# Enduring Understanding 5.E.2: Gibbs Free Energy

• Gibbs Free Energy is used to determine whether a reaction is favored or disfavored. It is given by the equation:
• ΔG = ΔH - TΔS
• Where ΔH is the enthalpy change, ΔS is the entropy change, and T is the temperature.
• If ΔG < 0, then products are favored at equilibrium (K > 1), and the forward reaction is "thermodynamically favored"
• Conversely, if ΔG > 0, then reactants are favored at equilibrium (K < 1), and the forward reaction is "thermodynamically disfavored"
• A "thermodynamically favored" reaction (ΔG < 0) is sometimes referred to as "spontaneous". However, this does not necessarily mean that the reaction will proceed at a detectable rate - sometimes, high kinetic barriers prevent a reaction from actually taking place.
• The sign of ΔG can sometimes be determined without extensive calculations:
• If a reaction's ΔH is negative, and ΔS is positive, the reaction is always thermodynamically favored.
• If a reaction's ΔH is positive, and ΔS is negative, the reaction is always thermodynamically disfavored.
• If ΔH and ΔS are either both negative, or both positive, the thermodynamic favorability of the reaction can depend on the temperature.
• Reactions can be 'driven by enthalpy' (where a very exothermic reaction (negative ΔH) overcomes a decrease in entropy) or 'driven by entropy' where an endothermic reaction occurs because of a highly positive ΔS.
• Example 1: The formation of NaCl(s) from its elements is spontaneous and releases a great deal of heat.
• Na(s) + Cl2(g) → 2NaCl(s)
• This process involves a gas molecule becoming a solid, and therefore must involve a decrease in entropy. Therefore, ΔS is negative. It is an exothermic reaction, releasing heat, therefore ΔH must also be negative. This reaction is 'driven by enthalpy', because the large negative ΔH is more negative than the -TΔS term is positive, resulting in a negative overall ΔG and a spontaneous reaction.
• Example 2: NaNO3(s) dissolves in water with a noticeable decrease in temperature.
• NaNO3(s) → Na+(aq) + NO3-(aq)
• This is an endothermic reaction, so ΔH is positive. However, the dissolution occurs, therefore the ΔG must be negative. This means the ΔS must be very positive. Therefore, this process is 'driven by entropy'.
• Even if a reaction has a positive ΔG, it can be driven by an external source of energy, such as an electric current, photons of light, or by coupling to a spontaneous reaction.
• Examples include the charging of a battery, photosynthesis of glucose from CO2, and biological reactions coupled to the hydrolysis of ATP.

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