Question

The concentration of a biomolecule inside a rod-shaped prokaryotic cell is .0031 M. Calculate the number of molecules inside the cell, which is 3.2 um long and 1.4 um in diameter.

Answer 1

Since the cell is rod shaped (cylindrical), the formula for volume is:

V = π r^2 h

V = π (0.7 um)^2 * 3.2 um

V = 4.926 um^3

 

So the number of moles is:

moles = 0.0031 mol / L * 4.926 um^3 * (1 x 10^-15 L / 1 um^3)

moles = 1.527 x 10^-17 mol

 

Using the avogadros number, we can calculate the number of molecules:

molecules = moles * Avogadros number

molecules = 1.527 x 10^-17 mol * 6.022 x 10^23 molecules / mol

molecules = 9,195,987.58 molecules

 

Taking the significant figures of 2:

molecules = 9.2 x 10^6 molecules