Question

Mycoplasma are the smallest cells known. Their volumes are ~ 2 X 10-17 L. If there were 120 protons in the cytoplasm of a mycoplasma what would be the approximate pH of the cytoplasm?

4?

9?

7?

12?

10?

6?

8?

5?

11?

3?

Answer 1

pH= -log[H+]

here there are 120 protons in the cell

number of moles of the protons= number of protons in the cell/ Avogadro number

Avagadro number= 6.022$\times$10^23

the number of moles of the protons= 120/(6.022$\times$10^23)=1.993$\times$10^-22

Molarity= number of moles/ volume of in litres

molarity of H+= number of moles of H+/volume of the cell in litres

=  1.993$\times$10^-22/ 2 X 10-17 L

= 9.965$\times$ 10^-6 M

pH= -log[ 9.965$\times$ 10^-6]

= 5

so the answer is 5