Surface Area to Volume Ratio Determines Diffusion Speed

Steps:

• Surface area (SA) of cube = 6 × side²; volume (V) = side³; ratio = SA/V = 6/side.
• For 2 cm cube: 6/2 = 3 (or 3:1).
• For 4 cm cube: 6/4 = 1.5 (or 3:2).
• For 5 cm cube: 6/5 = 1.2 (or 6:5).
• Highest ratio (2 cm cube) allows fastest acid diffusion to center, turning colorless quickest.

Why D is correct:

• 3.0:1 matches the 2 cm cube's ratio, where high SA:V enables rapid diffusion per Fick's law (rate proportional to surface area and concentration gradient).

Why the others are wrong:

• A: 0.3:1 is far too low, matching a ~20 cm cube with slow diffusion.
• B: 0.8:1 is low, matching a ~7.5 cm cube, slower than smaller cubes.
• C: 1:2 (0.5:1) is low, matching a 12 cm cube, even slower.

Final answer: D