Question

The units of ebullioscopic constant is :

• A. K kg mol$^{-1}$
• B. mol kg K$^{-1}$
• C. kg mol$^{-1}$ K$^{-1}$
• D. K mol kg$^{-1}$

Hint:

Both ebullioscopic ($K_b$) and cryoscopic ($K_f$) constants have the same units: K kg mol$^{-1}$.

Answer 1

The Correct Option is A

The ebullioscopic constant ($K_b$) relates the elevation in boiling point ($\Delta T_b$) to the molality ($m$) of the solution: $\Delta T_b = K_b \cdot m$.
Rearranging for $K_b$, we get $K_b = \frac{\Delta T_b}{m}$.
The unit of temperature change ($\Delta T_b$) is Kelvin (K).
The unit of molality ($m$) is mol kg$^{-1}$.
Therefore, the unit of $K_b$ is $\frac{\text{K}}{\text{mol kg}^{-1}} = \text{K kg mol}^{-1}$.