Question

The concentration of a biomolecule inside a rod shaped prokaryotic cell is 0.0023M. Calculate the number of molecules inside the cell, which is 3.7um long and 1.1um in diameter. Can you plese show work? I keep geting the wrong answer.

Answer 1

Given:

Rod shaped cell, length = 3.7 um , diameter = 1.1 um

[biomolecule]=0.0023 M

Solution:

We use following formulae to solve this problem.

Number of moles = Volume in L x Molarity (mol/L)

Volume of rod (cylinder) = pr²h

Here p=3.14 , r = radius = diameter / 2 , h is length

Step 1:

Conversion of length and diameter in m

h (length) = 3.7 um x ( 1 m / 1 E6 um) = 3.7 E-6 m

d = 1.1 E-6 m

Step 2 :

Calculation of volume

V (rod shaped cell)

            = (3.14 x (1.1E-6/2)²x 3.7 E-6 m

            = 4.07 E-12 m³

Step 3 : Calculation of volume in L

            =4.07 E-12 m³ x 1000 L/ 1 m³

            = 4.07 E-9 L

Step 4: Calculation of mol of biomolecule

n Biomolecule

            =4.07 E-9 L x 0.0023 mol/L

            = 9.36 E-12 mol

Step 5 : Calculation of molecules

Number of molecules of biomolecules inside cell

            = 9.36 E-12 mol x 6.02 E23 molecules / mol

            = 5.63E12 biomolecules

Ans : 5.6 E 12 biomolecules