Question

The number of iron (Fe) atoms present in a pure sample of solid iron with a mass of $10$grams is equal to. (The atomic mass of iron is $55.9$).
A. $\left ( 10.0 \right)\times \left( 55.9 \right)\times \left( 6.02\times {{10}^{23}} \right)atoms$
$\begin{aligned} & B.\dfrac{6.02\times {{10}^{23}}}{10.0\times 55.9} \\\ & C.\dfrac{10.0\times 6.02\times {{10}^{23}}}{55.9} \\\ & D.\dfrac{55.9}{10.0\times 6.02\times {{10}^{23}}} \\\ & E.\dfrac{10.0}{55.9\times 6.02\times {{10}^{23}}} \\\ \end{aligned}$

Answer 1

In this question we need to find out the number of atoms. Firstly, we need to calculate the number of moles. Once the number of moles are calculated we can find out the number of atoms by multiplying moles with the Avogadro number $\left( 6.02\times {{10}^{23}} \right)$.

Complete step-by-step answer: In order to find the number of atoms, we need to calculate the number of moles firstly.
In the question mass of iron is given to us as = $10$grams and
Molar mass of iron = $55.9$g/mole or
We, know that when in question mass of a substance is given to us and we need to find out the number of moles, we can find them using the formula,
Number of moles in a substance = $\dfrac{given\,mass}{molar\,mass}$
Therefore, number of moles of iron $\left( Fe \right)$present in the given sample is given as
Number of moles = $\dfrac{10}{55.9}$moles
Now we know that one mole of any substance contains = $6.02\times {{10}^{23}}$atoms/molecules/ions
So, if we want to find out the number of atoms in $\dfrac{10}{55.9}$moles, we need to multiply the moles with Avogadro's number, which is $6.02\times {{10}^{23}}$.
Therefore, number of atoms is $\dfrac{10}{55.9}$moles of iron will be given as,
$\Rightarrow \dfrac{10}{55.9}\times 6.02\times {{10}^{23}}$atoms
So, we can say that $10$grams of iron contain $\dfrac{10}{55.9}\times 6.02\times {{10}^{23}}$atoms in it.

Hence, the correct option is option C.

Note: In questions related to mole concept always determine the starting and the ending point, just as we did in the hint above. Then, write down what is given and then see what you need to calculate. Start solving by relating the given values and values which need to be calculated.