A liquid’s boiling point (BP) is the specific temperature at which its vapor pressure equals the external pressure surrounding the liquid. As the liquid is heated, molecules gain energy and escape into the gaseous phase, creating vapor pressure. When this internal pressure matches the external atmospheric pressure, the liquid begins to boil. The “normal boiling point” is a standardized reference, defined as the temperature at which a liquid boils specifically at one standard atmosphere of pressure (1 atm or 101.325 kilopascals). This standard allows for consistent comparison between different substances.
Calculating Boiling Point Elevation
Adding a non-volatile solute, such as salt or sugar, to a pure solvent changes the liquid’s boiling characteristics. This phenomenon, known as boiling point elevation, causes the resulting solution to have a higher boiling temperature than the pure solvent alone. The presence of solute particles interferes with the solvent molecules’ ability to escape into the vapor phase, effectively lowering the solution’s vapor pressure. A higher temperature is required for the solution’s vapor pressure to reach the external atmospheric pressure, causing the boiling point to rise.
This change in boiling point is a colligative property, meaning it depends only on the number of solute particles dissolved, not their chemical identity. The magnitude of this elevation is calculated using the formula: \(\Delta T_b = i K_b m\). The final boiling point of the solution is found by adding this temperature change (\(\Delta T_b\)) to the normal boiling point of the pure solvent.
The variable \(m\) represents the molality of the solution (moles of solute divided by mass of solvent in kilograms). The term \(K_b\) is the ebullioscopic constant, a value specific to the solvent; for water, \(K_b\) is approximately \(0.512\) °C·kg/mol. The factor \(i\), known as the van’t Hoff factor, accounts for the number of particles a solute dissociates into when dissolved.
For instance, a non-electrolyte like sugar remains as one particle in solution, so \(i\) equals 1. An electrolyte like sodium chloride (NaCl) dissociates into two ions (\(\text{Na}^+\) and \(\text{Cl}^-\)), giving it a van’t Hoff factor close to 2. If \(0.5\) moles of salt were dissolved in \(1\) kilogram of water, the molality (\(m\)) would be \(0.5\) mol/kg.
Plugging these values into the equation, the change in boiling temperature (\(\Delta T_b\)) would be \(2 \times 0.512\) °C·kg/mol \(\times 0.5\) mol/kg, resulting in a \(0.512\) °C elevation. Since water normally boils at \(100\) °C, this salt solution would boil at \(100.512\) °C.
Calculating Boiling Point Based on Pressure
The boiling point of a pure substance is highly dependent on the external pressure applied to it, which is important in applications like high-altitude cooking or industrial distillation. This calculation focuses on a pure liquid, unlike the effect of adding a solute. The relationship is inverse: when external pressure decreases, the liquid’s vapor pressure needs to reach a lower threshold to boil, causing the boiling point to drop.
This relationship between temperature and vapor pressure is governed by the Clausius-Clapeyron equation. This equation allows for the estimation of a liquid’s boiling point at a different pressure if its properties at one point are known. The two-point form is often used for calculations: \(\ln(P_2/P_1) = (\Delta H_{vap}/R) (1/T_1 – 1/T_2)\). This formula relates two pressure-temperature points, \((P_1, T_1)\) and \((P_2, T_2)\).
In this formula, \(P_1\) and \(P_2\) are the two vapor pressures, and \(T_1\) and \(T_2\) are the corresponding absolute temperatures in Kelvin. The term \(\Delta H_{vap}\) is the molar enthalpy of vaporization, which represents the energy required to convert one mole of the liquid into a gas. The variable \(R\) is the universal gas constant, used as \(8.314\) J/(mol·K).
If a liquid’s normal boiling point (\(T_1\) at \(P_1 = 1\) atm) and its enthalpy of vaporization are known, the equation can find its boiling point (\(T_2\)) at a new pressure (\(P_2\)). This is useful for calculating boiling points at lower pressures, such as those found at high altitudes. For example, water’s enthalpy of vaporization is approximately \(40.65\) kJ/mol.
Approximation Methods for Unknown Compounds
When a compound is new or experimental data is unavailable, precise constants like the enthalpy of vaporization may be unknown, making exact calculations difficult. In these cases, thermodynamic approximation methods can estimate the normal boiling point of the pure substance. These methods rely on general principles linking molecular properties to physical behavior.
One simple and widely used technique is Trouton’s Rule, which estimates the enthalpy of vaporization (\(\Delta H_{vap}\)) based on the boiling temperature (\(T_b\)). The rule states that the molar entropy of vaporization (\(\Delta S_{vap}\)) is roughly constant for most non-polar liquids, typically between \(85\) and \(88\) J/(mol·K). Since \(\Delta S_{vap}\) is defined as \(\Delta H_{vap} / T_b\), the \(\Delta H_{vap}\) can be estimated if the boiling point is known.
The rule works well for many simple, non-polar organic compounds, but it shows significant deviations for liquids with strong intermolecular forces, such as water or alcohols, which exhibit hydrogen bonding. For these liquids, the estimated entropy value is often higher, sometimes exceeding \(100\) J/(mol·K).
More complex estimation techniques, like group contribution methods, offer greater accuracy by breaking down a molecule into its constituent functional groups. Methods such as the Joback method assign specific numerical values to different molecular parts, like methyl groups (\(\text{CH}_3\)) or hydroxyl groups (\(\text{OH}\)). By summing the contributions of all the groups within a molecule, these methods can predict the normal boiling point with greater accuracy. These approximation tools are useful in the early stages of chemical and pharmaceutical research when experimental data collection is not feasible.