Question

The concentration of a biomolecule inside a rod-shaped prokaryotic cell is 0.0027 m. calculate the number of molecules inside the cell, which is 4.4 μm long and 1.2 μm in diameter.

Answer 1

Answer : The number of molecules inside the cell is, $8.08\times 10^6$

Solution :

First we have to calculate the volume of biomolecule cell.

Volume = Area of the base of the cell × length of the cell

$V=\pi r^2\times h$

where,

V = volume of the biomolecule cell

r = radius of the cell = $\frac{Diameter}{2}=\frac{1.2}{2}=0.6\mu m$

h = length of the cell = $4.4\mu m$

Now put all the given values in the above volume formula, we get

$V=\frac{22}{7}\times (0.6\mu m)^2\times (4.4\mu m)=4.978\mu m^3=4.978\times 10^{-15}L$

conversion : $(1\mu m^3=10^{-15}L)$

Now we have to calculate the moles of a biomolecule of the cell.

$Molarity=\frac{Moles}{Volume}\\\\Moles=Molarity\times Volume=(0.0027mole/L)\times (4.976\times 10^{-15}L)=0.01343\times 10^{-15}moles$

Now we have to calculate the number of molecules inside the cell.

$\text{Number of molecules}=Moles\times (6.022\times 10^{23})\\\\\text{Number of molecules}=(0.01343\times 10^{-15})\times (6.022\times 10^{23})=8.08\times 10^6$

Therefore, the number of molecules inside the cell is, $8.08\times 10^6$