What would the final freezing point of water be if 3 mol of sugar were added to 1 kg of water (Kf = 1.86C/(mol/kg) for water and i = 1 for sugar)?
-5.58
molality = mols sugar/kg solvent
Solve for molality
delta T = Kf*m
Solve for delta T and subtract from zero C to find the new freezing point.
To find the final freezing point of water after adding 3 mol of sugar to 1 kg of water, we need to calculate the change in freezing point caused by the presence of the sugar.
The equation to calculate the change in freezing point (ΔTf) is given by the equation:
ΔTf = Kf * m * i
Where:
ΔTf is the change in freezing point
Kf is the cryoscopic constant for water, which is 1.86 °C/(mol/kg)
m is the molality of the solute in kg of solvent
i is the van't Hoff factor
In this case, the molality (m) can be calculated by dividing the number of moles of sugar (3 mol) by the mass of water (1 kg).
m = moles of solute / mass of solvent
m = 3 mol / 1 kg
m = 3 mol/kg
Since sugar is a non-electrolyte, the van't Hoff factor (i) is 1.
Now, let's calculate the change in freezing point (ΔTf):
ΔTf = 1.86 °C/(mol/kg) * 3 mol/kg * 1
ΔTf = 5.58 °C
Therefore, the final freezing point of water after adding 3 mol of sugar would be 5.58 °C below its normal freezing point.
To calculate the final freezing point of water when sugar is added, we need to use the formula for freezing point depression.
Freezing point depression (ΔTf) is given by the equation:
ΔTf = Kf * m * i
Where:
ΔTf = freezing point depression
Kf = freezing point depression constant for the solvent (in this case, water)
m = molality of the solute (sugar)
i = van 't Hoff factor (the number of particles formed when the solute dissolves)
In this case, 3 mol of sugar is added to 1 kg of water. To find the molality of the solution, we divide the moles of solute (sugar) by the mass of the solvent (water).
Molality (m) = moles of solute / mass of solvent
Mass of solvent = 1 kg = 1000 g
Molality (m) = 3 mol / 1000 g = 0.003 mol/g
Since we are given that i = 1 for sugar (meaning it dissociates into one particle when it dissolves), we can substitute the values into the freezing point depression equation:
ΔTf = Kf * m * i
ΔTf = 1.86 C/(mol/kg) * 0.003 mol/g * 1
Calculating this gives us the freezing point depression (ΔTf). The final freezing point of water is the normal freezing point of water (0 degrees Celsius) minus the freezing point depression.
Final freezing point = 0 degrees Celsius - ΔTf
Substituting the value of ΔTf into the equation will give us the result.