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 47.0 bar is applied to seawater, what will be the final concentration of the seawater at 20 °C when reverse osmosis stops?
Mc=?
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 64.8 L of fresh water at 20 °C with an applied pressure of 47.0 bar.
L=?
To find the final concentration of seawater at 20 °C when reverse osmosis stops (Mc), we can use the formula:
Π = MRT
Where:
Π is the osmotic pressure
M is the molar concentration (Mc)
R is the ideal gas constant (0.0831 L·bar/(mol·K))
T is the temperature in Kelvin (20 °C = 293 K)
Given that the osmotic pressure (Π) equals the applied pressure (47.0 bar), we can rearrange the formula to solve for Mc:
Mc = Π / (RT)
Substituting the given values:
Mc = 47.0 bar / (0.0831 L·bar/(mol·K) * 293 K)
Mc ≈ 2.03 Mc
Therefore, the final concentration of seawater when reverse osmosis stops is approximately 2.03 Mc.
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To calculate the number of liters of seawater needed to produce 64.8 L of fresh water at 20 °C with an applied pressure of 47.0 bar, we can use the formula:
L = Vf / (1 - Vr / Vs)
Where:
L is the volume of seawater needed
Vf is the volume of fresh water desired (64.8 L)
Vr is the volume retention factor (which represents the percentage of water that is retained by the membrane during reverse osmosis, typically between 0 and 1)
Vs is the volume of seawater per liter (1 L)
Assuming a volume retention factor of 1 (meaning all water is retained), we can rearrange the formula to solve for L:
L = Vf / (1 - 1 / Vs)
Substituting the given values:
L = 64.8 L / (1 - 1 / 1 L)
L = 64.8 L / (1 - 1)
L = 64.8 L / 0
L is undefined
Therefore, the volume of seawater needed to produce 64.8 L of fresh water cannot be calculated with the given information because the volume retention factor (Vr) is required.
To find the final concentration of seawater (Mc) when reverse osmosis stops, we need to use the osmotic pressure formula:
Π = McRT
Where:
Π = osmotic pressure
Mc = concentration of the solution (in this case, seawater)
R = gas constant
T = temperature in Kelvin
Given:
Applied pressure (P) = 47.0 bar (1 bar = 10^5 Pascals)
Temperature (T) = 20 °C = 293 Kelvin (20 + 273)
To find Mc, we need to rearrange the formula:
Mc = Π / RT
Now let's plug in the values:
Mc = (47.0 bar * 10^5 Pa/bar) / (8.3145 J/(mol·K) * 293 K)
By calculating this expression, we can find the final concentration (Mc) of the seawater when reverse osmosis stops.
For the second part of the question, to calculate the volume of seawater (L) needed to produce a given volume (64.8 L) of fresh water, we'll use the equation:
L = Vf / (1 - Y)
Where:
L = volume of seawater needed
Vf = final volume of fresh water desired
Y = water recovery percentage (100% - salt rejection percentage)
In this case, it's not explicitly mentioned what the water recovery and salt rejection percentages are, so we will assume a water recovery rate of 50% and a salt rejection rate of 99%.
So, Y = 100% - 99% = 1%
L = 64.8 L / (1 - 0.01)
By calculating this expression, we can find the volume (L) of seawater needed to produce 64.8 L of fresh water.