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The cryoscopic constant is specific for a given solvent.
However, the cryoscopic constant is larger than the ebullioscopic constant and the freezing point is often easier to measure with precision, which means measurements using the freezing point depression are more precise.
If the solution is treated as an ideal solution, the extent of freezing point depression depends only on the solute concentration that can be estimated by a simple linear relationship with the cryoscopic constant: