Minimum Pressure applied by reverse osmosis?

In summary, the conversation discusses the calculation of the minimum pressure needed to purify seawater through reverse osmosis at 25 degrees Celsius. The correct formula for osmotic pressure is iMRT, where i represents the number of ions produced when the solute is dissolved. Therefore, using the given concentration of .60M NaCl and assuming i=2.0, the minimum pressure required is 29 atm. The conversation also briefly mentions the possibility of calculating the boiling point of the solution using delta t = iKb(m), but it is not clear if this is necessary for the question at hand.
  • #1
yeahyeah<3
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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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  • #2
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.
 
  • #3



Your calculation of osmotic pressure is correct. However, in order to determine the minimum pressure required for reverse osmosis, you need to consider the pressure difference between the osmotic pressure and the applied pressure. This pressure difference is known as the "osmotic pressure difference" and can be calculated using the following equation:

Osmotic pressure difference = osmotic pressure - applied pressure

In this case, the applied pressure is the minimum pressure required for reverse osmosis, so we can rearrange the equation to solve for it:

Applied pressure = osmotic pressure - osmotic pressure difference

To calculate the osmotic pressure difference, we first need to calculate the osmotic pressure of pure water. This can be done using the same formula as before, but with a concentration of 1M instead of 0.60M:

Osmotic pressure of pure water = 1M (.0821 Latm/mol K) (298 K)
= 24.51 Latm

Next, we need to calculate the concentration of seawater in terms of osmolarity, which takes into account the dissociation of NaCl into two ions (Na+ and Cl-). This can be done using the following formula:

Osmolarity = concentration x i

In this case, the concentration of seawater is 0.60M, so the osmolarity would be:

Osmolarity = 0.60M x 2 = 1.20 osM

Finally, we can calculate the osmotic pressure difference using the following formula:

Osmotic pressure difference = (osmolarity of seawater x osmotic pressure of pure water) - (osmolarity of pure water x osmotic pressure of seawater)

= (1.20 osM x 24.51 Latm) - (1 osM x 14.68 Latm)
= 29.41 Latm

Now, we can plug this value into the equation we derived earlier to solve for the minimum pressure required for reverse osmosis:

Applied pressure = 14.68 Latm - 29.41 Latm
= -14.73 Latm

This value is negative because the osmotic pressure is greater than the applied pressure, indicating that the applied pressure needs to be higher than the osmotic pressure in order for reverse osmosis to occur. Therefore, the minimum pressure required for reverse os
 

1. What is reverse osmosis?

Reverse osmosis is a water purification process that involves the use of a semi-permeable membrane to remove impurities and contaminants from water. The process works by applying pressure to the contaminated water, forcing it through the membrane and leaving behind pure, clean water.

2. How does reverse osmosis work?

Reverse osmosis works by using a high-pressure pump to push water through a semi-permeable membrane, which only allows water molecules to pass through. This process effectively removes impurities, such as salt, minerals, and other contaminants, from the water.

3. What is the minimum pressure required for reverse osmosis to work?

The minimum pressure required for reverse osmosis to work is typically around 35-40 psi (pounds per square inch). However, the exact pressure needed may vary depending on the specific system and the quality of the water being treated.

4. What happens if the pressure applied during reverse osmosis is too low?

If the pressure applied during reverse osmosis is too low, the process will not be effective in removing impurities from the water. This can result in poor water quality and potential health risks if the water is consumed.

5. Can the pressure applied by reverse osmosis be adjusted?

Yes, the pressure applied by reverse osmosis can be adjusted to achieve the desired level of water purity. However, it is important to note that increasing the pressure can also increase energy consumption and may shorten the lifespan of the system. It is best to consult with a professional before making any adjustments to the pressure in a reverse osmosis system.

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