Question

In reverse osmosis, water flows out of a salt solution until the osmotic pressure of the solution equals the applied pressure. Assume seawater has a colligative molarity of 1.10 M, and you want to use reverse osmosis to produce freshwater from the seawater. Calculate the volume of seawater (in liters) required to produce 21.0 liters of freshwater when a pressure of 65 atm is applied to the seawater at 25 °C. The ideal gas constant is 0.08206 L･atm/mol･K.

Answer 1

To produce 21.0 liters of freshwater through reverse osmosis, you would need approximately 31.69 liters of seawater.

To calculate the volume of seawater required to produce freshwater through reverse osmosis, we need to use the ideal gas law equation. The equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin by adding 273.15: 25°C + 273.15 = 298.15 K.

Next, we need to calculate the number of moles of salt in 21.0 liters of freshwater. Since seawater has a colligative molarity of 1.10 M, which means there are 1.10 moles of salt per liter, we can multiply the molarity by the volume: 1.10 M x 21.0 L = 23.10 moles.

Now we can rearrange the ideal gas law equation to solve for the volume of seawater:

V = (nRT) / P = (23.10 mol x 0.08206 L･atm/mol･K x 298.15 K) / (65 atm) = 31.69 liters