How many protons [or, more accurately, hydronium ions (H₃O⁺)] are there in a spherical lysosome that is about 0.6 µm in diameter and maintains an interior pH of about 5.0? Recall that the volume of a sphere of radius r is calculated as V = 4/3 × π × r³, and that pH = -log [H⁺]. Avogadro's constant is approximately 6 × 10²³ molecules/mole.

Question

Quizplus · Accepted Answer

The volume of the lysosome would be calculated as:
V = 4/3 × π × (0.3 × 10-⁶ m)³ = 1.1 × 10-¹⁹ m³ = 1.1 × 10-¹⁶ L
At approximately pH 5, the concentration of hydronium ions is 10-⁵ mol/L. Therefore, there is about 1.1 × 10-²¹ mole of these ions in this lysosome. This is equivalent to only approximately 660 ions.

How Many Protons [Or, More Accurately, Hydronium Ions (H₃O⁺)] Are