Question

What is the mass in grams of $9.357\times {{10}^{30}}$ atoms of iron?

Answer 1

One mole of any element contains an Avogadro number of atoms in it. We should consider the Avogadro number while calculating the number of atoms of any compound.
Avogadro number = 6.022$\times {{10}^{23}}$ atoms.

Complete answer:
- In the question it is asked to calculate the mass of the iron which contains $9.357\times {{10}^{30}}$ atoms in it.
- First we should recall that one mole of any substance contains Avogadro's number of atoms in it.
- Therefore one mole of iron contains 6.022$\times {{10}^{23}}$ atoms in it.
One mole of iron = 6.022$\times {{10}^{23}}$ atoms.
- First we have to calculate the one atom iron contains how much mass and it is as follows.
- The mass of the iron atom is equal to $\dfrac{\text{atomic weight of the iron}}{\text{Avogadro number}}$
- We know that the atomic weight of the iron = 55.845 g.
- Therefore the mass of one iron atom is = $\dfrac{55.845}{6.022\times {{10}^{23}}}=9.2735\times {{10}^{-23}}g$ .
- Now we have to calculate the mass of $9.357\times {{10}^{30}}$ iron atoms in 9.2735$\times {{10}^{-23}}$ grams and it is as follows.

& =(9.357\times {{10}^{30}})(9.2735\times {{10}^{-23}}) \\\ & =8.677\times {{10}^{8}}g \\\ \end{aligned}$$ \- Means $9.357\times {{10}^{30}}$ atoms of iron comprising $8.667\times {{10}^{8}}g$ of iron atoms in it. \- Therefore the mass of the $9.357\times {{10}^{30}}$ atoms of iron is $8.667\times {{10}^{8}}g$ . **Note:** First we have to calculate the mass of the one iron atom with the help of the atomic weight of the iron atom and later we have to calculate the mass of the given content of the iron atoms by using the mass of the one iron atom.