Q3.29P - Chemistry: Molecular Nature Of Matter And Change

Question

Hemoglobin, a protein in red blood cells, carries ${\mathbf{O}}_{\mathbf{2}}$ from the lungs to the body’s cells. Iron(as ferrous ion, ${\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}$) makes up 0.33 mass % of hemoglobin. If the molar mass of hemoglobin is 6.8 g/mol, how many ${\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}$ ions are in one molecule? 

Step-by-Step Solution

Answer

There are four ions in one molecule of hemoglobin.

Step 1: To Find the mass of Fe 2 + ,

Mass % of in hemoglobin=$0.33\%$

$\mathrm{M\omega }\mathrm{of}\mathrm{hemoglobin}=6.8\times {10}^4\frac{\mathrm{g}}{\mathrm{mol}}$

In 1 mol of hemoglobin, the mass is $6.8\times {10}^4\mathrm{g}$. The mass percent is defined as follows.

Mass % of $\hspace{0.17em}\mathrm{Fe}=\frac{\mathrm{total}\mathrm{mass}\mathrm{of}{\mathrm{Fe}}^{2+}}{\mathrm{mass}\mathrm{of}1\mathrm{mol}\mathrm{hemoglobin}}\times 100$

Total mass of $\begin{array}{c}{\mathrm{Fe}}^{2+}=\frac{\left(\mathrm{mass}\mathrm{\%}\mathrm{of}\mathrm{Fe}\right)\left(\mathrm{mass}\mathrm{of}1\mathrm{mol}\mathrm{hemoglobin}\right)}{100}\\ =\frac{\left(0.33\right)\left(6.8\times {10}^4\mathrm{g}\right)}{100}\\ =224.40\mathrm{g}\end{array}$.

Step 2: To Find the moles of Fe ,

The Molar mass of iron, Fe is $55.85\frac{\mathrm{g}}{\mathrm{mol}}$. Multiply the calculated total mass of Fe by the reciprocal of its molar mass.

Moles of Fe$=224.40\mathrm{g}\mathrm{Fe}\left(\frac{\mathrm{mol}\mathrm{Fe}}{55.85\mathrm{g}\mathrm{Fe}}\right)$

Moles of Fe$=224.02\mathrm{mol}\mathrm{Fe}\approx 4\mathrm{mol}\mathrm{Fe}$

This indicates that in 1 mol of hemoglobin molecules, there are 4 moles of Fe ions.

Consequently, There are 4 Fe ions in one molecule of hemoglobin.

There are four Fe ions in one molecule of hemoglobin.