Affect of volume on the rate of diffusion?

[Hammad Shahid]

Homework Statement

Hi guys. So for my biology class, we were doing a water chemistry experiment.
We placed potato cells into beakers of different [sucrose] (dissolved in water). The goal was to plot the change in mass % on a graph, make a linear trendline, and see which solution was isotonic with the [sucrose] in potato cells.
So the answer was the 0.31M solution of sucrose.

Now,
I need to determine all the experimental errors. The amount of solution in the beakers was not equivalent (neither was the mass of the potato cores).
My main question is:
Assume that we have 2 beakers with the same mass of potato cells placed into them, both sets of potato cells have an equal concentration of sucrose, and both beakers have an equal concentration of sucrose. Let’s also assume the solution is hypertonic to the potato cells (so net water movement will be towards the solution).
If one beaker has a higher volume of water than the other, will it take longer for it to reach the equilibrium concentration and why?
If so, could I list it as an experimental error as all solutions might not be at equilibrium (The beakers were placed overnight and 10-15 mL of water was used in conjunction with 5-10 grams of potato)

Homework Equations

I know the equation for rate of diffusion for gas molecules. I don’t know if that applies to liquid situations.

The Attempt at a Solution

My theory is that it will take longer for the concentration of sucrose to be equal inside and outside the cell because if the rate of diffusion is the same, then the water molecules have to travel farther distances to equalize the larger volume of water.
I could be completely wrong as I have not studied this concept to a high level degree.Thank you for any help guys.

 

[Borek]

Your task was to determine the isotonic concentration, yes? Is there a net diffusion for a potato in the isotonic solution?

 

[Hammad Shahid]

Yes; No, but there was no istonic solution. Solutions were pure water, 0.2M, 0.4, 0.6, 0.8, 1.0. After graphing, I determined 0.31 to be istonic via the trendline (y=0% mass change).

I know there’s no diffusion in isotonic solutions, but the solutions were either hypertonic or hypotonic.

I know that water will diffuse faster if there is a higher concentration gap between the gradients.
But does the actual amount of water in the 2 sets of solutions affect the rate of diffusion also or not?

 

[Borek]

OK, let me ask differently: does the speed of diffusion affect determination of which solution is isotonic?

 

[Hammad Shahid]

No. Am I right?

 

[Borek]

No. Am I right?

Yes, you are right - it doesn't affect the final result.

Your intuition is right that you can expect differences in diffusion speed and time required to reach the equilibrium, it just doesn't matter here.

 

[Hammad Shahid]

Okay thanks. But just to confirm this: if all variables are kept constant except volume, and a molecule has to diffuse from a higher concentration to a lower one, it will take longer to reach eqm in the higher volume, right? Even though the final result will still have the same concentration.

 

[Borek]

Yes, the longer path, the longer it takes to reach the diffusion equilibrium.

 

[Hammad Shahid]

Is there an equation for this?

 

[Borek]

Depends on what you mean by "an equation". Generally speaking diffusion is described by Fick's laws, but they don't give an easy answer to specific questions, more like they say what to solve to get these answers. And equations to solve are anything but trivial. For some very easy cases there are derived equations showing how the concentration changes as a function of time, but your case is not between these easy ones.