Colligative Properties
The freezing point of distilled water was determined by recording a thermogram: -0.176 degrees Celsius. The freezing point of a 0.200 m (molality) solution containing an unknown, ionic compound was determined by recording a second thermogram: -.904 degrees Celsius.
a. Determine the freezing point depression, (delta)Tf, for the ionic solution.
b. Determine effective molality (m_effective) for the ionic solution.
c. Determine the van't Hoff factor, i, for the ionic compound.
a. freezing pt depression: -.904+.176
b. freezing pt depression=effectivem*(-.52)
solvefor effective m
c. i*.200=effective molality
How did you get -.52?
a. To find the freezing point depression (ΔTf) for the ionic solution, subtract the freezing point of the 0.200 m solution from the freezing point of distilled water:
ΔTf = freezing point of distilled water - freezing point of 0.200 m solution
ΔTf = -0.904°C - (-0.176°C)
ΔTf = -0.904°C + 0.176°C
ΔTf = -0.728°C
The freezing point depression for the ionic solution is -0.728 degrees Celsius.
b. To determine the effective molality (m_effective) for the ionic solution, use the formula:
ΔTf = (i * Kf * m_effective)
where ΔTf is the freezing point depression, i is the van't Hoff factor, Kf is the cryoscopic constant, and m_effective is the effective molality.
Rearranging the equation:
m_effective = (ΔTf / (i * Kf))
Substituting the known values:
m_effective = (-0.728°C / (i * Kf))
Since the values for i and Kf are not provided, you would need those values to solve for m_effective.
c. The van't Hoff factor (i) represents the number of particles into which the compound dissociates in solution. It can be calculated using the formula:
i = (ΔTf experimental / ΔTf theoretical)
Given that ΔTf experimental is the freezing point depression of the 0.200 m solution (-0.728°C from part a), and ΔTf theoretical is the freezing point depression expected for a 0.200 m non-ionic solute, you would calculate the van't Hoff factor with those values. If the compound is known to be ionic, you would compare the experimental freezing point depression to the theoretical freezing point depression for a non-ionic compound (expected to be greater than the experimental value if ionization occurs).
However, the value for ΔTf theoretical is not provided in the given information, so you would need that value to calculate the van't Hoff factor (i).
To answer these questions, we need to understand colligative properties and how they relate to the freezing point depression, effective molality, and the van't Hoff factor.
a. The freezing point depression, (delta)Tf, can be calculated using the equation:
(delta)Tf = Tf (pure solvent) - Tf (solution)
Given that the freezing point of distilled water is -0.176 degrees Celsius and the freezing point of the solution is -0.904 degrees Celsius, we can calculate (delta)Tf as follows:
(delta)Tf = -0.904 - (-0.176)
(delta)Tf = -0.904 + 0.176
(delta)Tf = -0.728 degrees Celsius
Therefore, the freezing point depression, (delta)Tf, for the ionic solution is -0.728 degrees Celsius.
b. The effective molality (m_effective) of a solution takes into account the dissociation of ionic compounds. It is calculated using the equation:
m_effective = m_actual × i
where m_actual is the actual molality of the solute and i is the van't Hoff factor.
Since we are given the molality of the solution as 0.200 m (molality), we can use this value. To calculate the effective molality, we need to determine the van't Hoff factor first.
c. The van't Hoff factor, i, quantifies the degree of dissociation of an ionic compound in a solution. It can be determined using the equation:
i = (delta)Tf (experimentally) / (delta)Tf (theoretical)
Theoretical (delta)Tf can be calculated using the equation:
(delta)Tf (theoretical) = Kf × i × m_actual
where Kf is the cryoscopic constant, which depends on the specific solvent.
Since we do not have the cryoscopic constant or the actual molality of the solution yet, we cannot determine the van't Hoff factor directly. We need more information to proceed with part c.
In summary:
a. The freezing point depression, (delta)Tf, for the ionic solution is -0.728 degrees Celsius.
b. We need to determine the van't Hoff factor before calculating the effective molality, m_effective.
c. We need more information, such as the cryoscopic constant and the actual molality of the solution, to determine the van't Hoff factor.