# Free Energy and Equilibrium

JoVE Core
Cell Biology
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JoVE Core Cell Biology
Free Energy and Equilibrium

### Next Video3.9: Non-equilibrium in the Cell

The free energy change, or ΔG, of a particular reaction is the sum of the standard free energy and RT times the natural log of the ratio of the concentrations of products to reactants.

If the ΔG of a reaction is negative, then the reaction progresses forward. The ΔG becomes less negative as the concentrations of the reactants decrease, and that of the products increase.

Eventually, the ΔG equals zero when the reaction reaches equilibrium, where the forward and reverse reaction rates are equal.

At equilibrium, the ratio of the concentration of products and reactants equals the equilibrium constant, K.

The equation can be rearranged to show the mathematical relationship between ΔG0 and K.

## Free Energy and Equilibrium

The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔG is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).

The reaction quotient, Q, is a convenient measure of the status of an equilibrium system. Q is the numerical value of the mass action expression for the system, and it can be used to identify the direction in which a reaction will proceed in order to achieve equilibrium. When Q is lesser than the equilibrium constant, K, the reaction will proceed in the forward direction until equilibrium is reached and Q = K. Conversely, if Q > K, the process will proceed in the reverse direction until equilibrium is achieved.

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

ΔG = ΔG° + RT lnQ

R is the gas constant (8.314 J/K mol), T is the kelvin or absolute temperature, and Q is the reaction quotient. For gas-phase equilibria, the pressure-based reaction quotient, QP, is used. The concentration-based reaction quotient, QC, is used for condensed phase equilibria.

For a system at equilibrium, Q = K and ΔG = 0, and the previous equation may be written as

0 = ΔG° + RT lnK (at equilibrium)

ΔG° = −RT lnK

This form of the equation provides a useful link between these two essential thermodynamic properties, and it can be used to derive equilibrium constants from standard free energy changes and vice versa.

This text is adapted from Openstax, Chemistry 2e, Section 16.4: Free Energy.