Question

How many moles of ferric alum ${{(N{{H}_{4}})}_{2}}S{{O}_{4}}Fe{{(S{{O}_{4}})}_{3}}.24{{H}_{2}}O$ can be made from the sample of $Fe$ containing $0.0056\,g$ of it?
A. ${{10}^{-4}}mol$
B. $0.5\times {{10}^{-4}}mol$
C. $0.33\times {{10}^{-4}}mol$
D. $2\times {{10}^{-4}}mol$

Answer 1

Hint: Mole concept gives the relationship between the number of moles, weight and molar mass of the compound. Molecular mass is calculated by adding up the atomic masses of the elements combined to form a molecule.

Formula used:
$n=\dfrac{w}{M}$
where, $n$ is the number of moles, $w$ is the weight and $M$ is the molar mass of the compound.

Complete step by step answer:
Here, it is given that,
Molar mass of $Fe$ is $56\,g/mol$ and weight of $Fe$ is
To calculate the number of moles of $Fe$ $0.0056\,g$
  $n=\dfrac{w}{M}$
where, $n$ is the number of moles, $w$ is the weight and $M$ is the molar mass of the compound.
Now, on substituting the values in the above formula, we get,
 $n=\dfrac{0.0056}{56}$
$\Rightarrow n={{10}^{-4}}\,mol$
The molecular formula of ferric alum is ${{(N{{H}_{4}})}_{2}}S{{O}_{4}}Fe{{(S{{O}_{4}})}_{3}}.24{{H}_{2}}O$ . In this molecular formula, we can see that one mole of alum is equal to two moles of $Fe$ .
Now, applying the unitary method to find moles of ferric alum
 $2\,mol$ of $Fe$$=1\,mol$ of alum
 $\Rightarrow 1\,mol$ of $Fe$$=\dfrac{1}{2}\,mol$ of alum
$\Rightarrow {{10}^{-4}}\,mol$ of $Fe$$=\dfrac{1}{2}\,\times {{10}^{-4}}mol$ of alum
$\Rightarrow {{10}^{-4}}\,mol$ of $Fe$$=0.5\,\times {{10}^{-4}}mol$ of alum

So, the correct answer is Option B.

Additional information:
1. Mole is defined as the scientific unit which is used to measure large quantities of atoms, ions, and molecules. It is defined as the amount of substance present in the sample, and $1\,mole=6.022\times {{10}^{23}}$ particles. This number is known as Avogadro’s number $({{N}_{A}})$ .
2. It is calculated as the weight of the compound per molar mass of that compound.
3. Molar mass is defined as the addition of atomic masses of atoms combined in a molecule.
4. The mole is very important because it helps to study atoms, molecules and ions.

Note: Avogadro’s number is defined as the proportionality factor that tells the relationship between the number of constituent particles with the amount of substance in a sample. Its SI unit is $mo{{l}^{-1}}$ . It is denoted with a symbol, ${{N}_{A}}$ .${{N}_{A}}=6.023\times {{10}^{23}}mo{{l}^{-1}}$ It is the number of units in a mole of any substance.