Question

The concentration of a biomolecule inside a rod-shaped prokaryotic cell is 0.0021 M. Calculate the number of molecules inside the cell, which is 4.1 μm long and 1.3 μm in diameter.

Answer 1

length = 4.1 μm = 4.1 x 10^-6 m

diameter = 1.3 μm = 1.3 x 10^-6 m

radius (r) = 1/2 x diameter

                = 1/2 x 1.3 x 10^-6

                = 6.5 x 10^-7 m

volume (V) =    r^2 l

                   = 3.14 x (6.5 x 10^-7)^2 (4.1 x 10^-6)

                  = 5.44 x 10^-18 m^3

1 m^3 = 1000 L

volume (V) = 5.44 x 10^-18 x 1000 L

                   = 5.44 x 10^-15 L

we need to find out moles now

molarity = moles / volume

moles = molarity x volume

          = 0.0021 x 5.44 x 10^-15

          = 1.142 x 10^-17

1 mole conatin ----------------> 6.023 x 10^23 molecules

1.142 x 10^-17 moles contain -------------> ?? molecules

number of molecules = 6.023 x 10^23 x 1.142 x 10^-17

                                   = 6.88 x 10^6

number of molecules inside the cell = 6.88 x 10^6