Question

You need $2.5moles$ of aluminium for an experiment. How many atoms of aluminium is this?

Answer 1

Hint:
i) In order to find out the number of atoms of any element in a given mass of that element, at first we need to find out the number of moles of that element present in that specific amount.
ii) And then we will use Avogadro's number to find out the exact number of atoms present in it. In some cases the number of moles of a substance is already given, we just need to multiply that value with Avogadro’s number in order to get the number of atoms or particles.

Complete step-by-step answer:
The number of moles of any substance or an element is the amount of that substance present per molar mass of that substance in terms of moles. The simple formula is the given mass present per molar mass of the atom or a compound and can be mathematically expressed as,
$n=\dfrac{m}{M}$
Where $n$ symbolizes the number of moles of the element, $m$ represents the given mass of the element and $M$ is the molecular mass of the element.

Since in the question, the number of moles of the element is already provided to us, we will directly calculate the number of atoms present in that many moles of aluminium. We know that one mole of any substance contains \[6.0221409\times {{10}^{23}}\] number of particles, in this case atoms.

So we will multiply the number of moles with the Avogadro’s number which is \[6.0221409\times {{10}^{23}}\]. We get,
\[6.0221409\times {{10}^{23}}\times 2.5=1.5055\times {{10}^{22}}atoms\]

Thus the number of atoms are, \[1.5055\times {{10}^{22}}atoms\] which is the required answer.

Note: The number of atoms present per moles of a molecule is equal to the Avogadro’s number which is \[6.0221409\times {{10}^{23}}\], and this concept is also termed as the mole concept.
The number of moles of any element is the given mass of that atom present per molar mass of the atom or element.