Lysosomes are little sacs of acid in a cell. Their pH is about 5, and an electro

Question

Lysosomes are little sacs of acid in a cell. Their pH is about 5, and an electron micrograph suggests they have a diameter of 0.5 mu m. The increased hydrogen ion concentration inside lysosomes is due to the pumping of hydrogen ions across the lysosomal membrance from the surrounding cytosol, which has a pH of 7.2. Assuming that a lysosome has the shape of a sphere and that there is no buffering capacity inside the lysosome, how many hydrogen ions were moved to the inside of the lysosome to lead to an internal pH of 5?

Explanation / Answer

1) Volume of Sphere (Lysosome) = 4/3 pi r3

Diameter of lysosome = 0.5 um

radius = 0.25 um

Volume = 4/3 x pi x (0.25 um)3

V = 65.44 x 10 -9 m3

V = 65.44 x 10 -6 Liters (1 Litre = 1000 m3)

2a) Concentration of H+ in moles/L at pH 5

pH = - log10 [H+]

[H+] = 10 -pH

[H+] = 1 x 10 -5 mol /L (or M)

2b) Moles of H+ at pH 5

Moles = Molarity x Volume

Moles = 1 x 10 -5 mol /L x 65.44 x 10 -6 Liters

Moles of H+ = 65.44 x 10 -11 mol

2c) Number of Hydrogen ions at pH 5

1 mol = 6.023 x 10 23 particles

65.44 x 10 -11 mol = ?

Number of hydrogen ions at pH 5 = 3.9 x 10 14

3a) Concentration of H+ in moles/L at pH 7.2

pH = - log10 [H+]

[H+] = 10 -pH

[H+] = 1 x 10 -7.2 mol /L (or M) = 6.3 x 10 -8 mol/L

3b) Moles of H+ at pH 7.2

Moles = Molarity x Volume

Moles = 6.3 x 10 -8 mol /L x 65.44 x 10 -6 Liters

Moles of H+ = 412 x 10 -14 mol

3c) Number of Hydrogen ions at pH 7.2

1 mol = 6.023 x 10 23 particles

412 x 10 -14 mol = ?

Number of hydrogen ions at pH 7.2 = 2.48x 10 26

Number of hydrogen ions moved to the inside of lysosome to lead to an internal pH of 5 is 3.9 x 10 14

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