Determine the freezing point of an aqueous solution containing 10.50 g of magnesium bromide in 200.0 g of water.?
To determine the freezing point of the solution, we need to use the concept of freezing point depression. The freezing point depression is the lowering of the freezing point of a solvent when a solute is added to it.
First, we need to determine the molality (moles of solute per kilogram of solvent) of the magnesium bromide solution.
Step 1: Calculate the moles of magnesium bromide (solute)
To find the moles of magnesium bromide, we need to know the molar mass of magnesium bromide (MgBr2), which consists of one magnesium atom (Mg) with a molar mass of 24.31 g/mol and two bromine atoms (Br) with a molar mass of 79.90 g/mol each.
Molar mass of MgBr2 = (24.31 g/mol) + 2 * (79.90 g/mol) = 24.31 g/mol + 159.80 g/mol = 184.11 g/mol
Now, we can calculate the number of moles of magnesium bromide using its mass and molar mass:
moles of MgBr2 = mass of MgBr2 / molar mass of MgBr2
moles of MgBr2 = 10.50 g / 184.11 g/mol
moles of MgBr2 ≈ 0.057 moles
Step 2: Calculate the mass of water (solvent)
Given that the mass of water is 200.0 g, we can convert it to kilograms:
mass of water (kg) = mass of water (g) / 1000
mass of water (kg) = 200.0 g / 1000
mass of water (kg) = 0.200 kg
Step 3: Calculate the molality of the solution
Molality (m) is given by:
molality (m) = moles of solute / mass of solvent (kg)
molality (m) = 0.057 moles / 0.200 kg
molality (m) ≈ 0.285 mol/kg
Step 4: Determine the freezing point depression constant (Kf)
For water, the freezing point depression constant is approximately 1.86 °C/m.
Step 5: Calculate the freezing point depression (∆Tf)
Freezing point depression (∆Tf) is given by:
∆Tf = Kf * molality
∆Tf = 1.86 °C/m * 0.285 mol/kg
∆Tf ≈ 0.5301 °C
Step 6: Calculate the freezing point of the solution
The freezing point of the pure solvent (water) is 0°C. Since the solution has a freezing point depression of 0.5301°C, the freezing point of the solution will be:
Freezing point of solution = Freezing point of solvent - ∆Tf
Freezing point of solution = 0°C - 0.5301°C
Freezing point of solution ≈ -0.5301°C
Therefore, the freezing point of the aqueous solution containing 10.50 g of magnesium bromide in 200.0 g of water is approximately -0.5301°C.