Question

Haemoglobin contains $0.33\% $ of iron by weight. The molecular mass of haemoglobin is about $67200$. Find the number of iron atoms (atomic mass of Fe $ = 56$) present in the molecule of haemoglobin.
A. $6$
B. $4$
C. $2$
D. $1$

Answer 1

Hint:When a substance is present in a compound in percentage by weight then we consider the percentage to the weight of the substance and whole mass of the compound to be considered as $100{\text{g}}$.

Complete step by step answer:
As we know that the haemoglobin is a red coloured pigment present in the blood that carries the gas which we need to survive i.e. oxygen gas. and contains ions. It carries oxygen from lungs to the rest of the body. Now according to the question, the haemoglobin contains $0.33\% $ of iron by weight means that in a $100{\text{g}}$ of haemoglobin, $0.33{\text{g}}$ of iron is present. If $100{\text{g}}$ of haemoglobin contains $0.33{\text{g}}$ of iron, then ${\text{1g}}$ of haemoglobin contains $\dfrac{{0.33}}{{100}}$ i.e. ${\text{0}}{\text{.0033g}}$ of iron. We have to calculate the amount in one molecule of haemoglobin that is one mole whose mass is ${\text{67200g}}$.So, the amount of iron present in ${\text{67200g}}$ of haemoglobin is ${\text{67200g X 0}}{\text{.0033}}$ i.e. ${\text{221}}{\text{.76g}}$.This implies that in one molecule of haemoglobin, ${\text{221}}{\text{.76g}}$ of iron is present. Now, we have to calculate the atoms of iron present in one molecule of haemoglobin. The number of atoms can be calculated using the formula
${\text{No}}{\text{. of atoms of substance = }}\dfrac{{{\text{Given mass of substance}}}}{{{\text{Molecular mass of substance}}}}{\text{ }}......{\text{(1)}}$
We have to calculate the number of iron atoms whose molecular mass is ${\text{56g}}$ and given mass or calculated mass is ${\text{221}}{\text{.76g}}$
Putting values of given mass and molecular mass in eq $(1)$, we get
${\text{No}}{\text{. of atoms of iron = }}\dfrac{{221.76}}{{56}} = 3.96 \approx 4$
Hence, the number of iron atoms present in one molecule of haemoglobin is $4$.
So, the correct option is (B).

Note:
The mass of iron in the above question can be calculated by simply multiplying its percentage by weight with the molecular mass of haemoglobin as we only have to evaluate for one molecule of haemoglobin. This implies that ${\text{mass of iron = 0}}{\text{.33% }} \times {\text{67200 = }}\dfrac{{0.33}}{{100}} \times 67200$
        ${\text{ = 221}}{\text{.76g}}$.