The boiling point is the temperature at which a substance transitions from a liquid to a gaseous state. This transition is sensitive to surrounding atmospheric pressure, meaning a substance boils at different temperatures depending on altitude or weather. To standardize this measurement, chemists use the Normal Boiling Point (NBP). The NBP is the specific temperature at which a substance boils when the external pressure is exactly one standard atmosphere (1 atm or 101.325 kPa). Calculating the NBP is a common task in chemistry and engineering, serving as a reliable metric for confirming a substance’s identity and purity.
Understanding Vapor Pressure and Boiling
The physical phenomenon of boiling is governed by the concept of vapor pressure. Vapor pressure is the force exerted by the gaseous form of a substance when it is in thermodynamic equilibrium with its liquid phase. Molecules are constantly escaping the liquid surface to become gas, while gas molecules are simultaneously condensing back into the liquid. This dynamic balance creates the measurable pressure known as vapor pressure.
As the temperature of the liquid increases, the molecules gain kinetic energy, causing more of them to escape into the gas phase. This increase in escaped molecules elevates the vapor pressure of the substance. Boiling occurs precisely at the temperature where the liquid’s internal vapor pressure becomes equal to the external pressure pushing down on the liquid. For instance, a liquid will boil at a lower temperature on a high mountain, where the atmospheric pressure is reduced, compared to sea level. Therefore, calculating the NBP requires finding the temperature at which the vapor pressure reaches the specific value of 1 atm.
The Clausius-Clapeyron Equation
The relationship between a liquid’s vapor pressure and its temperature is described by the Clausius-Clapeyron equation. This thermodynamic equation is the primary tool used to calculate the NBP when the boiling point at a non-standard pressure is known. It allows scientists to extrapolate vapor pressure data across a range of temperatures. The integrated form of the equation is: \(\ln(P_2/P_1) = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right)\).
Each variable in this formula represents a specific physical quantity. \(P_1\) and \(P_2\) are the vapor pressures measured at two different absolute temperatures, \(T_1\) and \(T_2\). Temperatures must be expressed in Kelvin (K). 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 equation also incorporates \(R\), the universal gas constant (\(8.314 \text{ J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}\)). A fundamental assumption when using this integrated form is that the enthalpy of vaporization (\(\Delta H_{vap}\)) remains constant over the specific temperature range being investigated. This assumption simplifies the calculation and provides accurate results, especially when the temperature range between \(T_1\) and \(T_2\) is relatively small.
Applying the Equation to Find NBP
To determine the Normal Boiling Point using the Clausius-Clapeyron equation, variables must reflect the NBP definition. The NBP is the temperature where vapor pressure equals \(1 \text{ atm}\) (or \(101.325 \text{ kPa}\)). This standard pressure becomes \(P_2\), and the corresponding temperature, \(T_2\), is the unknown NBP to be solved for.
A reference point (\(P_1, T_1\)) is required to set up the problem, typically a known vapor pressure and its corresponding temperature obtained experimentally. The equation must then be algebraically rearranged to isolate the unknown \(T_2\) term. Careful attention to unit consistency is necessary, ensuring that the units for \(\Delta H_{vap}\) and the gas constant \(R\) cancel out.
To solve for \(T_2\), the equation is manipulated to isolate the term \(\frac{1}{T_2}\): \(\frac{1}{T_2} = \frac{1}{T_1} + \frac{R}{\Delta H_{vap}} \ln\left(\frac{P_2}{P_1}\right)\). The final step is to take the reciprocal of the resulting value to find \(T_2\) in Kelvin, which can then be converted to Celsius or another desired unit.
Quick Estimation Using Trouton’s Rule
For a rapid, less precise estimation of the NBP, especially when the enthalpy of vaporization is known, scientists can use Trouton’s Rule. This empirical rule states that the molar entropy of vaporization is approximately constant for many non-polar liquids. The entropy of vaporization is defined as the ratio of the enthalpy of vaporization (\(\Delta H_{vap}\)) to the Normal Boiling Point (\(T_{NBP}\)).
The rule is expressed as: \(\frac{\Delta H_{vap}}{T_{NBP}} \approx 85 \text{ J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}\). By knowing the \(\Delta H_{vap}\) for a substance, the NBP can be approximated by dividing this enthalpy by \(85 \text{ J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}\). While this method is fast, it is an approximation and is less accurate for liquids with strong intermolecular forces, such as water or ethanol, because their entropy of vaporization is higher than the typical value.