**Mole:** One mole of any species (Atoms, molecules, ions or particles) is that quantity in number having a mass equal to its atomic or molecules mass in grams.

**(a)** We will convert 1.0505 × 10^{23} atoms of C into number of moles:

We know, 1 mole = 6.022 × 10^{23} (N_{a }= Avogadro’s number)

The number of moles = \(\frac{Given\,number\,of\,atoms}{Avogadro's\,number}\)

Number of moles = \(\frac{3.011\times10^{23}}{6.022\times10^{23}}\)

Number of moles = 0.5

Thus, the number of moles in 3.011 × 10^{23} atoms of C is 0.5.

**(b) Given mass:** 32g

Molar mass of oxygen gas (O_{2} ) = 2 × atomic mass of oxygen = 2 × 16 u = 32g /mol

**To calculate the number of moles, we will apply the formula given below:**

Number of moles (n) = \(\frac{Given\,mass(m)}{Molar\,mass(M)}\)

Number of moles (n) = \(\frac{32g}{32g/mol}\)

Number of mole = 1

**Thus, the number of mole in 32 g of oxygen gas is 1.**