Chapter 14, Problem 1P

Hemoglobin has a molecular mass of $64500\text{u}.$ Find the mass $\left(\text{in}\text{kg}\right)$ of one molecule of hemoglobin.

To determine

To Find: The mass of one molecule of hemoglobin in kilograms.

Answer to Problem 1P

  $\text{1}\text{.07}\times {\text{10}}^{-22}\text{kg}$

Explanation of Solution

Given:

Molecular mass of hemoglobin, $M=64500\text{ u}$

Formula used:

Conversion of units

  $1\text{ u}=1\text{ g/mol}$

  $\text{1 mol}=\text{6}\text{.022}\times {\text{10}}^{23}\text{ molecules}$

  $1\text{ kg}=1.0\times {10}^3\text{ g}$

Calculation:

The mass of 1 mole of hemoglobin is $64500\text{ g}$ .

1 mole contains $\text{6}\text{.022}\times {\text{10}}^{23}\text{ molecules}$ .

Thus, mass of $\text{6}\text{.022}\times {\text{10}}^{23}\text{ molecules}$ of hemoglobin is $64500\text{ g}$ .

Mass of 1 molecule of hemoglobin can be calculated as follows:

  $\begin{array}{c}m=\frac{64500\text{ g}}{\text{6}\text{.022}\times {\text{10}}^{23}\text{ molecules}}\\ \text{=1}\text{.07}\times {\text{10}}^{-19}\text{g}\times {\text{10}}^{-3}\frac{\text{kg}}{\text{g}}\\ =\text{1}\text{.07}\times {\text{10}}^{-22}\text{kg}\end{array}$

Conclusion:

Thus, the mass of one molecule of hemoglobin in kilograms is $\text{1}\text{.07}\times {\text{10}}^{-22}$ .