Reading the isotonic point without reading it off the table
Four groups of students investigate osmosis in potato. A cork borer is used to cut strips of the same diameter, and each strip is trimmed to exactly 40 mm. Strips are placed in sucrose solutions of different concentration for 30 minutes, removed, blotted once on paper towel, and measured with a ruler marked in millimetres. Results for the best-behaved group:
| Concentration (mol/dm³) | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 |
|---|---|---|---|---|---|
| Final length (mm) | 44 | 41 | 38 | 35 | 33 |
Three other issues arise. A second group reports 44 mm for 0.2 mol/dm³. A third group blots each strip only by touching it once on the bench top and argues that is "close enough". A fourth group points out that its strip in 0.2 mol/dm³ measured 41 mm, the same as the first group's, but felt much softer.
1. Estimate the sucrose concentration of the potato tissue from the table. Show every step and state the assumptions behind your estimate.
Read the worked answer
The tissue's own concentration lies where there is no net water movement, i.e. where the length does not change. No row gives 40 mm, so the value must be interpolated between 0.2 and 0.4 mol/dm³.
- From 0.2 to 0.4 mol/dm³ (a change of 0.2 mol/dm³) the length falls from 41 mm to 38 mm, a change of 3 mm.
- So 1 mm of length change corresponds to 0.2 ÷ 3 = 0.067 mol/dm³.
- To reach 40 mm from 41 mm we need a fall of 1 mm, i.e. 0.067 mol/dm³.
- Isotonic concentration ≈ 0.2 + 0.067 = 0.27 mol/dm³ (accept roughly 0.25–0.30).
Note that the answer must lie between the two rows that bracket zero change; choosing 0.2 or 0.4 because it is the nearest value in the table is the common mistake.
Assumptions: the response is linear over 0.2–0.4 mol/dm³; all strips started at exactly 40 mm; the potato is uniform, so strips have the same internal solute concentration; temperature and immersion time were identical; blotting removed surface water equally.
2. A second group measures 44 mm for 0.2 mol/dm³, where the first group measured 41 mm. Give two plausible causes and describe how you would decide between them.
Read the worked answer
Two plausible causes, one random and one systematic:
- Random or procedural one-off error - the strip was cut noticeably thicker or wider (so less relative water uptake), was taken from a different part of the tuber (skin, cortex or pith differ in solute content), was left in the solution longer, was not blotted and carried surface water, or was a labelling slip in a crowded practical.
- A systematically different sample or method - this group used a different potato (different storage age, so different sugar content), a different borer diameter, or a different ruler held at an angle, in which case every reading from that group would be shifted, not just one.
How to decide: ask the group to repeat 0.2 mol/dm³ with three or more strips cut from the same tuber with the same borer, all immersed for the same time and blotted the same way. If the repeats cluster near 41 mm, the 44 mm was a stray result and is discarded with a stated reason. If the repeats again give about 44 mm while the first group's method is being copied exactly, the difference is systematic - most likely a different batch of potatoes - and the two groups' data cannot be pooled.
3. The fourth group's strip measured 41 mm, the same as the first group's, yet felt much softer. Explain how two strips of identical length can be in different states, and state which extra measurement you would add and why.
Read the worked answer
Length only records net water movement along one axis, and it conflates two different states.
A strip placed in a solution slightly weaker than the cell sap gains a little water. The cellulose walls resist stretching, so the cells become firm (turgid) while the strip barely lengthens. A strip placed in a solution slightly stronger than the cell sap loses a little water, but if it started fully turgid the cells can lose water without the strip getting much shorter, because the tissue only visibly shrinks once the cells lose turgor and the cytoplasm starts to pull away from the walls (plasmolysis). Firmness is therefore more sensitive than length near the isotonic point.
The best single addition is mass, recorded before and after immersion on a balance reading to 0.01 g. Water moving in or out changes mass directly, whereas length responds only after the water movement is large. A bend or firmness scoring by hand, or a microscope check for plasmolysis in a squashed strip, would confirm the state of the cells but is harder to quantify fairly between groups.