Q.2.79 - An Introduction to General, Organic, and Biological Chemistry

Question

a. Write an equality and two conversion factors for Greg's serum iron level. 

b. How many micrograms of iron were in the 8.0-ml Sample of Greg's blood?

Step-by-Step Solution

Answer

a. $42 \mathrm{mcg} \mathrm{of} \mathrm{iron} = 1 \mathrm{dL} \mathrm{of} \mathrm{blood}$

b. $3.4 \mathrm{mcg} \mathrm{of} \mathrm{iron}$

Step 1: Part (a) Given Information

To write two conversion factors.

Step 2: Part (a) Explanation

Micro and milli are used to measure smaller units. 

Greg's iron test showed a blood serum iron level of $42 \mathrm{mcg}/\mathrm{dL}$.

The unit conversion method that is used for Greg's serum iron level is:

$$\begin{gathered} 42 \mathrm{mcg} \mathrm{of} \mathrm{iron}=1 \mathrm{dL} \mathrm{of} \mathrm{blood} \\ \frac{42 \mathrm{mcg} \mathrm{of} \mathrm{iron}}{1 \mathrm{dL} \mathrm{of} \mathrm{blood}}\mathrm{and} \frac{1 \mathrm{dL} \mathrm{of} \mathrm{blood}}{42 \mathrm{mcg} \mathrm{of} \mathrm{iron}} \end{gathered}$$

Step 1: Part (b) Given Information

The volume of Greg's blood sample=8.0 mL

The density of the sample is 42 mcg/dL.

Step 2: part (b) Explanation

Unit conversion for mL into dL:

$$\begin{gathered} 1 \mathrm{dL}=100 \mathrm{mL} \\ \mathrm{or} \\ 1 \mathrm{mL}=\frac{1}{10}\mathrm{dL}=0.1 \mathrm{dL} \end{gathered}$$

The calculation for mass:

$$\begin{gathered} \mathrm{Mass} \mathrm{of} \mathrm{iron}= \mathrm{Volume} \mathrm{of} \mathrm{sample}\times \mathrm{Density} \\ \mathrm{Mass} \mathrm{of} \mathrm{iron}=0.08 \mathrm{dL}\times 42 \mathrm{mcg}/\mathrm{dL} \\ \mathrm{Mass} \mathrm{of} \mathrm{iron}=3.4 \mathrm{mcg} \end{gathered}$$

Thus, the mass of iron in the sample is 3.4 mcg.