Chapter 22, Problem 73AP

Chemical analysis shows that hemoglobin contains 0.34 percent of Fe by mass. What is the minimum possible molar mass of

hemoglobin? The actual molar mass of hemoglobin is about 65.000 g. How do you account for the discrepancy between your minimum value and the actual value?

Interpretation Introduction

Interpretation:

The minimum molar mass of hemoglobin with the given information is to be determined with given percent of $\text{Fe}$ by mass. The discrepancy between estimated minimum mass and actual mass is to be compared.

Concept introduction:

A molecule of hemoglobin composed of four polypeptide subunits: two alpha chains and two beta chains.

Iron in heme group exists in oxidation state of +2 and each ${\text{Fe}}^{2+}$ coordinately bonded to four $\text{N}$ atoms.

The number of moles of compound is calculated as:

$\text{Moles}=\frac{\text{mass}}{\text{Molar mass}}$

The amount of hemoglobinin one mole of iron is calculated as:

$\text{amount}\text{of}\text{hemoglobin}\text{=}\frac{\text{100}\text{g}\text{hemoglobin}}{\text{moles}\text{of}\text{Fe}}$

The actual mass of hemoglobin and estimated minimum molar mass is compared as: $\frac{\text{actual}\text{molar}\text{mass}}{\text{estimated}\text{minimum}\text{molar}\text{mass}}$

Answer to Problem 73AP

Solution: $1.6\times 10^{4}ghemoglobin\text{/}molFe$.

Explanation of Solution

Given information: Hemoglobin contains $\text{0}\text{.34\% of Fe}$ by mass. The actual molar mass of hemoglobin is 65,000 g.

A $100\text{ g}$ sample of hemoglobin contains $\text{0}\text{.34 g}$ of iron. The number of moles of iron is calculated as follows:

$\text{Moles}\left(\text{Fe}\right)=\frac{\text{mass}}{\text{Molar mass}}$ …… (1)

The molar mass of iron is $\text{55}\text{.85}\frac{\text{g}}{mol}$.

Substitute $\text{55}\text{.85}\frac{\text{g}}{mol}$ for molar mass and $\text{0}\text{.34 g}$ for mass in the equation (1) as follows:

$\begin{array}{c}\text{Moles}\left(\text{Fe}\right)=\left(\text{0}\text{.34}\text{g}\right)\text{×}\left(\frac{\text{1}\text{mol}}{\text{55}\text{.85}\text{g}}\right)\\ \text{=}\text{6}\text{.1}\text{×}{\text{10}}^{-\text{3}}\text{mol}\text{Fe}\end{array}$

In one mole of iron, the amount of hemoglobin is given as follows:

$\text{amount}\text{of}\text{hemoglobin}\text{=}\frac{\text{100}\text{g}\text{hemoglobin}}{\text{moles}\text{of}\text{Fe}}$

$\frac{\text{100}\text{.00}\text{g}\text{hemoglobin}}{\text{6}\text{.1}\text{×}{\text{10}}^{\text{-3}}\text{mol}\text{Fe}}\text{=}1.6\times 10^{4}ghemoglobin/molFe$

Therefore, the minimum molar mass of hemoglobin is $1.6\times 10^{4}ghemoglobin/molFe$.

The actual molar mass of hemoglobin is $6.5\times 10^4\frac{ghemoglobin}{molhemoglobin}$.

The actual mass of hemoglobin and estimated minimum molar mass is compared as follows:

$\frac{\text{actual}\text{molar}\text{mass}}{\text{estimated}\text{minimum}\text{molar}\text{mass}}$

$\left(6.5\times 10^4\frac{ghemoglobin}{molhemoglobin}\right)\left(\frac{1molFe}{1.6\times 10^{4}ghemoglobin}\right)=4molFe/1molhemoglobin$

The difference between the estimated minimum value of hemoglobin and the actual value can be explained by considering the fact that there are four iron atoms per mole of hemoglobin.

Conclusion

The minimum molar mass of hemoglobin is $1.6\times 10^{4}ghemoglobin\text{/}molFe$. The discrepancy between estimated minimum mass and actual mass is compared.