calculate the freezing and boiling points of each of the following solutions.
(a) 0.50 m glucose in ethanol
for the freezing point i got 58 but it said i have the wrong sign...?
To calculate the freezing point of a solution, we can use the formula:
∆Tf = i * Kf * m
Where:
∆Tf is the change in freezing point
i is the van't Hoff factor (which depends on the number of particles)
Kf is the cryoscopic constant (molality depression constant) of the solvent
m is the molality of the solution (moles of solute per kg of solvent)
For glucose in ethanol solution, the van't Hoff factor, i, can be assumed to be 1 because glucose does not dissociate in ethanol. The molality, m, is given as 0.50 m.
To find the freezing point, we need to know the cryoscopic constant, Kf, for ethanol. The Kf value for ethanol is 1.99 °C/m.
∆Tf = (1)(1.99 °C/m)(0.50 m)
∆Tf = 0.99 °C
To determine the freezing point, subtract ∆Tf from the freezing point of the pure solvent.
If the freezing point of pure ethanol is -114 °C, the freezing point of the solution would be:
Freezing point = -114 °C - 0.99 °C
Freezing point = -115 °C
So the freezing point of the 0.50 m glucose in ethanol solution is -115 °C.
If you obtained a positive value for the freezing point change (∆Tf), it means you made an error in the calculation or used incorrect units. Double-check your calculation steps and ensure that all units are consistent.
To calculate the freezing and boiling points of a solution, we need to use the formula known as the Van't Hoff factor. The Van't Hoff factor (i) takes into account how many particles the solute will dissociate into when it is dissolved in the solvent.
For glucose in ethanol, glucose does not dissociate or ionize in solution, so the Van't Hoff factor (i) for glucose is 1. However, ethanol also does not dissociate or ionize in solution, so the Van't Hoff factor (i) for ethanol is also 1.
The freezing point depression (ΔTf) can be calculated using the formula:
ΔTf = i * Kf * m
Where:
ΔTf is the freezing point depression
i is the Van't Hoff factor
Kf is the cryoscopic constant, specific for the solvent
m is the molality of the solution (moles of solute per kilograms of solvent)
The boiling point elevation (ΔTb) can be calculated using the formula:
ΔTb = i * Kb * m
Where:
ΔTb is the boiling point elevation
i is the Van't Hoff factor
Kb is the ebullioscopic constant, specific for the solvent
m is the molality of the solution (moles of solute per kilograms of solvent)
To find the correct sign for the freezing point depression, keep in mind that the freezing point will be lower than the pure solvent's freezing point. You may need to calculate the absolute value of the result, as some calculators and resources may give you the absolute value.
Without the specific values for the cryoscopic constant (Kf) and the molality of the solution (m), we cannot provide you with the exact value of the freezing point depression (ΔTf). However, if you input the correct values into the formula and consider the correct sign, you should be able to obtain the correct answer.
Remember to double-check your calculations and ensure you have used the correct units.