Avogadro’s number: choose the correct definition in molecules per gram-mole (mol).

Introduction / Context:
Avogadro’s number links the microscopic count of particles to macroscopic amounts in moles. It is fundamental to stoichiometry, gas laws, and conversion between mass and number of particles for any chemical species.

Given Data / Assumptions:

• One mole (gram-mole) is the amount of substance containing Avogadro’s number of specified entities (atoms, molecules, ions, etc.).
• Conventional value used in many textbooks: 6.023 × 10^23; modern exact value is 6.02214076 × 10^23 mol^−1.

Concept / Approach:
The definition associates the gram-mole (simply “mole” in SI) with 6.02×10^23 entities. Options using kilogram-mole would scale the count differently and are not the standard definition for “per gram-mole.” Thus, the correct choice is 6.023 × 10^23 molecules per gram-mole (mol).

Step-by-Step Solution:

Verification / Alternative check:
Consult any physical constants table; the count per mole is ~6.02 × 10^23, independent of substance.

Why Other Options Are Wrong:

• (a) mislabels per kmol; 1 kmol would contain 1000 × NA entities.
• (c), (d), (e) use incorrect magnitudes.

Common Pitfalls:
Confusing kmol and mol; industrial gas calculations often use kmol but the particle count scales accordingly.

Final Answer:
6.023 × 10^23 molecules per gram-mole