Lake Vida is an enormous hypersaline lake that lies under 19 m of ice in the Dry Valleys region of Antartica. The freezing point of the water is approximately -17 C owing to the fact that it is many times as salty as typical saltwater (assume all of the salt is NaCl). Calculate the osmotic pressure of this solution just at the freezing point. (the density of this hypersaline brine is 1.11g/mL)
To calculate the osmotic pressure of a solution, you need to know the concentration of the solute particles in the solution. In this case, the solute is NaCl, and we can assume all the salt in the solution is NaCl.
To determine the concentration of NaCl, we can use the density of the hypersaline brine. The density is given as 1.11 g/mL, which means 1.11 grams of solution occupy a volume of 1 mL.
Since we know the concentration of the solution, we can now calculate the concentration of NaCl in moles per liter (mol/L).
First, we need to calculate the molar mass of NaCl:
Na has an atomic mass of 22.99 g/mol, and Cl has an atomic mass of 35.45 g/mol.
So, the molar mass of NaCl = 22.99 + 35.45 = 58.44 g/mol.
Now, let's calculate the moles of NaCl in one liter of the solution:
Since the density is given as 1.11 g/mL, the mass of 1 liter (1000 mL) of the solution is:
1.11 g/mL * 1000 mL = 1110 g.
To calculate the moles of NaCl, we divide the mass by the molar mass:
moles of NaCl = 1110 g / 58.44 g/mol = 19.02 mol.
Now that we know the concentration of NaCl in moles per liter (19.02 mol/L), we can calculate the osmotic pressure using the formula:
osmotic pressure (π) = i * M * R * T
Where:
i = van't Hoff factor (the number of particles the solute dissociates into)
M = concentration of the solute (NaCl) in mol/L
R = gas constant (0.0821 L atm/(K mol))
T = temperature in Kelvin
In this case, since NaCl is a strong electrolyte, it dissociates into two particles, so i = 2.
The freezing point of the water is -17 °C, which needs to be converted to Kelvin:
T = -17 + 273.15 = 256.15 K
Now we can substitute the values into the formula:
osmotic pressure (π) = 2 * 19.02 mol/L * 0.0821 L atm/(K mol) * 256.15 K
Calculating this expression will give you the osmotic pressure of the solution just at the freezing point.