Glycerol is separated in soap industries by:

We recall a basic physical-chemistry fact: the normal boiling point of a liquid is the temperature at which its vapour pressure equals the external pressure. If we lower the external pressure, the temperature needed to reach that vapour pressure also lowers. This principle is used in “distillation under reduced pressure”, sometimes called “vacuum distillation”. The relation is expressed by the Clausius-Clapeyron equation, stated first:

$$\dfrac{d\ln P}{dT}= \dfrac{\Delta H_{\text{vap}}}{RT^{2}}$$

Here $$P$$ is the vapour pressure, $$T$$ is the absolute temperature, $$R$$ is the gas constant and $$\Delta H_{\text{vap}}$$ is the molar enthalpy of vaporisation. Although we are not required to integrate it fully for this problem, the equation tells us qualitatively that if we reduce $$P$$, then for a fixed $$\Delta H_{\text{vap}}$$, the corresponding equilibrium temperature $$T$$ must also decrease.

Now, let us apply this idea to glycerol, $$\mathrm{C_{3}H_{8}O_{3}}$$. Glycerol is a highly viscous, trihydric alcohol formed as a by-product in the saponification (soap-making) process:

$$\text{Fat or oil (ester)} + 3\,\text{NaOH} \;\longrightarrow\; \text{Soap (sodium salt of fatty acid)} + \text{Glycerol}$$

Important physical data: the normal (1 atm) boiling point of glycerol is about $$290^\circ\text{C}$$. At this high temperature glycerol tends to undergo partial decomposition, charring and colouration, which is undesirable for industrial recovery. Therefore we must choose a separation technique that enables evaporation at a lower temperature so that thermal decomposition does not occur.

We examine the four given options in turn.

Option A — Fractional distillation: This is effective when two liquids have different but reasonably low boiling points and do not decompose. Glycerol itself has a single high boiling point and decomposition risk, so mere fractional distillation at atmospheric pressure is not suitable.

Option B — Differential distillation: This is essentially batch distillation without a fractionating column, again performed at atmospheric pressure. The same problem of high temperature persists, hence it is also unsuitable.

Option C — Steam distillation: Steam distillation works nicely for volatile, water-immiscible substances whose boiling points are normally >100 °C but which form a heterogeneous azeotrope with water. Glycerol, however, is completely miscible with water and therefore does not distil over with steam; it stays in the aqueous layer. Consequently steam distillation cannot separate glycerol.

Option D — Distillation under reduced pressure: By purposefully lowering the external pressure, we lower the boiling temperature according to the relation we wrote earlier. For glycerol, reducing the pressure to about $$10^{2}$$-$$10^{3}$$ Pa (a few mm Hg) brings its boiling point down to roughly $$150^\circ\text{C}$$ or even lower, which is well below the temperature at which significant decomposition occurs. Industrial soap plants therefore connect the glycerol-containing liquor to a vacuum still, remove water first, and then distil pure glycerol safely under reduced pressure.

Thus, among the four techniques listed, only “distillation under reduced pressure” specifically addresses the high-boiling, decomposition-prone nature of glycerol.

Hence, the correct answer is Option D.