Explanation:

To understand why one mole of molecules may not be equal to a given number of particles (N), let's first understand what a mole is.

- Mole: A mole is a unit of measurement used in chemistry to express the amount of a substance. One mole of any substance contains the Avogadro number (6.022 x 10^23) of particles, which could be atoms, molecules, ions, or other entities.

Now, let's analyze each option to understand why option 'B' is the correct answer.

a) 6.022 x 10^23 number of molecules:
- This is the definition of a mole. One mole of any substance contains 6.022 x 10^23 molecules. So, this option is correct.

b) Given number of particles (N):
- This option states that one mole of molecules may not be equal to a given number of particles (N). It means that if a specific number of particles is given, it may or may not be equal to one mole of molecules. This is because the given number of particles might not be exactly 6.022 x 10^23, which is the Avogadro number. So, this option is correct.

c) Avogadro number:
- The Avogadro number is 6.022 x 10^23, which represents the number of particles in one mole of any substance. This option is incorrect because one mole of molecules is indeed equal to the Avogadro number.

d) Molecular mass in grams:
- The molecular mass of a substance is the mass of one molecule of that substance expressed in atomic mass units (amu) or grams per mole. This option is incorrect because the molecular mass in grams is the mass of one mole of molecules, which is equal to the Avogadro number.

Conclusion:
- One mole of molecules may not be equal to a given number of particles (N) because the given number of particles might not be exactly 6.022 x 10^23, which is the Avogadro number. Therefore, option 'B' is the correct answer.

Option 'a' .If I am right