When the diffusion bag contained 20% or 15% fructooligosaccharides, the net movement of water was from the beaker to the bag. However, the change in mass was greater when the dialysis bag contained 20% fructooligosaccharides than when it contained 15% fructooligosaccharides. Why

The change in mass of the bag was greater when it contained 20% fructooligosaccharides than when it contained 15% fructooligosaccharides because more water moved into the bag with 20% fructooligosaccharides than with 15% fructooligosaccharides.

Explanation:

Diffusion is the movement of substances from an area of high concentration to an area of comparatively lower concentration. Diffusion is said to be complete when both compartments/regions have equal concentration of the substance. The rate of diffusion increase with increase in concentration gradient, increase in temperature, and decrease in size of the diffusable substance.

In our example, the two compartments are the compartment in the diffusion beg which contains fructooligosaccharides and the compartment in the beaker which contains more water, because water (diffusing substance) moves from the beaker where it is more in concentration to the bag, where it is lesser in concentration. The bag, when it contained 15% fructooligosaccharides had relatively more water before diffusion than the bag when it contained 20% fructooligosaccharides, as a result of this, when diffusion starts, it will take a lesser volume of water to move into the 15% bag to attain equilibrium than it will take for the 20% fructooligosaccharides bag to attain equilibrium. Meaning that more water will move into the bag when it contained 20% fructooligosaccharides than 15% fructooligosaccharides making the overall volume in the bag higher.

Let me use hypothetical values; assume that before diffusion, both (15% and 20%) bags weighed 50 g of the solute (fructooligosaccharides) each, but had different concentration of the solute. Let us also assume that by the time 10g of water moves into the 15% bag, it attained equilibrium, bringing the total weight in the bag to 60g. It will take more than 10g of water to move into the 20% bag before it attains equilibrium, lets say it take 18g of water to move into the 20% bag to cause equilibrium, total weight of the 20% bag becomes (50 + 18 = 68g), hence the mass of the 20% bag will be higher than the 15% bag at equilibrium.