SOMEONE PLEASE HELP AND CONFIRM THE RIGHT ANSWER FOR ME...I HAVE ONE MORE ATTEMPT TO THIS PROBLEM AND I NEED HELP!!!!! PLEASE!!!!!!!!!!!!!!!!!!!! THANKS!
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 solve these problems, we need to use the formula for osmotic pressure:
π = MRT
Where:
π is the osmotic pressure
M is the molarity of the solution
R is the ideal gas constant
T is the temperature in Kelvin
Let's start with the first problem:
In reverse osmosis, water flows out of a salt solution until the osmotic pressure of the solution equals the applied pressure. Therefore, the osmotic pressure (π) equals the applied pressure of 47.0 bar.
We need to find the final concentration of the seawater (Mc) when reverse osmosis stops at 20 °C.
To find the concentration, we rearrange the formula:
Mc = π / (RT)
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20 + 273.15
T(K) = 293.15 K
Next, we need to convert the pressure from bar to Pascal:
1 bar = 100,000 Pascal
Therefore, the pressure is:
P(Pa) = 47.0 × 100,000
P(Pa) = 4,700,000 Pa
Now let's calculate the concentration:
Mc = 4,700,000 / (R * 293.15K)
The ideal gas constant, R, is 8.314 J/(mol·K).
Mc = 4,700,000 / (8.314 * 293.15)
Calculating this will give you the final concentration of the seawater (Mc).
Now let's move on to the second problem:
We are given that the total ion concentration (colligative molarity) of seawater is 1.10 Mc. We want to 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.
To solve this, we can use the equation:
L = (π × V) / (Mc × R × T)
Where:
L is the amount of seawater needed
π is the osmotic pressure (47.0 bar)
V is the volume of fresh water (64.8 L)
Mc is the concentration of seawater (1.10 Mc)
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin (293.15 K)
Now you can plug in the values and solve for L.