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 41.0 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 43.0 L of fresh water at 20 °C with an applied pressure of 41.0 bar.
Isn't this just pi = iMRT and you solve for M?
What about the second part? plz and thank you
To find the final concentration of the seawater at 20 °C when reverse osmosis stops, you'll need to use the Van't Hoff equation:
Π = i * M * R * T
Where:
Π is the osmotic pressure,
i is the van't Hoff factor (the number of particles the solute breaks into when it dissolves),
M is the molarity,
R is the ideal gas constant (0.0821 L*atm/mol*K), and
T is the temperature in Kelvin.
Since the seawater concentration is given in total ion concentration (colligative molarity), the van't Hoff factor (i) is equal to 2 for seawater because it contains various ions.
Given:
Applied pressure (P) = 41.0 bar
Temperature (T) = 20 °C = 20 + 273.15 = 293.15 K
Molarity (M) = 1.10 Mc (colligative molarity)
Van't Hoff factor (i) = 2 (for seawater)
Using the Van't Hoff equation, we can rearrange it to solve for M:
M = Π / (i * R * T)
Now substituting the given values:
M = (41.0 bar) / (2 * 0.0821 L*atm/mol*K * 293.15 K)
Simplifying the equation gives:
M = 0.6973 Mc
Therefore, the final concentration of the seawater when reverse osmosis stops is approximately 0.6973 Mc.
To calculate the number of liters of seawater needed to produce 43.0 L of fresh water, we can use the formula:
Liters of seawater = (Liters of fresh water) / (1 - (Molarity of fresh water / Molarity of seawater))
Given:
Liters of fresh water = 43.0 L
Molarity of fresh water = 0 Mc (since fresh water has negligible concentration)
Substituting the values:
Liters of seawater = 43.0 L / (1 - (0 Mc / 1.10 Mc))
Simplifying the equation gives:
Liters of seawater = 43.0 L / (1 - 0)
Liters of seawater = 43.0 L
Therefore, to produce 43.0 L of fresh water at 20 °C with an applied pressure of 41.0 bar, you would need 43.0 L of seawater.