Boiling Point Elevation and Dühring's Rule in Evaporator Design

Why Dissolved Solids Raise the Boiling Point

A non-volatile solute dissolved in water lowers the water's vapour pressure, because fewer solvent molecules sit at the surface ready to escape. To reach the same vapour pressure, and so to boil at the same pressure, the solution has to be hotter than pure water would be. The difference is the boiling point elevation, usually abbreviated BPE.

For dilute ideal solutions, BPE follows a simple colligative law, ΔT_b = K_b·m, with K_b = 0.512 K·kg/mol for water and m the molality of dissolved particles. That gives only fractions of a degree for most dilute solutions. Industrial evaporators, though, concentrate liquors to tens of percent solids, far beyond where the ideal law applies. A 50 wt% caustic soda solution at atmospheric pressure boils at roughly 140°C or more, around 40°C above pure water.

Dühring's Rule: A Straight Line From Sparse Data

Measuring the boiling point of every concentration at every pressure would be laborious. Dühring's rule, an empirical observation from the nineteenth century, removes most of that work. It states that if you plot a solution's boiling point against the boiling point of pure water at the same pressure, the result for a fixed concentration is very nearly a straight line.

So two measurements per concentration are enough to draw a Dühring line, and from it the boiling point at any other pressure can be read directly. In use, you look up the saturation temperature of water at the evaporator's operating pressure, go up to the line for the liquor concentration, and read across to the solution's actual boiling point. Handbooks publish families of Dühring lines for common liquors like caustic soda and salt solutions.

Where the Lost Temperature Goes

BPE matters because it reduces the temperature difference that drives heat transfer. Heating steam condenses at its own saturation temperature, but the liquor on the other side now boils hotter than pure water would at that pressure. The useful driving force is the steam temperature minus the solution boiling point, not minus the water saturation temperature, and using the wrong one overstates ΔT and undersizes the heating surface.

In a multiple-effect train the loss compounds. The vapour leaving each effect is superheated by the BPE, but when it condenses in the next effect's steam chest, it does so at the saturation temperature of pure water at that pressure. The superheat contributes very little, so the BPE in every effect is effectively subtracted from the total temperature span available to the whole train. With strongly elevating liquors, that can leave very little driving force for each effect and limit how many effects are economical.

Two More Effects Designers Watch

BPE is not the only reason liquor boils hotter than expected. In tall vertical tubes, the liquid near the bottom sits under a hydrostatic head that raises its local pressure and therefore its boiling point. In a short-tube evaporator, that can add several degrees on top of the BPE, especially under vacuum, where small pressure changes produce large changes in saturation temperature.

Concentrated solutions like caustic soda also release or absorb significant heat when their concentration changes, the heat of dilution. For these liquors, a simple energy balance using the heat capacity of water and the latent heat of pure steam gives poor results, and designers use enthalpy-concentration charts instead. Both effects, like BPE itself, are the reason evaporator calculations start from the liquor's real properties rather than those of water.

References

1. McCabe, W. L., Smith, J. C., & Harriott, P. (2005). Unit Operations of Chemical Engineering (7th ed.), Chapter 16. New York: McGraw-Hill.
2. Geankoplis, C. J. (2003). Transport Processes and Separation Process Principles (4th ed.), Chapter 8. Upper Saddle River, NJ: Prentice Hall.
3. Green, D. W., & Southard, M. Z. (Eds.). (2019). Perry’s Chemical Engineers’ Handbook (9th ed.). New York: McGraw-Hill.
4. Minton, P. E. (1986). Handbook of Evaporation Technology. Park Ridge, NJ: Noyes Publications.