Suppose that one wishes to use reverse osmosis to reduce the...

Suppose that one wishes to use reverse osmosis to reduce the salt content of brackish water containing $0.22 \mathrm{M}$ total salt concentration to a value of $0.01 M$, thus rendering it usable for human consumption. What is the minimum pressure that needs to be applied in the permeators (Figure $18.16$ ) to achieve this goal, assuming that the operation occurs at $298 \mathrm{~K} ?$ (Hint: Refer to Section 13.5.)

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Key Concepts

Osmotic Pressure

Osmotic pressure is the pressure that must be applied to a solution to prevent the osmotic flow of water through a semi-permeable membrane into the solution. It arises due to the concentration difference across the membrane and is critical in determining the operational requirements for processes like reverse osmosis.

van't Hoff Equation

The van't Hoff equation, given as ? = iMRT, relates the osmotic pressure (?) of a solution to its molar concentration (M), the absolute temperature (T), the universal gas constant (R), and the van't Hoff factor (i), which accounts for the number of particles into which a solute dissociates. This equation is fundamental in calculating the minimum pressure required in reverse osmosis applications.

Reverse Osmosis

Reverse osmosis is a water purification process that involves forcing water through a semi-permeable membrane to separate solutes (such as salts) from the water. It is widely used in desalination and water treatment because it allows water molecules to pass while retaining dissolved impurities.

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