What is the freezing point in ∘C of a solution prepared by dissolving 6.60 g of MgCl2 in 110 g of water? The value of Kf for water is 1.86 (∘C⋅kg)/mol, and the van't Hoff factor for MgCl2 is i = 2.7.
To find the freezing point of the solution, we can use the equation:
ΔT = Kf * m * i
where
ΔT is the freezing point depression,
Kf is the freezing point depression constant (1.86 (∘C⋅kg)/mol for water),
m is the molality of the solute (MgCl2), and
i is the van't Hoff factor.
First, we need to calculate the molality (m) of the MgCl2 solution. Molality is defined as the number of moles of solute (in this case, MgCl2) per kilogram of solvent (in this case, water).
Step 1: Calculate the number of moles of MgCl2.
To do this, we divide the mass of MgCl2 (6.60 g) by its molar mass.
The molar mass of MgCl2 can be calculated as follows:
Mg (24.31 g/mol) + 2Cl (35.45 g/mol) = 95.21 g/mol
So, moles of MgCl2 = 6.60 g / 95.21 g/mol
Step 2: Calculate the molality (m).
Molality (m) = moles of solute (MgCl2) / mass of solvent (water in kg)
We need to convert the mass of water from grams to kilograms.
mass of water = 110 g / 1000 = 0.110 kg
Now, we can calculate the molality (m) as follows:
Molality (m) = moles of MgCl2 / mass of water
Step 3: Calculate the freezing point depression (ΔT).
ΔT = Kf * m * i
Now we can substitute the given values into the equation:
ΔT = 1.86 (∘C⋅kg)/mol * molality (m) * 2.7
Finally, we can calculate the freezing point by adding the freezing point depression to the freezing point of pure water.
Freezing point = Freezing point of pure water - ΔT
The freezing point of pure water is 0∘C. So, we substitute the values and calculate the freezing point.
delta T = i*Kf*molality
i = 2.7
k = 1.86
molality = mols/kg solution. mols = 6.60/molar mass MgCl2 and kg solvent = 0.110
Finally, 0-delta T = new freezing point.