Answer:
The number of protein X molecules in the cell is 5.7 × 10⁸ proteins.
Explanation:
First, let´s calculate the volume of the cytoplasm:
Volume of cytoplasm = volume of the cell - volume of the nucleus - volume of the organelles
The volume of a sphere of radius "r" is:
4/3 · π · r³
The volume of the cell is:
4/3 · π · (10 um)³ = 4.2 × 10³ um³ = 4.2 × 10 ⁻⁹ ml = 4.2 pl
The volume of the nucleus is:
4/3 · π · (2 um)³ = 33.5 um³ = 3.35 × 10⁻¹¹ ml = 0.0335 pl
Then, the volume of the cytoplasm is:
volume of cytoplasm = 4.2 pl - 0.0335 pl - 0.15 pl = 4.02 pl = 4.02 × 10⁻⁹ ml
The mass of protein present in the cytoplasm will be:
4.02 × 10⁻⁹ ml · 35 mg/ml = 1.41 × 10⁻⁷ mg = 1.41 × 10⁻¹⁰ g
The number of moles of the protein in the cytoplasm will be:
1.41 × 10⁻¹⁰ g · (1 mol / 150000 g) = 9.4 × 10⁻¹⁶ mol.
The number of proteins will be:
9.4 × 10⁻¹⁶ mol · (6.022 × 10²³ molecules / mol) = 5.7 × 10⁸ molecules.
The number of protein molecules is 5.7 × 10⁸.
