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 × 1023 atoms of C into number of moles:
We know, 1 mole = 6.022 × 1023 (Na = 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 × 1023 atoms of C is 0.5.
(b) Given mass: 32g
Molar mass of oxygen gas (O2 ) = 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.