A student investigates the surface-area-to-volume effect on diffusion. She prepares agar cubes (containing the pH indicator phenolphthalein, pink in base) of three sizes: 1 cm, 2 cm, and 3 cm on a side. Cubes are placed in 0.1 M NaOH and timed for the pink color to fade completely (indicating NaOH has diffused throughout the cube and neutralized the indicator). The starting color is uniform pink in all cubes.
Which cube is predicted to lose its pink color first?
- Acheck_circle
The 1-cm cube
- B
The 2-cm cube
- C
The 3-cm cube
- D
All three at the same time
Explanation
Surface-to-volume ratio decreases with cube size. The 1-cm cube has the highest SA:V (6:1), so NaOH penetrates the entire volume fastest. Larger cubes have proportionally less surface for diffusion per unit volume.