Explain5 marksStandard
A student investigated the effect of the surface-area-to-volume ratio on the rate of diffusion using cubes of agar containing a pH indicator. The agar cubes were placed in a solution of dilute hydrochloric acid. The acid diffuses into the cubes and changes the colour of the indicator. The student recorded the time taken for the acid to reach the centre of each cube.
The dimensions of the cubes and the results are shown in the table.
| Cube side length (cm) | Surface area (cm²) | Volume (cm³) | Surface area : Volume | Time for acid to reach centre (min) |
|---|---|---|---|---|
| 1.0 | 6 | 1 | 6.0 : 1 | 5 |
| 2.0 | 24 | 8 | 3.0 : 1 | 20 |
| 3.0 | 54 | 27 | 2.0 : 1 | 45 |
| 4.0 | 96 | 64 | 1.5 : 1 | 80 |
Explain why the time taken for the acid to reach the centre of the agar cube decreases as the side length of the cube decreases.