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Molarity and diffusion

Page history last edited by Joe Redish 8 years, 3 months ago

4.3.3.P11

 

Prerequisite:

 

In a previous problem (Molarity and number density), we explored how the chemical concept of molarity (number of moles per liter), when applied to thinking about individual molecules, can help us build a mental picture of how different the environments are for a molecule  in a gas and in a liquid. A second valuable insight that can be developed is to ask the question, What drives diffusion?  In our reading, Diffusion and random walks, we stated that individual molecules in fluids undergo a random walk, moving in unpredictable ways. Yet somehow, there emerges from these random motions a flow from higher to lower concentration. (See Fick's Law.) 

 

One potential way of thinking about diffusive flow is that diffusing molecules collide with each other more often in regions of high concentration and are "driven away" towards regions of low where they don't have as many collisions. If this is true, diffusing molecules would have to be reasonably close to each other. Let's consider this in a realistic case, using our method of estimating number density and the distance between molecules.

 

A critical part of the signalling between neurons in the release of neurotransmitter chemicals from the neuron with an incoming signal into a space between neurons (synapse) where the chemical can diffuse and be detected by a receptor on the neuron receiving the signal. A picture is shown in the figure at the right. The diagram is schematic and doesn't give an idea of the density of the molecules. Let's figure them out.

 

A. A typical molarity for one such neurotransmitter, acetylcholine, is 100 micromolar (10-4 molar). Given that the molecular weight of acetylcholine is ~150 D, find a molecule's specific volume, s.

 

B. From the skills you learned in estimating the size of an actin molecule, estimate the molecular diameter of acetylcholine. 

 

C. To get a sense of how far apart molecules are, calculate the specific volume, s = 1/αm, and the average separation distance, d = s1/3, of the diffusing acetylcholine molecules.

 

D. Compare these to the specific volume and separation distances you found for the molecules of water. 

 

Source: Looie496, US National Institutes of Health, National Institute on Aging, public domain

 

E. Sketch a small volume of the region in the synapse that can be expected to contain only about 2 acetylcholine molecules. How many water molecules does that volume contain? Do you think that the motion of the acetylcholine molecules are primarily driven by collisions with the jiggling water molecules or by collisions with each other?

 

 

 

Joe Redish and Marco Colombini

11/19/15

 

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