Question

Which of the following solvent has highest value of molal elevation constant \( K_b \)?

• A. Cyclohexane
• B. Carbon disulphide
• C. Carbon tetrachloride
• D. Acetic acid
• E. Chloroform

Hint:

Lower molar mass $\Rightarrow$ higher colligative constant.

Answer 1

The Correct Option is C

Step 1: Understanding the Molal Elevation Constant (K\(_b\)):
The molal elevation constant, or ebullioscopic constant (K\(_b\)), is a property of a particular solvent. It relates the molality of a solution to the elevation of its boiling point. It is defined as the increase in boiling point for a 1 molal solution of a non-volatile solute.
Step 2: Key Formula or Approach:
The formula for K\(_b\) is derived from thermodynamics:
\[ K_b = \frac{R T_b^2 M}{1000 \cdot \Delta_{vap}H} \] where:
\(R\) is the ideal gas constant.
\(T_b\) is the boiling point of the pure solvent in Kelvin.
\(M\) is the molar mass of the solvent in g/mol.
\(\Delta_{vap}H\) is the enthalpy of vaporization of the solvent in J/g.
A high K\(_b\) value is favored by a high boiling point (\(T_b\)), high molar mass (\(M\)), and a low enthalpy of vaporization (\(\Delta_{vap}H\)).
Step 3: Comparing K\(_b\) Values:
This is a fact-based question. We need to compare the known K\(_b\) values for the given solvents (units are K kg mol\(^{-1}\)):
(A) Cyclohexane: K\(_b\) = 2.79
(B) Carbon disulphide: K\(_b\) = 2.37
(C) Carbon tetrachloride: K\(_b\) = 5.02
(D) Acetic acid: K\(_b\) = 3.07
(E) Chloroform: K\(_b\) = 3.63
Comparing these values, carbon tetrachloride has the highest molal elevation constant. This makes it a sensitive solvent for determining molar masses using boiling point elevation, as a small concentration of solute will produce a relatively large, easily measurable change in temperature.
Step 4: Final Answer:
Among the given solvents, Carbon tetrachloride has the highest value of the molal elevation constant, K\(_b\).