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# 6.6: Free Energy

## Free Energy

If we want to describe transformations, it is useful to have a measure of (a) how much energy is in a system, (b) the dispersal of that energy within the system and, of course, (c) how these factors change between the start and end of a process. The concept of free energy, often referred to as Gibbs energy or Gibbs enthalpy (abbreviated with the letter G), in some sense, does just that. Gibbs energy can be defined in several interconvertible ways, but a useful one in the context of biology is the enthalpy (internal energy) of a system minus the entropy of the system scaled by the temperature. The difference in free energy when a process takes place is often reported in terms of the change (Δ) of enthalpy (internal energy) denoted H, minus the temperature scaled change (Δ) in entropy, denoted S. See the equation below.

$ΔG=ΔH−TΔS \label{gibbs}$

The Gibbs energy is often interpreted as the amount of energy available to do useful work. With a bit of hand waving, we can interpret this statement by invoking the idea presented in the section on entropy, which states the dispersion of energy (required by the Second Law) associated with a positive change in entropy somehow renders some of the energy that is transferred less useful to do work. One can say that this is reflected in part in the $$T∆S$$ term of the Equation \ref{gibbs}.

To provide a basis for fair comparisons of changes in Gibbs energy amongst different biological transformations or reactions, the free energy change of a reaction is measured under a set of common standard experimental conditions. The resulting standard free energy change of a chemical reaction is expressed as an amount of energy per mole of the reaction product (either in kilojoules or kilocalories, kJ/mol or kcal/mol; 1 kJ = 0.239 kcal), when measured at a standard pH, temperature, and pressure conditions. Standard pH, temperature, and pressure conditions are generally standardized at pH 7.0, 25 degrees Celsius, and 100 kilopascals (1 atm pressure), respectively. It is important to note that cellular conditions vary considerably from these standard conditions, and so actual $$∆G$$ inside a cell will differ considerably from those calculated under standard conditions.

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