Question

A water desalination plant is set up near a salt marsh containing water that is 0.10\(M \mathrm{NaCl}\) . Calculate the minimum pressure that must be applied at \(20 .^{\circ} \mathrm{C}\) to purify the water by reverse osmosis. Assume NaCl is completely dissociated.

Short answer

The minimum pressure that must be applied at 20°C to purify the water by reverse osmosis is approximately 2.395 atm.

Step-by-step solution

Convert temperature to Kelvin

First, we need to convert the given temperature from Celsius to Kelvin. The conversion formula is: \[K = °C + 273.15\] Given the temperature in Celsius, 20°C, we can calculate the temperature in Kelvin: \[K = 20 + 273.15 = 293.15\]

Calculate the osmotic pressure

Now, using the formula for osmotic pressure (\(π = CRT\)), we can calculate the osmotic pressure required to purify the water: - \(C = 0.10 \: M\) - \(R = 0.0821 \: \frac{L \cdot atm}{mol \cdot K} \) - \(T = 293.15 \: K\) \[π = (0.10 \: M)(0.0821 \: \frac{L \cdot atm}{mol \cdot K})(293.15 \: K)\]

Calculate the minimum pressure

Now, we just need to perform the multiplication: \[π = 2.395 \: atm\] The minimum pressure that must be applied at 20°C to purify the water by reverse osmosis is approximately 2.395 atm.

Key concepts

Water Desalination

Water desalination is the process of removing salt and other minerals from seawater or saline water to produce fresh water. This procedure is crucial in areas where fresh water is scarce or in high demand. The most common method used for desalination is reverse osmosis.

• Reverse osmosis uses a special membrane that allows water molecules to pass through while blocking salt and other impurities.
• The result is potable water on one side of the membrane and a concentrated brine solution on the other.

By implementing water desalination, we can provide clean drinking water and support agricultural and industrial activities.

Osmotic Pressure

Osmotic pressure is a key concept in understanding reverse osmosis. It refers to the force required to prevent the flow of water through a semipermeable membrane. This natural phenomenon occurs when two solutions of different concentrations are separated by the membrane.

• The solvent, typically water, naturally moves from the side with lower solute concentration (like salt) to the one with a higher concentration.
• Applying external pressure greater than the osmotic pressure can reverse the flow, allowing for water desalination.

In reverse osmosis, calculating this pressure helps determine the minimum force needed to produce fresh water from salty water.

Chemical Solutions

Chemical solutions play an essential role in reverse osmosis and other chemical processes. A chemical solution consists of a solute dissolved in a solvent.

• In our case, salt (NaCl) is the solute, and water is the solvent.
• The concentration of the solution is crucial when calculating properties like osmotic pressure.

Understanding the behavior of solutions, including their interactions and reactions, is vital to tackling challenges like water desalination. It is also important in preparing solutions to meet specific requirements for industrial and domestic purposes.

Dissociation of NaCl

The dissociation of NaCl, or sodium chloride, is a fundamental process when discussing chemical solutions. When NaCl dissolves in water, it separates into its constituent ions: sodium (\(\text{Na}^+\)) and chloride (\(\text{Cl}^-\)).

• This dissociation is complete, meaning that all \(\text{NaCl}\) molecules split into ions when dissolved in water.
• As a result, the solution conducts electricity and contributes to osmotic pressure.

In processes like reverse osmosis, understanding ion dissociation helps in calculating the osmotic pressure effectively, ensuring the proper amount of pressure is applied to purify the water.