Minimum Pressure applied by reverse osmosis?

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SUMMARY

The minimum pressure required to purify seawater by reverse osmosis at 25 degrees Celsius is 29 atm, calculated using the osmotic pressure formula iMRT, where i is the van 't Hoff factor for NaCl, which is 2.0. The initial calculation of 14.68 atm was incorrect as it did not account for the dissociation of NaCl into two ions. The correct approach involves multiplying the molarity of the solution (0.60M) by the gas constant (0.0821 Latm/mol K) and the temperature in Kelvin (298 K), then adjusting for the van 't Hoff factor.

PREREQUISITES
  • Understanding of osmotic pressure and its formula
  • Familiarity with the van 't Hoff factor in colligative properties
  • Knowledge of the gas constant and its units
  • Basic principles of reverse osmosis technology
NEXT STEPS
  • Study the derivation and applications of the osmotic pressure formula iMRT
  • Learn about the van 't Hoff factor and its significance in solutions
  • Explore the principles of reverse osmosis and its industrial applications
  • Investigate the effects of temperature on osmotic pressure in various solutions
USEFUL FOR

Chemistry students, environmental engineers, and professionals involved in water purification technologies will benefit from this discussion.

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Homework Statement


Seawater is approximately .60M NaCl. What is the minimum pressure that must be applied at 25 degrees Celsius to purify seawater by reverse osmosis? Assume i=2.0 for NaCl.


Homework Equations


Osmotic pressure = MRT
R= gas constant, .0821 Latm/mol K


The Attempt at a Solution


I started by trying to find the osmotic pressure:
Osmotic pressure = .60M (.0821 Latm/mol K) (298 K)
= 14.68 Latm

I feel like this isn't correct because I didn't use the i=2.0 part.
Can someone tell me what I'm doing wrong?

should i first calculate the boiling point of the solution using delta t = i Kb(m) ?
If so, why and how can I calculate that using m?
 
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The correct formula for osmotic pressure is iMRT when M refers to the solute. So you need to multiple your earlier solution by i=2, giving an answer of 29 atm (don't give too many significant figures as the given NaCl concentration has only 2 significant figures). What i means is that each mol of NaCl when dissolved in water will give 2 mol of ions.

Hope that helps.
 

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