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Cell walls are selectively permeable to ions and organic molecules. Sometimes the selectivity is passive and a reflection of the physical laws governing diffusion. We can do simple experiments that strengthen intuition about transport across biological membranes. The following homework question concerns a situation which tests understanding of the basic ideas of osmosis and diffusion generally.

A bag made of a flexible semipermeable membrane is filled with a 10% glucose and 5% starch solution. This bag is permeable to water and glucose but NOT to starch. The bag is suspended in a a beaker containing a 10% glucose solution. In 30 minutes the bag can be expected to

(A) swell
(B) shrink slightly
(C) collapse entirely
(D) become impermeable to glucose
(E) remain the same

Since the bag is impermeable to starch, I know that the solution in the bag isn't going to diffuse outside so it won't shrink, but would water from outside flood into the bag to try to dilute the starch concentration to the point that it's isotonic? Or am I not understanding some fundamental principle of diffusion?

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  • $\begingroup$ The question is clever but I think you are right. It's the osmotic concentration that drives the movement. The 10% glucose has no net effect. The added starch means the osmotic conc. in the bag is higher and so water from the outside would enter the bag. $\endgroup$
    – daniel
    May 31, 2014 at 2:54
  • $\begingroup$ @daniel Note that starch will not form a true solution and cannot contribute to osmotic pressure. Colloidal dynamics are a little more complicated. $\endgroup$
    – WYSIWYG
    May 31, 2014 at 8:23
  • $\begingroup$ @WYSIWYG: I'm confident colloidal dynamics were not what the question contemplated, so if you are correct the question was badly written. $\endgroup$
    – daniel
    May 31, 2014 at 12:44
  • $\begingroup$ yes.. I understand that @daniel but if not looked at as a homework question, there are some interesting aspects to it. $\endgroup$
    – WYSIWYG
    May 31, 2014 at 13:21
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    $\begingroup$ This question appears to be off-topic because it doesn't have fit with the topics listed in the help center. Great question, though. Maybe better suited to Physics or Chemistry? $\endgroup$
    – J. Musser
    Jul 11, 2014 at 3:02

2 Answers 2

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The bag will swell.

Diffusion results in molecules moving down their concentration gradient.

In the set-up described only glucose and water are able to diffuse. Glucose is at the same concentration inside and out so there will be no changes in glucose concentration. Water will move into the bag because it is effectively at a lower concentration (more correctly - chemical potential) inside due to the presence of the starch. As water moves into the bag, increasing the volume, glucose will also move so that the glucose concentration remains equal on both sides. Thus there will be net movement of water and glucose into the bag.

@WYSIWYG has raised the spectre of colloids in the comments. I don't understand colloids so cannot comment, but I think that in the context of problems like this we are usually dealing with "soluble" starch. Here is an example of a calculation in which starch is treated as an osmolyte.

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    $\begingroup$ It should depend on the chemical nature of the suspended macromolecule (in this case starch and it will form a colloidal mixture). If the macromolecule is inert then it will just reduce the effective volume inside the bag. $\endgroup$
    – WYSIWYG
    May 31, 2014 at 8:22
  • $\begingroup$ @WYSIWYG are you saying that my answer is incorrect and the correct answer is E? $\endgroup$
    – Alan Boyd
    May 31, 2014 at 9:08
  • $\begingroup$ I think A) swelling is right answer. The water is at lower concentration in the bag than outside the bag so it will diffuse passively into the bag. Glucose concentration drops in the bag, but at the same time, glucose is diffused passively from outside into the bag so keeping the potential stable between glucose. Water will mostly diffuse, and some water. $\endgroup$
    – Léo Léopold Hertz 준영
    May 31, 2014 at 9:19
  • $\begingroup$ @AlanBoyd.. I am not sure.. that is why I commented. Considering that starch has polar groups it can interact with water and may reduce the bulk water - in that case your answer will hold correct. I cannot conclusively say if it can give rise to oncotic pressure. I am not an expert in this area but this is what I understand. If we are really interested in that aspect we can migrate this question (with appropriate edits) to ChemistrySE/PhysicsSE $\endgroup$
    – WYSIWYG
    May 31, 2014 at 13:13
  • $\begingroup$ glucose will equilibriate.. that's what Alan Boyd said in his answer $\endgroup$
    – WYSIWYG
    Jun 3, 2014 at 5:36
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DIY Diffusion Experiment

This procedure was done to see what happens qualitatively when semipermeable (dialysis) tubing containing a solution of glucose and protein is immersed in a solution of glucose alone. Given that water would diffuse into the bag, the question to be answered was whether there would be an equilibrium increase of sugar concentration outside the bag.

Equipment: one-inch dialysis tubing, bovine serum albumin (BSA), dextrose, an inexpensive commercial glucose meter, test strips for the meter.

General procedure: A control dextrose solution was divided between a sac made of dialysis tubing and a drinking glass. A small mass of powdered BSA was added to the sac. The sac was suspended in the sugar-only solution and the solution outside the bag checked at 13 times during a 33-hour period. At about 8 hours protein was added to the bag since neither diffusion nor osmosis was being observed. After this the bag began to swell. Due to concern that BSA would affect the reading the measurements were compared with the control solution and not the inside of the bag$^1$.

Results: Results are given in the table below. Addition of protein is indicated by the arrow in the graph.

Discussion: This procedure was suggested in this answer at the Chemistry SE. The meter requires some practice to use. Protein was added to the bag in roughly 200mg increments until an influx of water occurred. The solutions had probably reached equilibrium within a few hours of adding the extra protein but fluctuation in temperature made this difficult to determine. The gross trends correspond to air-conditioner use.

Conclusion: This procedure was done twice with similar results. The results are qualitative and suggest that sugar diffuses out through the membrane. This result is consistent with the answer at PhysicsSE and also this website (Figure 4.1) which indicates that diffusion and osmosis (diffusion of water) both occur. At equilibrium the concentration of sugar is slightly higher outside the bag.

Problems/issues : (1) The meter is very sensitive to temperature $^2.$ (2) Perhaps because the dextrose was incompletely dissolved the measurement of control solutions took about an hour to stabilize. That is why the measurements begin at 110 minutes. (3) The meter gave errors outside a range of 30-500 mg/dl and after checking the standard deviation for a few concentrations of dextrose a concentration of 90 mg/dl was chosen. (4) It was not assumed that the meter functioned properly in the presence of BSA. Except for the last measurements, the glucose was measured outside the bag only.

$^1$ Four measurements were taken with the meter within 2 minutes of the last measurement to check variability of the meter. The numbers [mg/dl] were: 90, 94, 93, 89, $\mu = 91.5, \sigma = 2.38.$ At the last measurement the glucose concentration inside the bag was checked twice and the meter gave: 72, 80.

$^2$ Concentration should remain the same after equilibrium [Fick equation] and should not be affected by temperature. Manufacture information for the meter omitted for this reason. Caveat emptor.

Table 1. Min.= minutes, contr. = control [mg/dl], dextr. = dextrose [mg/dl].

$$\begin{array}{c | c | c | c | c | c |c | c | c | c | c | c | c | c | } min. & 110 & 145 & 296 & 356 & 686 & 776 & 802 & 832 & 862 & 1352 & 1393 & 2053 & 2069 \\ \hline dextr. & 90 & 80 & 88 & 83 & 90 & 91& 88 & 88 & 89 & 84 & 93 & 86 & 90 \\ \hline contr.& 91 & 83 & 83 & 86 & 82 & 87 & 83 & 85 & 80 & 77 & 89 & 82 & 82 \\ \hline\end{array}$$

A graph (mg/dl v. minutes) was made from this table. The arrow indicates addition of protein to the bag.

enter image description here

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