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

Question

Suppose that one wishes to use reverse osmosis to reduce the salt content of brackish water containing 0.22 M total salt concentration to a value of 0.01 M, thus render- ing it usable for human consumption. What is the mini- mum pressure that needs to be applied in the permeators (Figure 18.20) to achieve this goal, assuming that the oper- ation occurs at 298 K? (Hint: Refer to Section 13.5.)

Accepted Answer

Identify the concept of reverse osmosis, which involves applying pressure to overcome the natural osmotic pressure and force water through a semipermeable membrane, leaving the solute (salt) behind.. Use the formula for osmotic pressure: $ \Pi = iMRT $, where $ \Pi $ is the osmotic pressure, $ i $ is the van't Hoff factor (which is 1 for non-ionizing solutes), $ M $ is the molarity of the solution, $ R $ is the ideal gas constant (0.0821 L·atm/mol·K), and $ T $ is the temperature in Kelvin.. Calculate the initial osmotic pressure of the brackish water using the given concentration of 0.22 M and the temperature of 298 K.. Calculate the osmotic pressure of the desired water concentration (0.01 M) at the same temperature.. Determine the minimum pressure needed by finding the difference between the initial osmotic pressure and the desired osmotic pressure. This difference is the minimum pressure that must be applied to achieve the desired reduction in salt concentration.

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Key Concepts

Osmosis and Reverse Osmosis

Osmotic Pressure

Ideal Gas Constant and Temperature