In reverse osmosis, water flows out of a salt solution until the osmotic pressure of the solution equals the applied pressure. If a pressure of 59.0 bar is applied to seawater, what will be the final concentration of the seawater at 20 °C when reverse osmosis stops?
Assuming that seawater has a total ion concentration (a.k.a colligative molarity) of 1.10 Mc, calculate how many liters of seawater are needed to produce 18.6 L of fresh water at 20 °C with an applied pressure of 59.0 bar.
To calculate the final concentration of the seawater when reverse osmosis stops, we need to use the van't Hoff equation. The van't Hoff equation relates the osmotic pressure to the concentration of the solute.
The van't Hoff equation is given as:
Π = i * c * R * T
Where:
Π is the osmotic pressure,
i is the van't Hoff factor (which depends on the number of particles in the solute),
c is the concentration of the solute (in mol/L),
R is the ideal gas constant (0.0831 L bar / mol K),
T is the temperature (in Kelvin).
In this case, the osmotic pressure is equal to the applied pressure of 59.0 bar. The temperature is 20 °C, which is 293 K. The total ion concentration (colligative molarity) of the seawater is 1.10 Mc.
Assuming seawater is a 1:1 electrolyte, the van't Hoff factor (i) is 2.
Now we can rearrange the van't Hoff equation to solve for the concentration of the solute:
c = Π / (i * R * T)
Substituting the given values:
c = 59.0 bar / (2 * 0.0831 L bar / mol K * 293 K)
c ≈ 1.00 mol/L
Therefore, the final concentration of the seawater when reverse osmosis stops is approximately 1.00 mol/L.
To calculate the number of liters of seawater needed to produce 18.6 L of fresh water, we can use the concept of mole ratio.
Since the molarity of the seawater is 1.10 Mc, this means that there are 1.10 moles of ions in 1 liter of seawater.
The equation for the mole ratio can be written as:
moles of ions / L of seawater = moles of fresh water / L of fresh water
Rearranging the equation:
L of seawater = (moles of fresh water / moles of ions) * L of fresh water
Substituting the given values:
L of seawater = (18.6 L / 1.10 moles) * 18.6 L
L of seawater ≈ 309.6 L
Therefore, approximately 309.6 liters of seawater are needed to produce 18.6 liters of fresh water at 20 °C with an applied pressure of 59.0 bar.