Thermodynamic activity adjusts our measurement of concentration to reflect how substances truly behave. It represents the “effective concentration” of a species in a mixture, which can differ from its measured, or analytical, concentration. In many situations, particularly in dilute mixtures, a substance’s activity is very close to its measured concentration. However, as particles become more crowded and interact with each other, their ability to participate in reactions changes. Activity provides a more precise value that reflects these interactive effects.
The Need for Activity
The concept of thermodynamic activity arises from the distinction between ideal and real systems. In an ideal system, such as a highly diluted gas or solution, particles are presumed to have no volume and to not interact with one another. Their behavior can be predicted with simple laws because each particle acts independently. Under these conditions, a substance’s measured concentration accurately reflects its chemical behavior.
Real systems, however, rarely meet this ideal standard. As the concentration of a solute increases or the pressure of a gas rises, the particles get closer together. At this proximity, intermolecular forces—attractions and repulsions between neighboring particles—become significant. These interactions alter how each particle behaves, changing its ability to react or escape from a solution.
This is analogous to people in a crowded subway car; their movement is restricted, and they are constantly interacting with those around them. In a crowded chemical solution, solute particles may be attracted to solvent molecules or repelled by other solute ions, reducing their “freedom” to participate in a chemical reaction. Activity was developed to quantify this deviation from ideal behavior.
The Activity Coefficient
To bridge the gap between measured concentration and effective concentration, scientists use a correction factor called the activity coefficient. This dimensionless number, represented by the Greek letter gamma (γ), quantifies the degree to which a solution deviates from ideal behavior. The relationship is straightforward: a substance’s activity (a) is its molal concentration (m) multiplied by its activity coefficient (a = γm).
In a perfectly ideal system, where particles do not interact, the activity coefficient is exactly 1. In this scenario, activity is identical to concentration. As a solution becomes more concentrated and intermolecular forces become more prominent, the activity coefficient deviates from 1. For example, in a concentrated solution of potassium hydrogen iodate, the activity of hydrogen ions can be 40% lower than their measured concentration, indicating significant ionic interactions.
For gases, a similar concept exists to adjust for non-ideal behavior, known as fugacity. Fugacity is the “effective pressure” of a real gas, serving the same purpose as activity by providing a corrected value that accounts for interactions between gas molecules at high pressures.
Defining the Standard State
Activity is always measured relative to a defined reference point, known as the standard state. This is an agreed-upon set of conditions, including a specific temperature, pressure, and concentration, that acts as a baseline. Because activity is a ratio of a substance’s properties in its actual state to its properties in the standard state, it is a dimensionless quantity.
The definition of the standard state depends on the phase of the substance. For a pure solid or liquid, the standard state is the substance in its pure form at a pressure of 1 bar, so their activity is always taken as 1. For a gas, the standard state is the pure gas behaving ideally at a pressure of 1 bar.
For a solute in a solution, the standard state is a hypothetical ideal solution with a concentration of 1 mole per kilogram of solvent (1 molal) at 1 bar. This state is hypothetical because a real 1-molal solution exhibits non-ideal behavior, but it allows for consistent comparison of activities.
Application in Chemical Equilibrium
The utility of thermodynamic activity is evident in the study of chemical equilibrium. The equilibrium constant (K) describes the ratio of products to reactants when a reversible reaction has reached a stable state. For this constant to be consistent across different conditions, it must be calculated using activities rather than concentrations. The resulting value is called the thermodynamic equilibrium constant.
When chemists use measured concentrations to calculate an equilibrium constant (denoted as Kc), they find its value can appear to change as the initial concentrations of reactants are varied. This occurs because Kc fails to account for intermolecular forces shifting the “effective concentrations.” Using activities resolves this discrepancy, yielding a single, accurate value for K that holds true in non-ideal systems.
This precision is important for predictions in various fields. In environmental chemistry, calculating the solubility of minerals in natural waters requires activity-based constants to account for high concentrations of dissolved salts. In industrial processes, using activities ensures that calculations for reaction yields are based on the actual chemical behavior of the substances involved.