Osmotic Pressure -- Height of Water Column Supported by 1 M Glocose Solution

[dxcrunner]

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What assumption am I violating in the following question.

A solution of pure water and 1 M glucose are separated by a semipermeable membrane (only water can pass through) in a u-shaped tube, what will the difference in height of the two columns have to be for the system to reach equilibrium?

Osmotic Pressure of 1 M Glucose Solution:
Osmotic Pressure (OP) = Molarity x Gas constant x Temperature
OP = 1M * .08216 Latm/molK * 273K
OP = 22.42 atm = 2,271,706 pascals

Hydrostatic Pressure of Water Column (should equal the osmotic pressure)
Pressure = density x gravity x height
2,271,706 pa = 1000kg/m^2 * 9.8m/s^2 * H
H = 231.8 m

So the difference in the height of the water columns must be 231.8 M

This is obviously not what is observed in the lab. When we did an experiment like this back in high school, the distance can be measured in centimeters...

 

[Cawolf]

Unless I am missing something also that seems correct.

You didn't mention the van't Hoff factor, but I assume it is 1 for glucose since it doesn't ionize in solution.

Maybe in school you had a much more dilute solution?

 

[dxcrunner]

Yeah it may be the case. Every time you see those U shaped tubes and what not, they all seem to depict a small difference in height.

 

[Cawolf]

Is this a question you came upon or created? I could not find anything comparable in my material.

 

[dxcrunner]

I was reading a medical physiology textbook for my class and it mentioned the osmotic pressure of a 1osmole/L (basically 1 mole/L) solution was 19,300 mmHg. And I was amazed at the pressure difference. Roughly 25 atm to prevent water movement across a semipermeable membrane. It just seems like a massive number.

 

[Cawolf]

Ah makes sense.

It also seems that your math corresponds well.

 

[dxcrunner]

This video proves my idea correct.