Assuming that sea water is a 3.5 wt% solution of NaCl in water, calculate its osmotic pressure at 20 deg C. The density of a 3.5% naCl solution at 20 deg C is 1.023 g/mL.
How do I go about solving this?
pi = MRT where pi is the osmotic pressure, M is the molarity, R = 0.08205 and T is in Kelvin. Use the density to calculate molarity.
To solve this problem, we need to use the concept of osmotic pressure and the properties of the given solution. Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is related to the concentration of solute particles in the solution.
First, let's calculate the molarity of the NaCl solution:
1. Convert the weight percent (wt%) to mass of NaCl:
3.5 wt% = 3.5 grams of NaCl per 100 grams of solution
2. Determine the mass of water present in the solution:
Mass of water = Total mass of solution - Mass of NaCl
= 100 g - 3.5 g = 96.5 g
3. Calculate the molarity of NaCl:
Molarity (M) = Moles of solute / Volume of solution (in liters)
To convert the mass of NaCl to moles, we need to divide it by the molar mass of NaCl (58.44 g/mol):
Moles of NaCl = Mass of NaCl / Molar mass of NaCl
= 3.5 g / 58.44 g/mol = 0.060 moles
The volume of the solution can be calculated using the density:
Volume of solution = Mass of solution / Density
= 100 g / 1.023 g/mL = 97.78 mL = 0.09778 L
Therefore, the molarity of the NaCl solution is:
Molarity = Moles of NaCl / Volume of solution
= 0.060 moles / 0.09778 L = 0.613 M
Now, let's calculate the osmotic pressure using the formula:
Osmotic pressure = Molarity * Gas constant * Temperature in Kelvin
The gas constant (R) is 0.0821 L·atm/(mol·K), and the temperature in Kelvin can be calculated by adding 273.15 to the temperature in Celsius.
Temperature in Kelvin = 20°C + 273.15 = 293.15 K
Now, substitute the values into the equation:
Osmotic pressure = 0.613 M * 0.0821 L·atm/(mol·K) * 293.15 K
Finally, calculate the osmotic pressure:
Osmotic pressure = 14.73 atm
Therefore, the osmotic pressure of the 3.5 wt% NaCl solution at 20°C is 14.73 atm.