 grams/mol (12 grams/mol for carbon + 1 gram/mol for each of the four hydrogen atoms).
Number of moles = mass / molar mass Number of moles = 32 g / 16 g/mol Number of moles = 2 mol
Since one mole of methane contains one mole of carbon atoms and four moles of hydrogen atoms, we can determine the total number of atoms by multiplying the number of moles by Avogadro's number:
Total number of atoms = Number of moles * Avogadro's number Total number of atoms = 2 mol * 6.022 x 10^23 atoms/mol Total number of atoms ≈ 1.204 x 10^24 atoms
Therefore, there are approximately 1.204 x 10^24 atoms in 32 grams of methane.