Calculate Height Difference Given Osmotic Pressure

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In summary, the conversation discusses calculating the height that the osmotic pressure of a solution would raise a column of water with a given cross sectional area. The formula P=ρgh is mentioned, with g representing the force of gravity. The density of the solution is not given, but it is suggested that it may change as the osmotic process continues. The effect of the cross sectional area on the answer is also considered, with the assumption that the density of water would be used in the calculation. It is mentioned that the solution would rise to a height above the surface of the water.
  • #1
kthejohnster
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i calculated osmotic pressure of a solution (nkt/V) and now i need to figure out how high this pressure would raise a column of water with a cross sectional area of 1cm^2. The force of gravity given is 980 dynes. How would i figure out height difference, i know it has to do with pressure difference but not sure how.
 
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  • #2
I guess it would have something to do with P=ρgh
Pressure = density x g x height, g= 9,81m/s^2 (980 dynes)
 
  • #3
256bits said:
I guess it would have something to do with P=ρgh
Pressure = density x g x height, g= 9,81m/s^2 (980 dynes)

thanks but i wasnt given density of the solution is there any other way?
i believe it has to do with cross section because next part asks for answer if cross section is 10^6 cm^2
 
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  • #4
When water moves across the membrane the solution concentration changes so you have to take that into account.
 
  • #5
the question asks for the affect of the amount of pressure (maybe so we avoid taking conc changes)
 
  • #6
kthejohnster said:
thanks but i wasnt given density of the solution is there any other way?
i believe it has to do with cross section because next part asks for answer if cross section is 10^6 cm^2

As an aside, if you prepared your solution to a given molarity then you can find the density of the initial solution, but as the osmotic process continues the solution concentration will change.

Since the question asks for how high the osmotic pressure of the solution would raise a column of water of a area A, then I would assume the density used would be that of water.

Right now I don't see why a difference in the area would change the answer. Assume an unlimited amount of solvent separated from the solution by the semi-permeable membrane. The solution would rise h above the surface of the solvent ( water ).

I hope I am not missing something just so basic that I do see it.
 
  • #7
kthejohnster said:
thanks but i wasnt given density of the solution is there any other way?
i believe it has to do with cross section because next part asks for answer if cross section is 10^6 cm^2
It says "a column a water", doesn't it?
 

1. What is osmotic pressure and why is it important?

Osmotic pressure is the pressure required to prevent the flow of solvent through a semipermeable membrane from a region of low solute concentration to a region of high solute concentration. It is important because it drives many biological processes, such as the uptake of nutrients and the movement of water in and out of cells.

2. How do you calculate the height difference given osmotic pressure?

The height difference can be calculated using the formula: h = (πRTi)/Mg, where h is the height difference, π is the osmotic pressure, R is the gas constant, T is the temperature, i is the van't Hoff factor (a measure of the number of particles a solute dissociates into), and M is the molar mass of the solute.

3. Can osmotic pressure be measured experimentally?

Yes, osmotic pressure can be measured experimentally using an osmometer. This device measures the pressure required to stop the flow of solvent through a semipermeable membrane.

4. How does temperature affect osmotic pressure?

As temperature increases, osmotic pressure also increases. This is because higher temperatures result in increased kinetic energy and therefore, increased movement of solute particles, leading to a higher osmotic pressure.

5. What are some real-world applications of calculating height difference given osmotic pressure?

Some real-world applications include understanding the movement of water in plant cells, predicting the effects of osmotic pressure on organisms living in different environments, and designing filtration systems for water purification.

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