Question

Calculate the number of moles in
1. in $8g$ of oxygen atom
2. $4.088 \times {10^{21}}$ number of oxygen atoms. ( Atomic mass of $O = 16amu$)

Answer 1

Number of moles is the ratio of the given mass to the molecular mass. Avogadro’s number gives a relationship between the number of moles and the number of atoms also. Avogadro’s number is also universally applicable to all elements.

Complete step by step answer:
Let us write down the formula which we will be needing for this question
$moles = \dfrac{{given\,mass}}{{molecular\,mass}}$
So the element given to us is oxygen. Oxygen has the atomic number six and has the atomic mass as sixteen or $16amu$ where amu refers to the atomic mass unit.
For the first part of the question, we have been given
Given mass as $8g$
And the molecular mass of $O = 16amu$ (Since, it is mentioned atom in the question, we only take the mass of atom)
Substituting these values, we get:
$moles = \dfrac{8}{{16}} \Rightarrow 0.5$
Hence, for the first part, the answer is $0.5moles$

Now, let's move on to the second part.
We know that there are $6.022 \times {10^{23}}atoms$ in $1mole$
Hence, to find out the number of moles that make up $4.088 \times {10^{21}}$ we have to use a unitary method.
Since, we know that $6.022 \times {10^{23}}atoms$ make up $1mole$
Then,$4.088 \times {10^{21}}$ atoms will make up:
$\dfrac{{4.088 \times {{10}^{21}}}}{{6.022 \times {{10}^{23}}}} \Rightarrow 0.67 \times {10^{ - 2}}moles$

So the answer to the second part is: $0.67 \times {10^{ - 2}}moles$ .

Note: The concept of moles were first introduced because even a very small quantity of an element has an extraordinarily large number of atoms. Hence, in order to interpret data on the basis of this number was rather difficult. Avogadro’s number is a constant value which states every species in this world which has $6.022 \times {10^{23}}atoms$ will make up $1mole$ .