Assume that a portable reverse-osmosis apparatus operates on seawater, whose effective concentration (the concentration of dissolved ions) is 1.12 M, 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?

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Identify the formula for osmotic pressure: \( \pi = iMRT \), where \( i \) is the van't Hoff factor, \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Determine the van't Hoff factor \( i \) for seawater. Since seawater contains a mixture of ions, assume \( i \approx 2 \) for simplicity.

Calculate the osmotic pressure of seawater using its molarity (1.12 M) and the given temperature (297 K). Use \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \).

Calculate the osmotic pressure of the desalinated water using its molarity (0.02 M) and the same temperature.

Find the minimum pressure required for reverse osmosis by subtracting the osmotic pressure of the desalinated water from that of the seawater.

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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 for desalination.

Osmotic Pressure

Osmotic pressure is the pressure required to stop the flow of solvent into a solution through a semipermeable membrane. It 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 of the solution, R is the ideal gas constant, and T is the temperature in Kelvin. This concept is crucial for determining the minimum pressure needed to achieve reverse osmosis.

Ideal Gas Constant

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 typically 0.0821 L·atm/(K·mol) or 8.314 J/(K·mol). Understanding this constant is important for calculating osmotic pressure and, consequently, the pressure required for reverse osmosis in the given scenario.

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Textbook Question

Suppose that you want 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 rendering it usable for human consumption. What is the minimum pressure that needs to be applied in the permeators (Figure 13.26) to achieve this goal, assuming that the operation occurs at 298 K?

Textbook Question

You make a solution of a nonvolatile solute with a liquid solvent. Indicate if each of the following statements is true or false.

a. The solid that forms as the solution freezes is nearly pure solute.

Textbook Question

You make a solution of a nonvolatile solute with a liquid solvent. Indicate if each of the following statements is true or false.

b. The freezing point of the solution is independent of the concentration of the solute.