When HClO2 is dissolved in water, it partially dissociates according to the equation
HClO2 → H+ + ClO2-. A solution is prepared that contains 5.850 g of HClO2 in 1.000 kg of water. Its freezing point is -0.3473oC. Calculate the fraction of HClO2 that has dissociated
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homework
To calculate the fraction of HClO2 that has dissociated, we need to use the formula for calculating the freezing point depression, which is given by the equation:
ΔT = Kf * m
Where:
ΔT is the freezing point depression,
Kf is the cryoscopic constant for the solvent (water), and
m is the molality of the solute (HClO2).
First, let's calculate the molality (m) of the HClO2.
Molality (m) is defined as the moles of solute (HClO2) divided by the mass of the solvent (water) in kilograms.
To calculate the molality, we need to find the number of moles of HClO2 and convert the mass of water from grams to kilograms.
The molar mass of HClO2 can be calculated as follows:
1 atom of Hydrogen (H) = 1g/mol
1 atom of Chlorine (Cl) = 35.5 g/mol
2 atoms of Oxygen (O) = 16 g/mol * 2 = 32 g/mol
Therefore, the molar mass of HClO2 = 1 + 35.5 + 32 = 68.5 g/mol.
Next, we can calculate the number of moles of HClO2 by dividing the mass of HClO2 by its molar mass:
moles of HClO2 = mass of HClO2 / molar mass of HClO2
moles of HClO2 = 5.850 g / 68.5 g/mol
Now, let's convert the mass of water from grams to kilograms:
mass of water = 1.000 kg = 1000 g
Now we can calculate the molality:
m = moles of HClO2 / mass of water in kg
m = (5.850 g / 68.5 g/mol) / 1.000 kg
After calculating the molality (m), we can use the cryoscopic constant for water to calculate the change in freezing point (ΔT).
The cryoscopic constant for water (Kf) is 1.86 °C/m.
ΔT = Kf * m
ΔT = 1.86 °C/m * (5.850 g / 68.5 g/mol) / 1.000 kg
The resulting ΔT value represents the freezing point depression. In this case, we know that the freezing point is -0.3473 °C, so we need to find the difference between the freezing point (0 °C) and the depression (-0.3473 °C):
Freezing point depression = 0 °C - (-0.3473 °C) = 0.3473 °C
Finally, we can determine the fraction of HClO2 that has dissociated by dividing the freezing point depression by the cryoscopic constant:
Fraction of HClO2 dissociated = Freezing point depression / Kf
Fraction of HClO2 dissociated = 0.3473 °C / 1.86 °C/m
Calculating this division will give us the fraction of HClO2 that has dissociated.