(the solute) has different properties. That is because its molecules experience essentially the same environment that they do in the absence of the solute. By contrast, each solute molecule is surrounded by solvent molecules, so it obeys a different law known as Henry's law. By Henry's law, the fugacity of the solute is proportional to its concentration. The constant of proportionality (a measured Henry's constant) depends on whether the concentration is represented by the mole fraction, molality or molarity. Temperature and pressure dependence The pressure dependence of fugacity (at constant temperature) is given by and is always positive. The temperature dependence at constant pressure is where is the change in molar enthalpy as the gas expands, liquid vaporizes, or solid sublimates into a vacuum. Also, if the pressure is , then Since the temperature and entropy are positive, decreases with increasing temperature. Measurement The fugacity can be deduced from measurements of volume as a function of pressure at constant temperature. In that case, This integral can also be calculated using an equation of state. The integral can be recast in an alternative form using the compressibility factor Then This is useful because of the theorem of corresponding states: If the pressure and temperature at the critical point of the gas are and , we can define reduced properties and . Then, to a good approximation, most gases have the same value of for the same reduced temperature and pressure. However, in geochemical applications, this principle ceases to be accurate at pressures where metamorphism occurs. For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is This formula is difficult to use, since the pressure depends on the molar volume through the equation of state; so one must choose a volume, calculate the pressure, and then use these two values on the right-hand side of the equation. History The word fugacity is derived from the Latin fugere, to flee. In the sense of an "escaping tendency", it was introduced to thermodynamics in 1901 by the American chemist Gilbert N. Lewis and popularized in an influential textbook by Lewis and Merle Randall, Thermodynamics and the Free Energy of Chemical Substances, in 1923. The "escaping tendency" referred to the flow of matter between phases and played a similar role to that of temperature in heat flow. See also Electrochemical potential Excess chemical potential Fugacity capacity Multimedia fugacity