Potato Cylinders and a Cylinder That Left the Solution
A student investigates osmosis in potato tissue. Cylinders are cut from one potato with a 5 mm cork borer, trimmed to 30 mm, blotted, weighed, and five cylinders are placed in each of six sucrose solutions (0.0, 0.2, 0.4, 0.6, 0.8 and 1.0 mol/L) for 30 minutes before being blotted and reweighed. Mean percentage mass changes are: 0.0 mol/L +6.2 %; 0.2 mol/L +3.1 %; 0.4 mol/L −0.4 %; 0.6 mol/L −4.8 %; 0.8 mol/L −8.9 %; 1.0 mol/L −13.6 %. In the 0.8 mol/L dish one cylinder gave −3.5 % while the other four gave between −9.3 % and −9.5 %; the student's notes record that this cylinder stuck to the side of the dish above the liquid for part of the time. A classmate argues that the 0.4 mol/L result should be thrown away because it is almost zero and therefore obviously a mistake.
1. Estimate the sucrose concentration at which the potato tissue would show no net mass change, showing your working and stating the assumption you make.
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Zero change must lie between 0.2 mol/L (+3.1 %) and 0.4 mol/L (−0.4 %), because the sign of the mass change reverses across that interval.
Interpolating linearly, the fraction of the interval travelled from +3.1 % down to zero is 3.1 / (3.1 + 0.4) = 3.1 / 3.5 = 0.886. So the balance point is at about 0.2 + 0.886 × 0.2 = 0.377 mol/L, roughly 0.38 mol/L.
Assumption: percentage mass change is linear in sucrose concentration between the two measured solutions. That is only an approximation - the response usually curves as the tissue approaches equilibrium - so the honest claim is 'between about 0.35 and 0.40 mol/L', not '0.377 mol/L'. The data bracket the answer only within a 0.2 mol/L window, so the estimate carries roughly ±0.05 mol/L. To narrow it she must add solutions at 0.30, 0.35 and 0.40 mol/L rather than compute to three decimal places from a two-point line.
2. Evaluate both suggestions: deleting the 0.4 mol/L result because it is near zero, and deleting the −3.5 % cylinder.
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These look similar but are opposite cases.
The −0.4 % value is not an outlier - it is the most informative point in the set. It sits between swelling and shrinking and is what a genuine isotonic treatment should give. Deleting it would remove the bracket needed for interpolation and bias the estimate towards shrinkage. Keep it.
The −3.5 % cylinder is anomalous for an identified physical reason, not merely because it is far from the mean: the other four in the same dish gave −9.3 % to −9.5 %, and the notes record that this cylinder was out of the solution for part of the time, so it had less contact and less time for water to leave. Because the cause was recognised independently of the size of the number, excluding it is justified - and the reason must be stated, not hidden.
Effect on the conclusion: keeping it would pull the 0.8 mol/L mean to about (4 × −9.4 − 3.5)/5 ≈ −8.2 %, flattening the high-concentration part of the curve. The isotonic estimate itself barely moves, since the 0.2–0.4 mol/L bracket is unaffected; what changes is the apparent steepness of the trend.
3. Her conclusion is that potato cell sap has a water potential equal to that of 0.38 mol/L sucrose. Give two reasons this overreaches the evidence, and one change that would strengthen the investigation.
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First, 30 minutes is not equilibrium. Mass change measures net water movement up to that moment; a zero net change can mean the inward and outward movements happen to balance at 30 minutes rather than that the water potentials are equal. Weighing the same cylinders at 10, 20, 30, 60 and 90 minutes would show whether the masses had plateaued, which is what equilibrium requires.
Second, whole-cylinder mass is not cell-sap water potential. The cylinder contains cell wall and apoplast water, air spaces and a cut surface of damaged cells; sucrose can also enter damaged cells and add mass without any osmosis. The balance point is a property of the cylinder in that solution, not a measurement of sap alone. A single potato also gives no replication across tubers, so the value need not be a species property.
Strengthening change: use finer concentration steps (0.30, 0.35, 0.40, 0.45 mol/L), several tubers, a verified equilibration time, and identical blotting and weighing routine for every cylinder, reporting percentage mass change so that differences in cylinder size do not dominate.