Question

One way to produce freshwater from seawater is "reverse osmosis," in which high hydrostatic pressures are used to force water to move against its osmotic gradient, from seawater to freshwater, across a membrane. How would you calculate the minimal hydrostatic pressures required? Why might it be preferable to use salty water from a coastal bay diluted with river water rather than full-strength seawater as the water source?

Short answer

The minimal hydrostatic pressure required for reverse osmosis can be calculated using the osmotic pressure equation \( \Pi = CRT \), where \( \Pi \) is the osmotic pressure, \( C \) is the molar concentration of the solute, \( R \) is the ideal gas constant, and \( T \) is the absolute temperature. It may be more preferable to use diluted seawater as it requires less hydrostatic pressure, making the process more efficient and cost-effective.

Step-by-step solution

Understand Osmosis and Reverse Osmosis

Osmosis is a natural process where fluid moves from an area with a lower concentration of solutes to an area with a higher concentration through a semi-permeable membrane. In reverse osmosis, pressure is applied to the side with the higher concentration, forcing the fluid to move against its concentration gradient. The minimum hydrostatic pressure required is the osmotic pressure of the solution.

Calculate Osmotic Pressure

To calculate the osmotic pressure of the solution, the following equation is used: \( \Pi = CRT \) where \( \Pi \) is the osmotic pressure, \( C \) is the molar concentration of the solute, \( R \) is the ideal gas constant, and \( T \) is the absolute temperature.

Compare Seawater and Diluted Seawater

Diluted seawater or brackish water from a coastal bay has a lower concentration of solutes than full-strength seawater. This means its osmotic pressure is lower, so less hydrostatic pressure is needed to force freshwater across a membrane in reverse osmosis. Therefore, it takes less energy and is more cost-effective to use diluted seawater.

Key concepts

Osmotic Pressure

Osmotic pressure is an essential concept in understanding fluid movement across membranes. It represents the minimum pressure that should be applied to a solution to prevent the inward flow of water through a semi-permeable membrane. This pressure is crucial when considering processes like osmosis and reverse osmosis.

Osmotic pressure depends heavily on the solute concentration. It can be calculated using the formula \[ \Pi = CRT \] where:

• \( \Pi \) is the osmotic pressure.
• \( C \) is the molar concentration of solutes.
• \( R \) is the ideal gas constant.
• \( T \) is the absolute temperature in Kelvin.

For reverse osmosis to occur, the applied hydrostatic pressure must be greater than the osmotic pressure of the seawater to push water molecules against their natural osmotic flow.

Semi-Permeable Membrane

A semi-permeable membrane plays a crucial role in both osmosis and reverse osmosis. It is a selective barrier that only allows certain substances, especially water molecules, to pass through while blocking others like salts or large molecules.

In the process of reverse osmosis, the semi-permeable membrane is responsible for separating freshwater from seawater. It allows water to flow from the concentrated saltwater side to the freshwater side when sufficient pressure is applied. This selective permeability is what makes reverse osmosis an effective method for desalination and purification.

• Essential for filtering impurities.
• Allows passage of water but not solutes.
• Crucial in controlling the flow of molecules.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. In reverse osmosis, it is an applied force necessary to overcome osmotic pressure and drive water against its natural concentration gradient.

For reverse osmosis to function, the hydrostatic pressure applied must exceed the osmotic pressure of the saltwater solution. This pressure difference is what allows the process to effectively separate pure water from dissolved salts and other solutes.

• Derived from the weight of the liquid column above a certain depth.
• Helps in pushing water molecules through the membrane.
• Must be higher than the osmotic pressure for effective desalination.

Using coastal bay water with lower salinity reduces the required hydrostatic pressure, making the process more energy-efficient and cost-effective.

Saltwater Desalination

Saltwater desalination involves removing minerals, primarily salts, from seawater to produce freshwater suitable for human consumption or irrigation. Reverse osmosis is the most common method used in modern desalination plants around the world.

This process is vital in regions with limited access to natural freshwater sources. It provides a sustainable solution to meet increasing water demands. By using reverse osmosis, desalination plants can convert seawater into potable water by:

• Using high-pressure pumps to apply the necessary hydrostatic pressure.
• Forcing saltwater through semi-permeable membranes.
• Collecting freshwater on the opposite side as the membranes filter out salts and impurities.

Using diluted seawater reduces energy costs, as lower osmotic pressure is easier to overcome, highlighting the advantages of blending freshwater sources for desalination.