Question

Explain why reverse osmosis is (theoretically) more desirable as a desalination method than distillation or freezing. What minimum pressure must be applied to seawater at \(25^{\circ} \mathrm{C}\) for reverse osmosis to occur? (Treat seawater as a \(0.70 M \mathrm{NaCl}\) solution.)

Short answer

Reverse osmosis is more energy-efficient than distillation or freezing. Minimum 34.23 atm pressure is required.

Step-by-step solution

Understand Reverse Osmosis

Reverse osmosis is a process that uses a semi-permeable membrane to separate solvent molecules (like water) from solutes. It is considered more energy-efficient than conventional distillation or freezing because it requires less energy to push water through a membrane than to change its phase (heating for distillation or cooling for freezing).

Establish Osmosis Principle

In osmosis, solvent molecules spontaneously move from a region of lower solute concentration to a region of higher solute concentration through a semi-permeable membrane. To reverse this flow (reverse osmosis), we apply external pressure that exceeds the natural osmotic pressure.

Calculate Osmotic Pressure using Van 't Hoff's Law

For reverse osmosis, osmotic pressure (\(\pi\)) is calculated using \(\pi = iMRT\), where \(i\) is the van 't Hoff factor, \(M\) is the molarity, \(R\) is the gas constant (0.0821 L atm mol⁻¹ K⁻¹), and \(T\) is temperature in Kelvin.

Determine van 't Hoff Factor

For NaCl, which dissociates into two ions, \(i = 2\).

Convert Temperature to Kelvin

Convert Celsius to Kelvin: \(T = 25^{\circ} \mathrm{C} = 298 \mathrm{K}\).

Plug Values into the Equation

Use \(M = 0.70\), \(i = 2\), \(T = 298\), and \(R = 0.0821\) to find \(\pi\): \(\pi = 2 \times 0.70 \times 0.0821 \times 298\).

Calculate Osmotic Pressure

Calculate \(\pi = 2 \times 0.70 \times 0.0821 \times 298 = 34.23\, \text{atm}.\)

Interpret the Result

A minimum of 34.23 atm must be applied to seawater for reverse osmosis to occur at 25°C. This pressure is needed to overcome the natural osmotic pressure and allow freshwater to be separated from the salty solution.

Key concepts

Desalination Methods

Desalination is the process of removing salts and other impurities from seawater or brackish water. Several methods can achieve this, each with distinct mechanisms and energy requirements. Reverse osmosis is one of the most popular methods due to its energy efficiency and effectiveness in producing potable water.

• Distillation: This involves heating water to produce steam and then condensing the steam back into liquid form. It requires significant energy to heat the water, making it less energy-efficient compared to reverse osmosis.
• Freezing: Based on the principle that ice forms without salt, the water is frozen, and pure ice is removed before melting it back into water. This method is rarely used commercially due to the complexities and energy needed to manage temperatures.

Reverse osmosis stands out because it requires no phase change—only pressure to push water through a membrane without applying heat or freezing, thus conserving energy.

Osmotic Pressure

Osmotic pressure is a critical concept in understanding reverse osmosis. It refers to the pressure required to stop the natural movement of solvent molecules across a semi-permeable membrane. In typical osmosis, water moves from an area of low solute concentration (more pure water) to an area of high solute concentration (less pure water) in an attempt to equalize concentrations on both sides.
To reverse this natural flow, you need to apply enough pressure to overcome osmotic pressure, effectively moving water from a higher solute concentration (like seawater) to a lower solute concentration (freshwater). This process allows desalination to occur without heating or freezing the water, making it an efficient method.

van 't Hoff's Law

Van 't Hoff's law provides a way to calculate osmotic pressure, which is crucial for determining the pressure needed in reverse osmosis. It states that osmotic pressure (\(\pi\)) can be determined using the formula \(\pi = iMRT\).

• i: The van 't Hoff factor, which accounts for ion dissociation in the solution. For NaCl, which dissociates into two ions (Na⁺ and Cl^-), \(i = 2\).
• M: The molarity of the solution, indicating the concentration of solutes in water.
• R: The gas constant, \(0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1}\).
• T: The temperature in Kelvin. Converting from Celsius, \(25^{\circ} \text{C} = 298 \text{ K}\).

This equation helps us compute the osmotic pressure required to perform reverse osmosis at a given temperature.

Semi-Permeable Membrane

The semi-permeable membrane is the heart of the reverse osmosis process. It selectively allows water molecules to pass through while blocking salts and other impurities. These membranes are typically made from materials like cellulose acetate or thin-film composites.

• In osmosis, they facilitate the natural movement of water from low to high solute concentrations. Reverse osmosis, however, demands that water moves from a salt-rich solution to pure water through external pressure.
• Despite their effectiveness, these membranes require regular maintenance since they can become fouled or clogged over time, impacting the desalination efficiency.

Thus, understanding and maintaining these membranes is crucial for achieving efficient and long-lasting desalination results.

NaCl Solution

Seawater is a complex mixture, but NaCl (sodium chloride) is its principal component. Understanding the behavior of NaCl in water is essential when discussing reverse osmosis for desalination.

• NaCl dissociates into sodium (Na⁺) and chloride (Cl^-) ions. This dissociation increases the osmotic pressure since each molecule of salt forms two ions.
• In a typical seawater solution, roughly at \(0.70 \text{ M}\), a considerable osmotic pressure is developed, demanding significant external pressure to reverse the natural movement of water across the semi-permeable membrane.
• The necessity to overcome this high osmotic pressure with external force is why the calculated pressure needed for reverse osmosis in the step-by-step solution was 34.23 atm.

Hence, recognizing the role of NaCl is fundamental in understanding and calculating the requirements for successful desalination through reverse osmosis.