Question

Number of atoms in 560 grams of $\text{Fe}$is:
A.Twice that of 70 g ${{\text{N}}_{\text{2}}}$
B.Half that of 20 g ${{\text{H}}_{\text{2}}}$
C.Both A and B
D.None of the above.

Answer 1

This problem is based on the concept of “mole”, which is a unit of measurement and is equal to $6.023\times {{10}^{23}}$particles of any substance, where the word “particles” refer to atoms, molecules, ions, and other subatomic particles.

Complete step by step answer:
The atomic weight of iron = 56 grams
One gram atomic weight of iron is equal to one mole of iron atoms.
Therefore, 56 grams of iron =$6.023\times {{10}^{23}}$ atoms of iron.
Hence, 560 grams of iron =$6.023\times {{10}^{24}}$ atoms of iron = 10 times the Avogadro’s number of atoms.
Now, the molecular weight of nitrogen = 28 grams,
Therefore, 28 grams of nitrogen =$6.023\times {{10}^{23}}$ molecules of nitrogen =$2\times 6.023\times {{10}^{23}}$ atoms of nitrogen, as each molecule of nitrogen has 2 atoms.
Therefore 70 gram of nitrogen =$2\times 6.023\times {{10}^{23}}\times \dfrac{70}{28}$ atoms of nitrogen = $5\times 6.023\times {{10}^{23}}$ atoms of nitrogen = 5 times the Avogadro’s number.
Therefore the number of atoms in 560 grams of iron is twice that in 70 grams of nitrogen.
Molecular weight of hydrogen = 2 grams, therefore 2 grams of hydrogen = $6.023\times {{10}^{23}}$ molecules of hydrogen =$2\times 6.023\times {{10}^{23}}$ atoms of hydrogen, as each molecule of hydrogen has 2 atoms.
Therefore 20 grams of hydrogen = $2\times 6.023\times {{10}^{23}}\times \dfrac{20}{2}$ atoms of nitrogen = $20\times 6.023\times {{10}^{23}}$ atoms of nitrogen = 20 times the Avogadro’s number.
Therefore the number of atoms in 560 grams of iron is half that in 70 grams of nitrogen.
Hence, both A and B are correct answers.

So, option C is correct.

Note:
The gram molecular weight of a compound is equal to the sum of the atomic weights of all the atoms present in the molecule, expressed in grams, while the gram atomic weight can be defined as the weight of the atoms expressed in grams. The atomic weight of an element will be twice its molecular weight when it forms homo-atomic compounds.