At typical storage temperatures and humidities for pharmaceutical solids (5–40 °C and <85% relative humidity), water behaves like an ideal gas, and the activity of water in a solid can be related to the headspace relative humidity by the following (5, 6):
A w ~ (PW ÷ PWS ) = (relative humidity ÷ 100)in which PW is the partial pressure of water in the headspace, and PWS is the saturated vapor pressure of water at the temperature of interest.
Thus, the relative humidity in the package headspace over a pharmaceutical solid at equilibrium can be directly related to the water activity and is an indication of the amount of water present with potential to cause undesirable changes in the pharmaceutical product.
Currently, two different types of water activity instruments are commercially available: one based on a chilled-mirror dew-point technology to measure humidity and the other based on a polymeric thin-film capacitance sensor that is responsive to headspace moisture. In both of these techniques, the sample of interest is equilibrated in a sealed chamber until equilibrium between the solid and headspace moisture is reached. The chilled-mirror instrument consists of an optical reflectance sensor that detects the exact point at which condensation first appears at the mirror–headspace gas interface. This point is determined by directing a beam of infrared light onto the mirror surface and reflecting the beam of light to a photodetector, which detects reflectance changes upon initiation of condensation. A thermoelectric (Peltier) cooler helps to control the mirror temperature precisely, and a thermocouple attached to the mirror accurately measures the dew-point temperature. Both the dew-point and measured sample-surface temperatures are then used to determine the water activity.