Understanding the Problem
To find the mass of hydrochloric acid (HCl) that contains the same number of hydrogen atoms as 16 g of methane (CH4), we first need to analyze the composition of both compounds.
Hydrogen Atoms in Methane
- Methane (CH4) contains 4 hydrogen atoms per molecule.
- The molar mass of methane is approximately 16 g/mol.
- Therefore, 16 g of methane corresponds to 1 mole of CH4.
Calculating Hydrogen Atoms in Methane
- Since 1 mole of CH4 contains 4 moles of hydrogen atoms:
- 1 mole of CH4 = 4 moles of H.
- Using Avogadro's number (approximately 6.022 x 10^23), we find:
- Total hydrogen atoms in 16 g of CH4 = 4 moles × 6.022 x 10^23 atoms/mole = 2.4088 x 10^24 hydrogen atoms.
Hydrogen Atoms in Hydrochloric Acid
- Hydrochloric acid (HCl) contains 1 hydrogen atom per molecule.
- To match the number of hydrogen atoms from methane:
- We need 2.4088 x 10^24 hydrogen atoms from HCl.
Calculating the Required Mass of HCl
- Since 1 mole of HCl contains 1 mole of hydrogen, we need:
- 2.4088 x 10^24 atoms = 2.4088 x 10^24 / 6.022 x 10^23 = 4 moles of HCl.
- The molar mass of HCl is approximately 36.5 g/mol.
- Therefore, the mass of HCl required = 4 moles × 36.5 g/mol = 146 g.
Conclusion
To obtain the same number of hydrogen atoms as in 16 g of methane, a mass of 146 g of hydrochloric acid is required.