Consider the below three solvents and the corresponding values of Kf for each. Prove, using the formula for Kf, which one of these solvents would allow for the most sensitive procedure for determining the molar mass by the freezing point depression method. Explain well to receive any credit at all. [NOTE: An appropriate definition of “sensitivity” might be “giving the biggest detection signal (in this case, temperature change) for a small amount (molality) of unknown present.”]
Solvent Kf (oC·kg/mol)
water 1.86
benzene 4.90
cyclohexane 20.00
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To determine which solvent allows for the most sensitive procedure for determining molar mass using the freezing point depression method, we need to calculate the value of Kf for each solvent.
The formula for freezing point depression (ΔTf) is given by:
ΔTf = Kf * m
Where:
ΔTf is the change in freezing point
Kf is the cryoscopic constant for the solvent
m is the molality of the solute (the unknown substance)
For a given molality, a larger value of ΔTf indicates a greater decrease in the freezing point, which leads to a more significant temperature change or detection signal.
Let's calculate the values of ΔTf using the respective Kf values:
For water:
ΔTf(water) = (1.86) * m
For benzene:
ΔTf(benzene) = (4.90) * m
For cyclohexane:
ΔTf(cyclohexane) = (20.00) * m
Comparing the three solvents, we can see that the value of ΔTf increases with the Kf value. Therefore, the solvent with the largest Kf value, cyclohexane (Kf = 20.00), would allow for the most sensitive procedure in determining the molar mass by the freezing point depression method.
In other words, cyclohexane would provide the biggest detection signal (temperature change) for a small amount (molality) of the unknown substance, making it the most suitable solvent for this method.