Which of the following solvents is having its lowest Ebullioscopic constant?

Diethyl Ether

The correct answer is Option (2) → Diethyl Ether.

Let us explore the concept of ebullioscopic constant (\(K_b\)) and its relationship with the boiling point of solvents in more detail, as well as explain why Diethyl ether has the lowest ebullioscopic constant.

The ebullioscopic constant (\(K_b\)) is a property that defines how much the boiling point of a solvent will increase (elevate) when a non-volatile solute is dissolved in it. The equation that relates the boiling point elevation to the ebullioscopic constant is

\(\Delta T_b = K_b m\)

Where:

\( \Delta T_b \) is the boiling point elevation (the increase in boiling point),

\( K_b \) is the ebullioscopic constant (expressed in K·kg/mol),

\( m \) is the molality of the solute (moles of solute per kilogram of solvent).

Key Point: A higher \(K_b\) value means the solvent will experience a greater increase in its boiling point for the same concentration of solute, while a lower \(K_b\) value means a smaller increase in boiling point.

Factors Affecting Ebullioscopic Constant:

The ebullioscopic constant is influenced by the boiling point and properties of the solvent, such as:

The amount of energy required to convert the liquid into vapor (i.e., the heat of vaporization).

The nature of intermolecular forces within the solvent (such as hydrogen bonding, van der Waals forces, etc.).

In general, solvents with lower boiling points tend to have lower ebullioscopic constants. This is because the lower the boiling point of the solvent, the easier it is to bring it to the boiling state, and consequently, the elevation in boiling point will be smaller when a solute is added.

Boiling Points of the Solvents:

Chloroform: 334.4 K

Diethyl Ether: 307.8 K

Benzene: 353.3 K

Carbon disulfide: 319.4 K

Reasoning Based on Boiling Points:

Diethyl Ether has the lowest boiling point of 307.8 K among the given solvents. Since it takes less energy to boil diethyl ether compared to the other solvents, it will also experience the smallest increase in boiling point when a solute is added.

Thus, Diethyl ether is expected to have the lowest ebullioscopic constant because its boiling point is the easiest to elevate.

Benzene, with the highest boiling point (353.3 K), will have a higher \(K_b\), as it takes more energy to boil it and thus the boiling point elevation is more pronounced.

Chloroform and Carbon disulfide have intermediate boiling points (334.4 K and 319.4 K, respectively), and their \(K_b\) values will be higher than diethyl ether but lower than benzene.

Relationship Between Boiling Point and \(K_b\):

In many cases, solvents with lower boiling points have lower \(K_b\) values because:

Less energy is required to vaporize the solvent at lower temperatures.

Weaker intermolecular forces in lower boiling point solvents lead to smaller changes in vapor pressure when solutes are added.

Since Diethyl Ether has the lowest boiling point (307.8 K), it is expected to have the smallest ebullioscopic constant, meaning that adding a solute will cause a relatively small elevation in its boiling point.

Conclusion:

Among the given solvents, Diethyl ether has the lowest boiling point and is therefore expected to have the lowest ebullioscopic constant.

The solvent with the lowest ebullioscopic constant is Diethyl ether