Counting entities in one gram-mole of methane:\nOne gram-mole (1 mol) of methane, CH4, contains which of the following?

Introduction / Context:
Chemical stoichiometry hinges on interpreting moles, molecules, and gram-atoms correctly. Methane (CH4) has one carbon atom and four hydrogen atoms per molecule, so one mole of CH4 contains Avogadro’s number of molecules and four times that number of hydrogen atoms.

Given Data / Assumptions:

• Avogadro’s number N_A ≈ 6.02 × 10^23 per mole.
• Formula of methane: CH4.
• “Gram-atom” of an element means 1 mole of that element’s atoms.

Concept / Approach:
For a compound A_xB_y, one mole contains x gram-atoms of A and y gram-atoms of B. Therefore, 1 mol CH4 contains 1 gram-atom of carbon and 4 gram-atoms of hydrogen. Converting to counts: hydrogen atoms = 4 N_A; methane molecules = 1 N_A. Mass-wise, 1 mol CH4 contains 12 g of carbon and 4 g of hydrogen, total 16 g.

Step-by-Step Solution:
Map stoichiometry: CH4 → 4 H per molecule.Per mole: hydrogen gram-atoms = 4 mol.Hence, “4 gram-atoms of hydrogen” is correct.

Verification / Alternative check:
Atom count check: H atoms = 4 × 6.02 × 10^23 ≈ 2.41 × 10^24; greater than 6.02 × 10^23 in option (a), confirming (a) is too small.

Why Other Options Are Wrong:
6.02 × 10^23 H atoms: undercounts by a factor of four.3.01 × 10^23 CH4 molecules: equals 0.5 mol, not 1 mol.3 g of carbon: 1 mol CH4 contains 12 g of carbon, not 3 g.

Common Pitfalls:
Confusing “molecules per mole” with “atoms per mole”; misreading gram-atom terminology.

Final Answer:
4 gram-atoms of hydrogen