Understanding the Diffusion in Agar Cubes Lab
This lab is a standard biology exercise that demonstrates how surface area to volume ratio affects the rate of diffusion. You cut agar cubes of different sizes, soak them in a solution like sodium hydroxide or phenolphthalein, then measure how far the substance diffuses into each cube over a set time period. The answer key typically asks you to calculate percent diffusion based on cube size, explain why smaller cubes show higher diffusion rates, and connect the results to real biological systems like cell size limitations. Here is the straightforward procedure I use when students ask for help. First, prepare three agar cubes: 1 cm, 2 cm, and 3 cm on each side. This means your volumes are 1 cm³, 8 cm³, and 27 cm³ respectively. Your surface areas are 6 cm², 24 cm², and 54 cm². The surface area to volume ratios come out to 6:1, 3:1, and 2:1.
Important detail most guides skip: You need to know whether your agar contains phenolphthalein or whether the NaOH does. Standard protocol uses phenolphthalein-agar cubes soaked in NaOH. The NaOH turns the phenolphthalein pink as it diffuses inward. Soak the cubes for exactly ten minutes. Some teachers say five, some say fifteen. Stick to the time your instructor specifies because the percent diffusion changes significantly depending on duration. Ten minutes is the most common default. After soaking, remove the cubes, blot dry, and cut each one in half. Measure the distance the pink color penetrated from the surface to the center. That distance is your diffusion depth, and here is the thing that catches people off guard: the diffusion depth should be roughly the same across all cube sizes. The NaOH travels at approximately the same rate no matter the cube size. What changes is the percentage of the cube's total volume that gets reached.
To calculate percent diffusion, divide the volume of the cube that turned pink by the total volume. If the diffusion depth is 0.5 cm in the 1 cm cube, the entire cube is pink. That is 100% diffusion. In the 2 cm cube, the outer 0.5 cm on each side turns pink, leaving a 1 cm x 1 cm x 1 cm uncolored core. The diffusion volume is 8 minus 1, which is 7 cm³. That is 87.5%. For the 3 cm cube with the same 0.5 cm diffusion depth, the uncolored core is 2 cm x 2 cm x 2 cm, which is 8 cm³. Diffused volume is 27 minus 8, or 19 cm³. That gives you about 70.4%. The pattern is clear. Smaller cubes have a higher percentage of diffusion because they have more surface area relative to their volume. This directly supports the biological principle that cells stay small. If cells grew too large, diffusion alone could not supply their interior with enough nutrients or remove waste quickly enough.
I ran into a specific problem once that every student eventually hits: the cubes do not always absorb uniformly. On a batch I was preparing, the 2 cm cube had a slightly translucent edge where the agar mixed unevenly. The NaOH had nowhere to react and the pink color did not form cleanly there. This threw off the measurement entirely. The workaround was simple but annoying. I made sure to mix the agar solution thoroughly while it was still warm and liquid before pouring it into the mold, and I let it set completely before cutting. Once I started doing that, the uniformity issue disappeared. Another common mistake students make is measuring the diffusion depth incorrectly. They measure from the outside of the cube rather than from the cut surface. Always measure from the flat cut face inward, not from the original outer edge of the cube. This distinction matters because the cut exposes fresh surface to the solution. The standard answer key section on the conclusion asks you to relate your findings to cell biology. The key points are: smaller cells exchange materials faster, large organisms are made of many small cells rather than fewer large ones, and there is a physical limit to how large a single cell can grow before diffusion becomes inadequate. Keep those points tight and reference your actual percentages rather than just stating general principles.
If you need the numeric answers quickly, here is the typical result set for a ten-minute soak with a diffusion depth of approximately 0.5 cm: 1 cm cube: 100% diffusion 2 cm cube: approximately 87.5% diffusion
3 cm cube: approximately 70.4% diffusion Your actual numbers may vary slightly depending on the exact soaking time and the specific diffusion depth your teacher's answer key uses. Some keys use 0.4 cm or 0.6 cm as the measured depth, which shifts the percentages a bit. Always check what measurement your lab instructions specified.
