Question

The concentration of a biomolecule inside a rod-shaped prokaryotic cell is 0.0047 m. calculate the number of molecules inside the cell, which is 3.8 μm long and 1.6 μm in diameter.

Answer 1

First find the volume:

length = 3.8  um 
diameter =  1.6 um
so, radius = 1.6 / 2  = 0.8 um

so, volume = $\pi r^2 l$  
=$3.14 \times 0.8^2 \times 3.8$  
$Volume= 7.63 um^3$

1 um = 10^{-6} m
convert volume into m^3
so, $Volume= 7.63 um^3$ = $7.63 \times (10^{-6})^3 = 7.63 \times 10^{-18} m^3$

Now, Concentration is always in moles/Litre. So, we need to change the volume to litre.
1 m^3 = 10^{-3} L
So, $7.63 \times 10^{-18} m^3 = 7.63 \times 10^{-18} \times 10^{-3}L = 7.63 \times 10^{-21}L$


Now, number of moles =  concentration x volume 
= $0.0047 \times 7.63 \times 10^{-21}= 3.5 \times 10^{-23}$ 

so no. of molecules = $3.5 \times 10^{-23} \times 6.022 \times 10^{24} = 210$