Difference Between Ebullioscopic Constant and Cryoscopic Constant

The key difference between ebullioscopic constant and cryoscopic constant is that ebullioscopic constant is related to the boiling point elevation of a substance whereas cryoscopic constant is related to the freezing point depression of a substance.

Ebullioscopic constant and cryoscopic constant are terms used mainly in thermodynamics to describe the properties of a substance in relation to the changes in temperature. These two constants give the same value for a particular substance at similar conditions via different routes.

CONTENTS

1. Overview and Key Difference
2. What is Ebullioscopic Constant
3. What is Cryoscopic Constant
4. Side by Side Comparison – Ebullioscopic Constant vs Cryoscopic Constant in Tabular Form
5. Summary

What is Ebullioscopic Constant?

An ebullioscopic constant is a thermodynamic term that relates the molality of a substance to its boiling point elevation. We can denote ebullioscopic constant as Kb, boiling point elevation as ΔT and molality as “b”. The constant is given as the ratio between boiling point elevation and molality (boiling point elevation divided by molality equals ebullioscopic constant, Kb). We can give the mathematical expression for this constant as follows:

          ΔT = iK_bb

In this equation, “i” is the Van’t Hoff factor. It gives the number of particles the solute can split into or forms when the substance is dissolved in a solvent. “b” is the molality of the solution formed after this dissolution. In addition to this simple equation, we can use another mathematical expression to calculate the ebullioscopic constant theoretically:

          K_b = RT²_bM/ ΔH_vap

In this equation, R refers to the ideal (or universal) gas constant, Tb refers to the boiling point of the solvent, M refers to the molar mass of the solvent, and ΔH_vap refers to the molar enthalpy of vaporization. However, in the calculation of the molar mass of a substance, we can use a known value for this constant using a procedure called ebullioscopy. Ebullioscopy refers to the “boiling measurement” in Latin meaning.

Figure 01: Freezing Point Depression and Boiling Point Elevation in a Graph

The property of elevation of boiling point is considered as a colligative property where the property depends on the number of particles dissolved into the solvent and not the nature of those particles. Some known values for ebullioscopic constant include acetic acid having 3.08, benzene having 2.53, camphor having 5.95, and carbon disulfide having 2.34.

What is Cryoscopic Constant?

A cryoscopic constant is a thermodynamic term that relates the molality of a substance to the freezing point depression. Freezing point depression is also a colligative property of substances. The cryoscopic constant can be given as below:

          ΔT_f = iK_fb

Here, “i” is the Van’t Hoff factor, which is the number of particles the solute can split into or can form when dissolved in a solvent. Cryoscopy is the process we can use to determine the cryoscopic constant of a substance. We can use a known constant to calculate an unknown molar mass. The term cryoscopy comes from the Greek meaning, “freezing measurement”.

Since the freezing point depression is a colligative property, it depends only on the number of solute particles that are dissolved and not on the nature of those particles. Therefore, we can say that cryoscopy is related to ebullioscopy. The mathematical expression for this constant is as follows:

          K_b = RT²_fM/ ΔH_fus

Where R is the ideal gas constant, M is the molar mass of the solvent, T_f is the freezing point of the pure solvent and ΔH_fus is the molar enthalpy of fusion of the solvent.

What is the Difference Between Ebullioscopic Constant and Cryoscopic Constant?

Ebullioscopic constant and cryoscopic constant are terms used in thermodynamics. The key difference between ebullioscopic constant and cryoscopic constant is that ebullioscopic constant is related to the boiling point elevation of a substance whereas cryoscopic constant is related to the freezing point depression of a substance.

Below infographic summarizes the differences between ebullioscopic constant and cryoscopic constant.

Summary – Ebullioscopic Constant vs Cryoscopic Constant

The key difference between ebullioscopic constant and cryoscopic constant is that ebullioscopic constant is related to the boiling point elevation of a substance whereas cryoscopic constant is related to the freezing point depression of a substance.

Reference:

1. “Cryoscopic Constant.” Wikipedia, Wikimedia Foundation, 4 Feb. 2020, Available here.

Image Courtesy:

1. “Freezing point depression and boiling point elevation” – Modified Freezing_point_depression_and_boiling_point_elevation.png by Tomas er (CC BY-SA 3.0) via Commons Wikimedia

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