Question

Glucose is the major energy yielding nutrient for most cells. Assuming a cellular concentration of 1 mM, calculate how many molecules of glucose would be present in our hypothetical (& spherical) eukaryotic cell of size 50 micrometer.

Answer 1

As hypothetical cell is spherical we can apply equation for the volume of sphere:

$V=\frac{1}{6}\pi d^3$

where d is diameter (size) of the cell.

Concentration of glucose in the cell is $c=\frac{n}{V}$

where n is the amount of glucose in moles and V is the volume of cell.

Number of molecules is linked to the number of moles via Avogadro's number:

$n=\frac{N}{N_A}$

Combining together all three equations, we can find number of glucose molecules in the cell:

$N=nN_A=cVN_A=\frac{1}{6}c\pi d^3N_A=\frac{1}{6}\cdot 1\times 10^{-3}\frac{mol}{L} \cdot 3.14 \cdot (5 \times 10^{-4}dm)^3 \cdot 6.02 \times 10^{23}mol^{-1}=3.9\times10^{10}$