A solution is made by dissolving 10.20 grams of glucose (C6H12O6) in 355 grams of water. What is the freezing point depression of the solvent if the freezing point constant is -1.86 °C/m?
delta T = Kf*m
Kf = 1.86
m = mols/kg solvent and mols = grams/molar mass. Substitute and solve for m.
Then substitute into dT = KfM and solve for dT. Post your work if you get stuck.
To calculate the freezing point depression of the solvent, we need to use the following formula:
ΔT = Kf * m
Where:
ΔT is the change in freezing point (in °C),
Kf is the freezing point constant (in °C/m), and
m is the molality of the solution (in mol/kg).
First, let's calculate the molality of the solution:
Step 1: Calculate the number of moles of glucose (C6H12O6)
To find the number of moles, we divide the given mass of glucose by its molar mass.
Molar mass of glucose (C6H12O6):
(6 * atomic mass of carbon) + (12 * atomic mass of hydrogen) + (6 * atomic mass of oxygen)
Carbon (C) has an atomic mass of 12.01 g/mol,
Hydrogen (H) has an atomic mass of 1.01 g/mol,
Oxygen (O) has an atomic mass of 16.00 g/mol.
Molar mass of glucose = (6 * 12.01) + (12 * 1.01) + (6 * 16.00)
Now, divide the given mass of glucose by its molar mass to find the number of moles.
Number of moles of glucose = mass of glucose / molar mass of glucose
Now, plug in the values to calculate the number of moles of glucose.
Number of moles of glucose = 10.20 g / molar mass of glucose
Step 2: Calculate the molality of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
To calculate molality, we divide the number of moles of glucose by the mass of the water in kilograms.
Mass of water = 355 g
Mass of water in kg = 355 g / 1000
Molality (m) = number of moles of glucose / mass of water in kg
Now, plug in the values to calculate the molality of the solution.
Molality (m) = number of moles of glucose / mass of water in kg
Now that we have the molality and freezing point constant, we can calculate the freezing point depression using the formula:
ΔT = Kf * m
Plug in the values to calculate the freezing point depression:
ΔT = -1.86 °C/m * molality (m)