Question

The concentration of a biomolecule inside a rod‑shaped prokaryotic cell is 0.0051 M . Calculate the number of molecules inside the cell, which is 2.7 μm long and 1.7 μm in diameter.

Answer 1

The volume of the rod is given by r²l.

r = radius of the cell

l = length of the rod.

Given that the diameter is 1.7 μm. It means that radius is 0.85  μm.

So volume of cells will be 3.14 * 0.85*0.85 * 2.7 = 6.13  μm³.

1ul = 1um³.

6.13  μm3 = 6.13 μl

Molarity = Mole * 1/ volume in litre.

Given that molarity is 0.0051M

Volume = 6.13*10^-6 l

Moles = 0.0051 * 6.13 * 10^-6 = 0.0132 * 10^-6 = 3.12 * 10^-8 moles

1 mole = 6.023*10²³ molecules

So 1.32 * 10^-8 moles = 3.12 * 10^-8 * 6.023*10²³ molecules = 18.82 * 10¹⁵ molecules or 1.882 * 10¹⁶ molecules.

The number of molecules inside the cell is 1.882 * 10¹⁶ molecules.