Biological cells can only survive if materials can move in and out of them. In this Snack, you used cubes of agar to visualize how diffusion changes depending on the size of the object taking up the material.
Diffusion occurs when molecules in an area of higher concentration move to an area of lower concentration. As hydrogen ions from the vinegar move into the agar cube, the color of the cube changes allowing you to see how far they have diffused. While random molecular motion will cause individual molecules and ions to continue moving back and forth between the cube and the vinegar solution, the overall concentrations will remain in equilibrium, with equal concentrations inside and outside the agar cube.
How did you find the percentage of the cube that was penetrated by the hydrogen ions at the various time intervals? One way to do this is to start with the volume of the cube that has not been penetrated—in other words, the part in the center that has not yet changed color. To determine the volume of this inner cube, measure the length of this inner cube and multiply it by the width and height. Subtract this from the original volume of the cube and you obtain the volume of the cube that has been penetrated. By dividing this number by the original volume and multiplying by 100%, you can determine the percentage penetration for each cube.
You may have noticed that the bigger the vinegar-soaked cube gets, the time it takes for additional vinegar to diffuse into the cube also increases—but not in a linear fashion. In other words, if the cube dimensions are doubled, the time it takes for the hydrogen ions to completely diffuse in more than doubles. When you triple the size, the time to diffuse MUCH more than triples. Why would this happen?
As the size of an object increases, the volume also increases, but by more than you might think. For example, when the cube doubles from a length of 1 cm to a length of 2 cm, the surface area increase by a factor of four, going from 6 cm2 (1 cm x 1 cm x 6 sides) to 24 cm2 (2 cm x 2 cm x 6 sides). The volume, though, increases by a factor of eight, increasing from 1 cm3 (1cm x 1 cm x 1 cm) to 8 cm3 (2 cm x 2 cm x 2 cm).
Because the volume is increasing at a greater factor than the surface area, the surface-area-to-volume ratio decreases. As the cube size increases, the surface-area-to-volume ratio decreases (click to enlarge the table below). The vinegar can only enter the cube through its surface, so as that ratio decreases, the time it takes for diffusion to occur throughout the whole volume increases significantly.
Anything that comes into a cell (such as oxygen and food) or goes out of it (such as waste) must travel across the cell membrane. As cells grow larger, the ratio of surface area to volume decreases dramatically, just like in your agar cubes. Larger cells must still transport materials across their membranes, but have a larger volume to supply and a proportionately smaller surface area through which to do so.
Bacterial cells are fairly small and have a comparatively larger surface-area-to-volume ratio. Eukaryotic cells, such as those in plants and animals, are much larger, but have additional structures to help them conduct the required amount of transport across membranes. A series of membrane-bound structures continuous with the plasma membrane, such as the endoplasmic reticulum, provide additional surface area inside the cell, allowing sufficient transport to occur. Even with these strategies, though, there are upper limits to cell size.