[Elciteeve]

Hello! I'm studying biology and I'm a bit confused by certain situational osmosis problems. The problem type I keep encountering which I keep getting marked as wrong is a scenario like this,

A cell has [2m K⁺] and [1m glucose]. A solution has [2m glucose] and [1m K⁺]. The cell membrane is permeable to K⁺ and impermeable to glucose. The cell is dropped in the solution. What is the tonicity before equilibrium is reached?

Ok, so my understanding is that tonicity is explicitly pertaining to solutes which *can't* permeate the membrane. So essentially the potassium ion is a non factor, ie. the potassium ion can move freely, and therefore it lacks the ability to create tonicity. That would mean that the glucose is the only solute affecting tonicity, therefore the cell would be hypotonic to the solution before equilibrium is achieved. The cell will crenate, water moves out of the cell into the solution to achieve equilibrium.

1.) is this correct?
2.) why or why not?
3.) what are some resources that explain this specific aspect of osmosis more directly? Everything i read just talks about how to calculate osmotic pressure or a basic explanation of what tonicity / osmosis is, and doesn't explain compound variables well, with respect to determining these hypothetical non-real scenarios.

My teacher is a self professed "non biochemist" and her ability to explain is limited in certain areas. I think she maybe has memorized the answer, but doesn't know the "why." Or maybe she does and is sick of me pestering her with questions. Either way, I'd love some help with this.

I have read several resources, including my BI231 text book, BI112 textbook, wikipedia, and a few science journals. I can't find any direct explanation to contradict my understanding for this issue, but my teacher insists I'm wrong. Well it would be helpful to know *why* I'm wrong. Any help would be appreciated, thank you.

[Borek]

1. Neither solution can exist (you need a counterion for the solution to be electroneutral), so the question is incomplete (as - when it comes to osmotic pressure and tonicity - solution containing Cl^- as a counterion is substantially different from solution containing SO₄^2-).

2. Can tonicity exist without a difference of osmotic pressure?

3. What does "before equilibrium" mean? Just when you have these two initial solutions? What are their osmotic pressures? Are they different?

[Elciteeve]

1.) This is for bio-chem / cellular functioning for medical. The theory is that this would be a (academic) representation of a real cell. Since it's in a cell, that is exactly the point - to create an electronegative membrane potential. So the question is basically asking, if we could place the cell in solution without time passing, what would the tonicity be? It is supposed to represent a cell and its interactions with the extracellular fluid / interstitial fluid.

2.)Well that's sort of my point - and even if it could, it's solely dependent upon which solutes are permeable to the membrane, right? So that's why I'm having trouble with these questions. They seem, from what I can tell, off.

3.) I think she's asking what the tonicity is before the cell is placed in solution or as I was trying to describe above, if we could magically place a cell in solution without time passing, what would its tonicity be before we allowed the solutes / water to diffuse?

[Borek]

Nah, I think you are missing the point.

Wikipedia defines tonicity as "a measure of the effective osmotic pressure gradient" - if there is no osmotic pressure between two sides of the membrane, there is no tonicity. Assuming for now that the counterion is identical osmotic pressures are initially identical, so there is no tonicity.

Note that I wrote "initially". There is no magic involved - the process of the ion transfer through the membrane is not instantaneous, it takes time. Initial situation and the situation at equilibrium are separated by seconds at least, minutes or even hours most likely.

Despite the initial lack of osmotic pressure system is not at equilibrium. You have a permeable membrane and two different concentrations of an ion on both sides - that means different chemical potentials, so the ions will actually travel. That will create an osmotic pressure - and tonicity. Not sure ATM how to calculate exact concentrations of K⁺ at the equilibrium - there will be some balance between the chemical potential gradient and pressure gradient, definitely concentrations of K⁺ will be a bit closer to each other than they are at the initial point.

[Elciteeve]

Ok, so your saying that initially we must evaluate K+ even though it crosses the membrane?

Basically there will initially be water movement, and K+ movement, but essentially no net movement fast enough to create a net movement of water in one direction.

That would mean that initially it's isotonic.

Is that more or less the idea?