Potato Cylinders and the Isotonic Point
Mr. Okafor's class investigates osmosis in potato tissue. Each group cuts cylinders with a 5 mm cork borer from the same potato. One group soaks a single cylinder in each of five sucrose solutions (0.0, 0.2, 0.4, 0.6 and 0.8 mol/L) for 30 minutes, then measures length with a plastic ruler marked in millimetres. Their results as length change: 0.0 mol/L +2 mm; 0.2 mol/L +1 mm; 0.4 mol/L 0 mm; 0.6 mol/L -1 mm; 0.8 mol/L -1 mm. They conclude that the potato cytoplasm is 0.4 mol/L sucrose. Several complications appear in the lab notes: the 0.0 mol/L cylinder still had a strip of skin on one side; the 0.8 mol/L cylinder was cut 35 mm long by mistake; the ruler's end is worn; two cylinders sat on the bench for 10 minutes before soaking; and the 0.6 mol/L reading was recorded twice by a student who measured the same cylinder two times.
1. Sort the complications by how much they threaten the conclusion: which could change the size or sign of a result, and which are harmless?
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Serious - changes the result.
- Skin on the 0.0 mol/L cylinder. Potato skin is a low-permeability barrier, so water uptake is reduced. The +2 mm is probably an underestimate, which flattens the curve at the dilute end and could pull the apparent isotonic point toward 0.4 mol/L when it is really lower.
- Bench drying before soaking. Ten minutes of evaporation removes water from the cylinder surfaces and increases solute concentration in the tissue, shifting every point downward. It is a systematic bias applied unevenly, since not all cylinders waited.
Moderate - affects one data point.
- The 35 mm cylinder. Length change is a difference, so a longer initial cylinder is fine if the initial length was recorded. If the student instead subtracted from an assumed 30 mm, the change is wrong by 5 mm, which is huge on a +/-1 mm scale. Whether this matters depends entirely on the record-keeping.
Harmless or nearly so.
- Worn ruler end. A constant offset shifts all initial and final readings equally, so the changes - and the isotonic point - are unaffected.
- Measuring the same cylinder twice. This is a recording confusion, not a physical effect; the reading itself is not corrupted, just duplicated.
2. The group used length change. Argue whether mass change would have been a better measurement, and how you would decide.
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Mass change is generally the better measure here. Potato tissue swells anisotropically - it expands mostly in one direction but also thickens - so a single length measurement captures only part of the water taken up. Mass change integrates the whole cylinder. It is also more sensitive: a 0.5 g cylinder on a 0.01 g balance resolves 2 %, whereas a 30 mm length on a 1 mm ruler resolves about 3 % and has to be read twice.
Practical requirements for mass to work: blot every cylinder identically (same paper, same pressure, same time) before each weighing, or surface water will swamp the signal; keep soak time identical; cap the tubes to prevent evaporation; use a closed container on a balance to reduce draught error; and express results as percentage mass change so cylinders of slightly different size can be compared.
When length is acceptable: for a quick demonstration of direction - swell in pure water, shrink in strong sucrose - length is fine and cheaper. For locating an isotonic point, mass is preferable, and the strongest design measures both, so that a length result can be checked against a mass result. Agreement between two independent measures is far more convincing than either alone.
3. How confident can the class be that 0.4 mol/L is isotonic? Describe the follow-up that would put an uncertainty on that value.
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Not confident at all. With one cylinder per concentration and no repeats, there is no estimate of variability - the difference between +2 and +1 mm is within the uncertainty of a worn millimetre ruler. The zero crossing is bracketed only between 0.2 and 0.6 mol/L, so the true isotonic point could plausibly lie anywhere in that band. The 0.4 mol/L result of exactly 0 mm is also suspiciously tidy; real single measurements rarely land on zero.
Follow-up design.
- Five cylinders per concentration, from the same potato, randomised to tubes.
- A finer series across the bracket, for example 0.3, 0.35, 0.4, 0.45 and 0.5 mol/L, so the crossing can be interpolated rather than guessed.
- Measure percentage mass change, not just length, with standardised blotting and a fixed 30-minute soak.
- Plot mean percentage mass change against concentration with error bars, fit a straight line through the linear region, and read off where it crosses zero. Report that value with a range from the replicate spread.
- Repeat on a second potato to check that the answer is a property of the tissue, not of one tuber.