Question

In a typical mammalian cell, the protein content is 20 % of its net weight. If the density and volume of the cell are 1.2 g/mL and 4 × 10\(^{-9}\) mL, respectively, then the concentration (in mg/mL) of the protein is

• A. 60
• B. 600
• C. 166
• D. 240

Hint:

To calculate concentration, divide the mass of the solute by the volume of the solution and convert units as necessary.

Answer 1

The Correct Option is D

Step 1: Given data.
- Protein content = 20% of the cell weight. - Density of cell = 1.2 g/mL. - Volume of cell = \( 4 \times 10^{-9} \) mL.

Step 2: Calculate the mass of the cell.
Mass of the cell = Density × Volume = \( 1.2 \, \text{g/mL} \times 4 \times 10^{-9} \, \text{mL} = 4.8 \times 10^{-9} \, \text{g} \).

Step 3: Calculate the mass of protein.
Mass of protein = 20% of the mass of the cell = \( 0.2 \times 4.8 \times 10^{-9} \, \text{g} = 9.6 \times 10^{-10} \, \text{g} \).

Step 4: Convert mass of protein to mg.
Mass of protein in mg = \( 9.6 \times 10^{-10} \, \text{g} = 9.6 \times 10^{-7} \, \text{mg} \).

Step 5: Calculate the concentration of protein.
Concentration = \( \frac{\text{Mass of protein}}{\text{Volume of cell}} = \frac{9.6 \times 10^{-7} \, \text{mg}}{4 \times 10^{-9} \, \text{mL}} = 240 \, \text{mg/mL} \).

Step 6: Conclusion.
The correct answer is (D) 240.