I need help solving this question, I have no idea what I'm supposed to do.
What is the minimum pressure in kPa that must be applied at 25 °C to obtain pure water by reverse osmosis from water that is 0.165 M in sodium chloride and 0.029 M in magnesium sulfate? Assume complete dissociation for electrolytes.
I know that the equation for osmosis is
pi= MRT, but how am I supposed to find pressure from that. do I use the r value of 0.018 because it's units include that of atm? Or do I solve for r?
Please help!
VonHOffpressure=iMRT
i is von hoff constant (number ions per particle)
M is molarity
R is universal gas constant
T is temperature in Kelvins
for NaCl, i=2; for MgSO4, i=2
figure the pressure for each, then add
R is 0.08205746(14) L atm K−1 mol−1
To solve this question, we need to understand the principles of reverse osmosis and how to calculate the minimum pressure required to obtain pure water.
First, let's clarify the equation you mentioned, π = MRT. This equation is known as the Van 't Hoff equation and relates the osmotic pressure (π) of a solution to its molarity (M), the ideal gas constant (R), and the absolute temperature (T). It is commonly used in osmotic pressure calculations.
However, in this specific question, we are dealing with reverse osmosis. Reverse osmosis is a process used to separate solutes from a solvent by applying pressure to overcome the natural flow of solvent through a semipermeable membrane.
To find the minimum pressure required for reverse osmosis, we need to consider the solute concentrations and their effect on the vapor pressure of the solvent.
In this case, we have a solution containing sodium chloride (NaCl) and magnesium sulfate (MgSO4), both of which fully dissociate into ions when dissolved. The dissociation is assumed to be complete, meaning that both sodium chloride and magnesium sulfate break down into their respective ions: Na+ and Cl- for sodium chloride, and Mg2+ and SO42- for magnesium sulfate.
To calculate the minimum pressure required to obtain pure water through reverse osmosis, we need to determine the osmotic pressure due to the solutes in the solution. The osmotic pressure can be calculated using the following equation:
π = iMRT
Where:
π = osmotic pressure
i = Van 't Hoff factor (the number of particles produced per molecule of solute)
M = molarity of the solution
R = ideal gas constant (8.314 J/(mol·K))
T = absolute temperature (in Kelvin)
For sodium chloride (NaCl), the Van 't Hoff factor is 2 because it dissociates into two ions (Na+ and Cl-). For magnesium sulfate (MgSO4), the Van 't Hoff factor is 3 because it dissociates into three ions (Mg2+, SO42-, and SO42-).
Now, let's plug in the values given in the question:
M sodium chloride (NaCl) = 0.165 M
M magnesium sulfate (MgSO4) = 0.029 M
T = 25 °C = 298 K (since temperature must be in Kelvin)
We can calculate the osmotic pressure for each solute using the equation π = iMRT, and then sum them up to get the total osmotic pressure.
πNaCl = 2 * (0.165 M) * (8.314 J/(mol·K)) * (298 K)
πMgSO4 = 3 * (0.029 M) * (8.314 J/(mol·K)) * (298 K)
After obtaining the individual osmotic pressures, add them together to get the total osmotic pressure:
πtotal = πNaCl + πMgSO4
Now, we have the total osmotic pressure. But for reverse osmosis, we need the minimum applied pressure necessary to overcome this osmotic pressure.
Since the question asks for the minimum pressure in kPa, divide the total osmotic pressure by 1000 to convert it from pascals (Pa) to kilopascals (kPa).