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* 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* h`

where,

V = volume of the biomolecule cell

r = radius of the cell =
`(Diameter)/(2)=(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=(22)/(7)* (0.6\mu m)^2* (4.4\mu m)=4.978\mu m^3=4.978* 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=(Moles)/(Volume)\\\\Moles=Molarity* Volume=(0.0027mole/L)* (4.976* 10^(-15)L)=0.01343* 10^(-15)moles`

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

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

Therefore, the number of molecules inside the cell is,
`8.08* 10^6`