Boiling Point Elevation Calculator

Boiling point elevation is one of the four classical colligative properties, alongside vapor pressure lowering, freezing point depression and osmotic pressure. A liquid boils when its vapor pressure equals ambient pressure, 101.325 kPa at sea level. A non-volatile solute reduces the mole fraction of solvent at the surface and therefore its vapor pressure, so a higher temperature is required before the vapor pressure catches up with the atmosphere. The ebullioscopic constant Kb is not arbitrary: it follows from the pure solvent through Kb = R * Tb^2 * M / deltaH_vap. Inserting Tb = 373.15 K, M = 0.01802 kg/mol and deltaH_vap = 40.66 kJ/mol for water returns 0.512 K kg/mol, the tabulated figure. Benzene is 2.53, chloroform 3.63, carbon tetrachloride 5.03 and camphor 5.95. Molality rather than molarity appears in the formula because moles per kilogram of solvent does not drift as the sample is heated. The factor i counts dissolved particles: 1 for sucrose or urea, 2 for sodium chloride, 3 for calcium chloride. Interionic attraction pulls measured values below the ideal ones, so 0.1 molal NaCl behaves closer to i = 1.87, and the linear model degrades badly above roughly 0.5 molal. Two cautions matter in practice. The kitchen effect is negligible, since 10 g of salt in a liter of pasta water is only 0.17 molal and raises the boiling point under 0.2 degrees C. And solutes that associate rather than dissociate, such as carboxylic acids dimerizing in benzene, yield apparent particle counts near half the expected value.

Systematic measurement of colligative effects grew out of vapor pressure research in the 1870s and 1880s. Francois-Marie Raoult, working at Grenoble between 1878 and 1887, measured freezing point and vapor pressure lowering across a large range of solutions and distilled the results into the proportionality law that carries his name. Boiling point work advanced alongside it, and the term ebullioscopy entered laboratory usage in the same period. Jacobus Henricus van Hoff supplied the thermodynamic derivation in the mid 1880s and introduced the correction factor i to account for solutions that misbehaved, and Svante Arrhenius explained that anomaly in 1887 with his theory of electrolytic dissociation. The method became practical because of instrumentation. Ernst Otto Beckmann described his differential thermometer in 1888, using an adjustable mercury reservoir so that a fine scale spanning only a few degrees could be positioned near any solvent boiling or freezing point, resolving temperature changes on the order of 0.01 degrees C. Ebullioscopic and cryoscopic molar mass determination became routine bench chemistry and stayed in organic laboratories well into the twentieth century, until mass spectrometry, membrane osmometry and size exclusion chromatography displaced them. Modern Kb values are recomputed from enthalpy of vaporization data rather than measured directly, and the property survives mainly in teaching and in de-icing and antifreeze engineering.