Chemistry fundamentally studies energy: how it is stored in chemical bonds and how it transforms during reactions. Chemical formulas provide the mathematical framework for tracking and predicting these energy transformations. Derived from thermodynamics, these equations allow scientists to quantify energy changes in physical processes and chemical reactions. Applying these formulas helps determine the energy required to start a reaction, the energy released upon completion, and whether a reaction will occur.
The Core Relationship: Internal Energy and The First Law
The foundational formula in chemical thermodynamics relates the total energy change within a system to the energy exchanged with its surroundings. This concept is captured by the change in internal energy, symbolized as \(\Delta U\). Internal energy represents the sum of all kinetic and potential energies of the particles within a substance. This relationship is often expressed as \(\Delta U = q + w\), which is a formal statement of the Law of Conservation of Energy, or the First Law of Thermodynamics.
This formula states that any change in a system’s internal energy (\(\Delta U\)) must be equal to the net heat (\(q\)) transferred to or from the system plus the net work (\(w\)) done on or by the system. The conservation principle means that energy is never created or destroyed, only exchanged or converted between the forms of heat and work. Understanding the direction of energy flow requires careful attention to sign conventions, which dictate the perspective of the system.
Heat (\(q\)) is positive when energy flows into the system from the surroundings (endothermic), increasing internal energy. Conversely, a negative \(q\) indicates an exothermic process where heat flows out of the system and into the surroundings. Work (\(w\)) is positive when the surroundings do work on the system, such as compressing a gas. Work is negative when the system does work on the surroundings, like an expanding gas.
Quantifying Energy Transfer: Heat and Work
To calculate the components of internal energy, specific formulas are employed to quantify the heat (\(q\)) and work (\(w\)) transferred. Heat transfer is most commonly quantified by observing the temperature change of a known mass of substance, a process known as calorimetry. The formula used to calculate this thermal energy exchange is \(q = mc\Delta T\).
In this equation, \(m\) represents the mass of the substance. The term \(c\) is the specific heat capacity, a unique physical property indicating the energy required to raise the temperature of one gram of a substance by one degree Celsius or Kelvin. The final variable, \(\Delta T\), is the change in temperature (final minus initial). This formula calculates heat absorbed or released, provided no phase change occurs.
The other component of energy transfer, work (\(w\)), is often expressed in chemistry as pressure-volume work, particularly in reactions involving gases. The relevant formula is \(w = -P\Delta V\). Here, \(P\) represents the external pressure acting on the system, and \(\Delta V\) is the change in the system’s volume.
The change in volume, \(\Delta V\), is calculated as the final volume minus the initial volume. The negative sign maintains the thermodynamic sign convention: work done by the system (positive \(\Delta V\)) results in a negative \(w\), signifying a loss of internal energy. This formula applies primarily where the volume of gases changes against a constant external pressure.
Predicting Chemical Reactions: Gibbs Free Energy
A distinct thermodynamic formula is used not just to track energy, but to predict the direction of a chemical change, a concept known as spontaneity. This predictive ability is achieved through the Gibbs Free Energy change, symbolized as \(\Delta G\). The formula that relates the driving forces of a reaction is \(\Delta G = \Delta H – T\Delta S\).
This equation balances the two primary forces influencing a reaction: the change in enthalpy (\(\Delta H\)) and the change in entropy (\(\Delta S\)). Enthalpy change (\(\Delta H\)) is the heat content change of the system at constant pressure. A negative \(\Delta H\) indicates an exothermic reaction that releases heat, favoring spontaneity. The second term, \(T\Delta S\), incorporates temperature (\(T\)) and the change in entropy (\(\Delta S\)), which measures the system’s disorder. A positive \(\Delta S\) (increased disorder) also favors spontaneity.
The overall sign of \(\Delta G\) determines the reaction direction: a negative \(\Delta G\) indicates a spontaneous process that proceeds without continuous external energy input. Temperature (\(T\)) acts as a weighting factor, determining the relative significance of the entropy term compared to the enthalpy term. At high temperatures, the \(T\Delta S\) term can become dominant, potentially causing a reaction unfavorable at low temperatures to become spontaneous.