Question

The concentration of a biomolecule insdie a rod-shaped prokaryotic cell is 0.0051 M. Calculate the number of molecule inside the cell, which is 3.1 micrometers long and 1.7 micrometers in diameter?

Answer 1

Answer: The number of molecules inside the cell are $2.2\times 10^6$

Explanation:

We are given a prokaryotic cell, which is in the shape of rod or cylinder.

The equation used to calculate the volume of cylinder is:

$V=\pi r^2h$

where,

V = volume of cell = ?

r = radius of the celle = $\frac{d}{2}=\frac{1.7\mu m}{2}=0.85\mu m=8.5\times 10^{-7}m$     (Conversion factor: $1m=10^6\mu m$ )

h = length of the cell = $3.1\mu m=3.1\times 10^{-6}m$

Putting values in above equation, we get:

$V=(3.14)\times (8.5\times 10^{-7})^2\times 3.1\times 10^{-6}\\\\V=7.033\times 10^{-18}m^3$

To calculate the number of moles for given molarity of solution, we use the equation:

$\text{Molarity of the solution}=\frac{\text{Moles of solute}}{\text{Volume of solution (in L)}}$

Molarity of biomolecule = 0.0051 M

Volume of solution =  $7.033\times 10^{-18}m^3=7.033\times 10^{-15}L$     (Conversion factor:  $1m^3=1000L$ )

Putting values in above equation, we get:

$0.0051M=\frac{\text{Moles of biomoleculel}}{7.033\times 10^{-15}L}\\\\\text{Moles of biomolecule}=(0.0051mol/L\times 7.033\times 10^{-15}L)=3.59\times 10^{-17}mol$

According to mole concept:

1 mole of a compound contains $6.022\times 10^{23}$ number of molecules

So, $3.59\times 10^{-17}$ moles of a biomolecule will contain = $(3.59\times 10^{-17}\times 6.022\times 10^{23}=2.2\times 10^6$ number of molecules

Hence, the number of molecules inside the cell are $2.2\times 10^6$