Question

You have come down with a nasty cold and would like to understand why the virus that infected you is making you feel so lousy. With a few basic facts, given here within the problem, you can show that each infected cell is now very full of virus particles, resulting in your current condition.
a. Given that a typical cell is about 10 um in diameter, calculate its volume in liters.
b. Find the concentration (in Molarity) of a single virus within that cell.
c. Find the concentration (in Molarity) of 100 virus particles within that cell.

Answer 1

Answer:

a) The volume is 5.236x10⁻¹³L

b) The molarity of a single virus is 1.91x10¹² mol/L

c) The molarity for a 100 virus particles is 1.91x10¹⁴ mol/L

Explanation:

a) Given:

D = diameter of the cell = 10 μm

r = radius = 10/2 = 5 μm

The volume of the spherical cell is equal:

$V=\frac{4}{3} \pi r^{3} =\frac{4}{3} \pi *(5)^{3} =523.6\mu m^{3}$

If 1 μm³ = 1x10⁻¹⁵L, then 523.6 μm³ = 5.236x10⁻¹³L

b) The molarity is:

$M=\frac{number-of-moles}{volume-of-solution}$

For a single virus within the cell

$M=\frac{1}{5.236x10^{-13} } =1.91x10^{12} mol/L$

c) For a 100 virus particles the molarity is:

$M=\frac{100}{5.236x10^{-13} } =1.91x10^{14} mol/L$