The concentration of a biomolecule inside a rod‑shaped prokaryotic cell is 0.0035 M. Calculate the number of molecules inside the cell, which is 4.2 μm long and 1.3 μm in diameter

Answer: This rod-shape prokaryotic cell has 3.740,734725‬ molecules

Explanation:

Step 1 : given data

Molarity of the prokaryotic cell = 0.0035 M

Length of the cell = 4.2 μm = 4.2 * 10^-6 m

diameter of the cell = 1.3 μm = 1.3 * 10^-6 m

Step 2: calculate volume

To calculate volume of a rod, weneef to know the radius.

V = r ² * l

The radius = half of the diameter : r = d/2 ⇒ (1.3 * 10^-6 m) / 2 = 0.65 * 10^-6 m

V = (0.65 * 10^-6 m) ² * 4.2 * 10^-6 m = 1.7745 * 10 ^-18 L

Step 3: Calculating number of moles

Number of moles = Concentration * Volume

moles = 0.0035 M * 1.7745 * 10 ^-18 L = 6.21075 * 10^-21 moles‬

Step 4: calculating number of molecules

1 mole contains 6.023 * 10 ^-23 molecules

6.21075 * 10^-21 moles contain : 6.21075 * 10^-21 * 6.023 * 10 ^-23 molecules = 3.740,734725‬ molecules

This rod-shape prokaryotic cell has 3.740,734725‬ molecules