Assume that a portable reverse-osmosis apparatus operates on seawater, whose concentrations of constituent ions are listed in Table 18.5, and that the desalinated water output has an effective molarity of about 0.02 M. What minimum pressure must be applied by hand pumping at 297 K to cause reverse osmosis to occur? (Hint: Refer to Section 13.5.)

Verified step by step guidance

Identify the concept of reverse osmosis, which involves applying pressure to overcome the natural osmotic pressure and force water through a semipermeable membrane, leaving solutes behind.

Use the formula for osmotic pressure: \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor, \( M \) 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.

Determine the effective molarity of the seawater solution using the given data or reference table. Assume the van't Hoff factor \( i \) is approximately equal to the number of ions produced per formula unit of the solute.

Substitute the values into the osmotic pressure formula: \( \Pi = iMRT \), using the effective molarity of the seawater, the ideal gas constant, and the temperature (297 K).

Calculate the minimum pressure required for reverse osmosis by ensuring it is greater than the calculated osmotic pressure. This pressure must be applied to the seawater to achieve desalination.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Reverse Osmosis

Reverse osmosis is a water purification process that uses a semipermeable membrane to remove ions, molecules, and larger particles from drinking water. In this process, pressure is applied to overcome osmotic pressure, allowing water to flow from a region of higher solute concentration (seawater) to a region of lower solute concentration (desalinated water). This is essential for understanding how to calculate the pressure needed to achieve desalination.

Osmotic Pressure

Osmotic pressure is the pressure required to stop the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the molarity of the solute in the solution and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molarity, R is the ideal gas constant, and T is the temperature in Kelvin. This concept is crucial for determining the minimum pressure needed for reverse osmosis.

Ideal Gas Constant (R)

The ideal gas constant (R) is a fundamental constant used in various equations in chemistry, including those related to gas laws and osmotic pressure. Its value is approximately 0.0821 L·atm/(K·mol) or 8.314 J/(K·mol), depending on the units used. In the context of reverse osmosis, R is used in the osmotic pressure equation to relate temperature and molarity to the pressure required for the process.

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