Question

Question: Number of atoms $558.5g$ $Fe$ (At.wt. of $Fe$ is $55.85gmo{l^{ - 1}}$) is:
A) Twice that in $60g$ carbon
B) $6.023 \times {10^{23}}$
C) Half that of $8g$ $He$
D) $558.5 \times 6.023 \times {10^{23}}$

Answer 1

Hint: By using the data given in the question one can find a conclusion and compare the options given in the question. One can analyze them in comparison to the number of atoms or the number of moles of the given option with respect to the $Fe$ atom.

 Complete step by step answer:
1) As per the given data let's find out the number of moles of $Fe$ atom, as per the number of moles formula, $n = \dfrac{{{\text{Given weight in grams}}}}{{{\text{Atomic weight in grams}}}} = \dfrac{{558.5}}{{55.85}} = 10moles$
Hence, as per question data, there are ten numbers of moles $Fe$ are present.
2) Now let's analyze all options one by one, in option A $60g$ of carbon is given hence, the number of moles of carbon atoms in the $60g$ carbon is $n = \dfrac{{{\text{Given weight in grams}}}}{{{\text{Atomic weight in grams}}}} = \dfrac{{60}}{{12}} = 5$
As the number of atoms of $Fe$ is ten and the number of atoms of carbon is five it shows $Fe$ atoms are twice that of the carbon which shows option A is true.
3) In option B the Avogadro's number is given and let's compare that value with Avogadro's number of $Fe$ atoms, As one mole of $Fe$ the atom shows $6.023 \times {10^{23}}$ Avogadro's number than ten $Fe$ atoms will show as following $10 \times \;\left( {6.023 \times {{10}^{23}}} \right) = 6.023 \times {10^{24}}$ which does not match with the option B which is incorrect.
4) In option C, $8g$ of $He$ will give four moles which are not half of the ten $Fe$ atoms which shows option C as an incorrect option.
5) In option D, the total weight $Fe$ is multiplied by Avogadro's number which isn’t correct, and hence option D is also incorrect.

So, the correct answer is Option A.

Note:
The number of moles of an atom present in the total molecular weight is equal to the number of atoms present. The Avogadro's number shows the number of constituent particles present in the sample or compound with the total amount of the substance present in that sample.