Assuming that the osmotic pressure of a sample of sea water at 10 C is 25.5 atm, calculate the work required under reversible conditions at this constant temperature to prepare 9 litre of pure water from this sea water. (Take the available volume of sea water as infinite and therefore unchanging in composition as 9 litre of pure water is extracted). Express your answer in Joules.

To calculate the work required to prepare 9 liters of pure water from the given sea water sample, we need to understand the concept of osmotic pressure and apply the formula for the work done in reversible processes.

Osmotic pressure is the pressure required to stop the flow of solvent molecules across a semipermeable membrane due to the difference in solute concentration on either side.

The formula for calculating the work done under reversible conditions is W = -PΔV, where W is the work done, P is the osmotic pressure, and ΔV is the change in volume.

In this case, we want to extract 9 liters of pure water from the sea water sample. Since the available volume of sea water is assumed to be infinite and unchanging, we can consider this extraction as the reduction in the volume of the sea water.

ΔV = -9 liters

Given:
Osmotic pressure (P) = 25.5 atm

Now we can substitute the values into the formula:

W = -PΔV

W = -25.5 atm * (-9 liters)

To calculate the work in Joules, we need to convert the units. 1 atm = 101325 Pa and 1 liter = 0.001 m^3.

W = -25.5 atm * (-9 liters) * (101325 Pa / 1 atm) * (0.001 m^3 / 1 liter)

W = 25.5 * 9 * 101325 * 0.001 Joules

W = 230,980.775 Joules

Therefore, the work required under reversible conditions to prepare 9 liters of pure water from the given sea water sample at 10°C is approximately 230,980.775 Joules.