Henry’s Law describes how a gas partitions between a gas phase and a liquid phase. The law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas immediately above the liquid surface. This relationship holds true when the system has reached equilibrium. The proportionality factor connecting these two values is the Henry’s Law constant, symbolized as \(K_H\). This constant is unique for every combination of gas, solvent, and temperature, allowing scientists to predict gas solubility under varying conditions.
Understanding the Henry’s Law Constant and Units
The Henry’s Law constant is not a single, universal value, as it depends on how concentration and pressure are defined in the mathematical expression. One common form is the solubility constant (\(K_{pc}\)), which is the ratio of the dissolved gas concentration (C) to its partial pressure (P), represented as \(K_{pc} = C/P\). The units for this form reflect concentration per pressure, such as \(\text{mol}/(\text{L} \cdot \text{atm})\) or \(\text{M}/\text{atm}\).
A second widely used expression is the volatility constant (\(K_{cp}\)), which is the inverse of the solubility constant, defined as \(K_{cp} = P/C\). This constant has units of pressure per concentration, such as \(\text{atm} \cdot \text{L}/\text{mol}\). The choice between these forms is largely a matter of convention within a specific field of study, so it is necessary to check the units associated with a reported \(K_H\) value before using it in any calculation. Other forms exist, including dimensionless constants based on mole fractions or mixing ratios.
The constant can also be expressed by relating the partial pressure to the mole fraction of the gas in the liquid, resulting in units like \(\text{atm}/\text{mole fraction}\). A high \(K_{pc}\) (solubility constant) indicates high gas solubility, while a high \(K_{cp}\) (volatility constant) indicates low gas solubility. Since the constants are reciprocals of one another, converting between them is a simple inversion, provided the concentration and pressure units are appropriately matched.
Calculating \(K_H\) from Measured Solubility Data
The most direct way to calculate the Henry’s Law constant is by using measured data points for dissolved gas concentration and partial pressure obtained during an experiment. The experiment requires placing the gas in contact with the liquid in a closed system until thermodynamic equilibrium is reached. Once equilibrium is established, the concentration of the dissolved gas (C) in the liquid is measured, and the partial pressure (P) of the gas above the liquid is recorded.
The calculation is a straightforward application of the chosen Henry’s Law definition. If the solubility constant is desired, the formula is \(K_{pc} = C/P\). If the volatility constant is preferred, the calculation is \(K_{cp} = P/C\). Multiple measurements at different pressures are typically taken to confirm linearity and ensure the constant is determined accurately, as Henry’s Law applies best at low gas concentrations.
To calculate the solubility constant (\(K_{pc}\)) for a gas dissolved in water, consider a measurement where the dissolved concentration (C) is \(0.00048 \text{ mol}/\text{L}\) and the partial pressure (P) is \(0.79 \text{ atm}\). The constant is calculated by dividing the concentration by the pressure: \(K_{pc} = 0.00048 \text{ mol}/\text{L} / 0.79 \text{ atm}\). This yields a Henry’s Law constant of \(0.00061 \text{ mol}/(\text{L} \cdot \text{atm})\). The constant represents the slope of the line when concentration is plotted against partial pressure.
Accounting for Temperature Dependence
Gas solubility generally decreases as temperature increases, meaning the Henry’s Law constant is highly dependent on temperature and must be recalculated if the temperature changes. This dependency is modeled using a modified form of the Van’t Hoff equation. This calculation is useful when a constant is known at a reference temperature, \(T_1\), but is needed for a different temperature, \(T_2\).
The relationship is expressed using the formula \(\ln \left(\frac{K_{H, T_2}}{K_{H, T_1}}\right) = -\frac{\Delta H_{sol}}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right)\). Here, \(K_{H, T_2}\) is the constant at the new temperature and \(K_{H, T_1}\) is the known constant at the reference temperature. The variables required for this calculation are the molar gas constant (\(R\)) and the temperatures \(T_1\) and \(T_2\), which must be expressed in Kelvin.
The most important parameter is \(\Delta H_{sol}\), which represents the enthalpy of dissolution, or the heat change associated with the gas dissolving into the liquid. The enthalpy of dissolution is assumed to remain constant over the temperature range between \(T_1\) and \(T_2\), allowing the integrated Van’t Hoff equation to be used. For a gas dissolving in water, \(\Delta H_{sol}\) is typically negative, indicating that the process is exothermic and gas solubility decreases with increasing temperature. By knowing the Henry’s Law constant at one temperature and the enthalpy of dissolution, this formula allows for the extrapolation or interpolation of the constant to other temperatures of interest.