free energy
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What is free energy in thermodynamics?
In thermodynamics, free energy is an energylike property that determines how systems change and how much work they can produce. It is a state function, meaning its value depends on the system's current state, not its history.
Free energy is expressed in two forms:
- Helmholtz free energy ((F = U - TS)): Useful for constant temperature and volume conditions.
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Gibbs free energy ((G = U + PV - TS) or (G = H β TS)): Useful for constant temperature and pressure conditions.
- (U) is internal energy.
- (P) is pressure.
- (V) is volume.
- (T) is the temperature above absolute zero.
- (S) is entropy.
- (H) is enthalpy.
Changes in free energy ((\Delta F) or (\Delta G)) indicate the direction of spontaneous change and the maximum work obtainable from reactions. A process will occur spontaneously if the change in free energy is negative.
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Why is free energy important in science?
Free energy, a concept in thermodynamics, is an energylike property that helps scientists determine how systems change and the maximum work they can produce. It is expressed as Helmholtz free energy (F) and Gibbs free energy (G). Changes in free energy help to determine if state changes can occur spontaneously. Under constant temperature and volume, transformation happens spontaneously if the Helmholtz free energy is smaller in the final state than in the initial state. The transformation of state will occur spontaneously if the change in the Gibbs free energy, is negative, under constant temperature and pressure.
Living systems use free energy to grow and develop, creating structures of greater internal energy from nutrients they absorb.
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How is free energy related to chemical reactions?
Free energy is a thermodynamic property that determines the spontaneity of chemical reactions. It combines enthalpy (heat) and entropy (disorder) to predict whether a reaction will occur spontaneously at a given temperature. The Gibbs free energy (G) is commonly used, especially under constant temperature and pressure.
The change in Gibbs free energy ((\Delta)G) during a reaction indicates its spontaneity:
* If (\Delta)G < 0: The reaction proceeds spontaneously, favoring product formation.
* If (\Delta)G > 0: The reaction is non-spontaneous and requires energy input.
* If (\Delta)G = 0: The reaction is at equilibrium.By measuring or deriving standard free energies of reactants and products, the equilibrium constant, or the relative amounts of products and reactants present at equilibrium, can be calculated.
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What is the difference between Gibbs free energy and Helmholtz free energy?
Both Gibbs free energy (G) and Helmholtz free energy (F) are energylike properties used to determine how systems change and how much work they can produce.
The formulas for each are:
* (F = U - TS)
* (G = U + PV - TS) or (G = H β TS)Where:
* (U) is internal energy
* (P) is pressure
* (V) is volume
* (T) is temperature
* (S) is entropy
* (H) is enthalpyChanges in F determine the maximum useful work in a reversible process at constant temperature and volume. Changes in G determine maximum useful work at constant temperature and pressure. F is useful for describing processes inside a container with rigid walls, while G is useful for describing processes that occur under constant pressure.
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How does temperature affect free energy?
Free energy, a concept in thermodynamics, helps determine how systems change and how much work they can produce. It comes in two forms: Gibbs free energy (G) and Helmholtz free energy (F). Temperature plays a crucial role in determining free energy.
The Gibbs free energy equation (G = U + PV β TS) shows this relationship, where T stands for temperature. Similarly, the Helmholtz free energy is represented as (F\u00a0=\u00a0U\u00a0\u2212\u00a0TS). In these equations, increasing the temperature (T) while holding entropy (S) constant will decrease free energy (G or F), influencing the spontaneity and equilibrium of processes. Gibbs free energy is named after J.W. Gibbs.
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How do scientists use free energy to predict if a reaction will occur spontaneously?
Scientists use free energy to predict the spontaneity of a reaction by examining the change in Gibbs free energy ((\Delta G)). A reaction will occur spontaneously at a constant temperature and pressure if (\Delta G) is negative, indicating that the system's free energy decreases during the process. The Gibbs free energy is expressed as (G = U + PV β TS), where (U) is internal energy, (P) is pressure, (V) is volume, (T) is temperature, and (S) is entropy.
The change in Gibbs free energy is calculated by subtracting the total free energies of the reactants from the total free energies of the products, (\Delta G = G_\text{products} - G_\text{reactants}). If (\Delta G) is less than zero, the forward reaction occurs spontaneously. If (\Delta G) is greater than zero, the reaction is non-spontaneous.
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free energy, in thermodynamics, energylike property or state function of a system in thermodynamic equilibrium. Free energy has the dimensions of energy, and its value is determined by the state of the system and not by its history. Free energy is used to determine how systems change and how much work they can produce. It is expressed in two forms: the Helmholtz free energy F, sometimes called the work function, and the Gibbs free energy G. If U is the internal energy of a system, PV the pressure-volume product, and TS the temperature-entropy product (T being the temperature above absolute zero), then F = U β TS and G = U + PV β TS. The latter equation can also be written in the form G = H β TS, where H = U + PV is the enthalpy. Free energy is an extensive property, meaning that its magnitude depends on the amount of a substance in a given thermodynamic state.
The changes in free energy, ΞF or ΞG, are useful in determining the direction of spontaneous change and evaluating the maximum work that can be obtained from thermodynamic processes involving chemical or other types of reactions. In a reversible process the maximum useful work that can be obtained from a system under constant temperature and constant volume is equal to the (negative) change in the Helmholtz free energy, βΞF = βΞU + TΞS, and the maximum useful work under constant temperature and constant pressure (other than work done against the atmosphere) is equal to the (negative) change in the Gibbs free energy, βΞG = βΞH + TΞS. In each case, the TΞS entropy term represents the heat absorbed by the system from a heat reservoir at temperature T under conditions where the system does maximum work. By conservation of energy, the total work done also includes the decrease in internal energy U or enthalpy H as the case may be. For example, the energy for the maximum electrical work done by a battery as it discharges comes both from the decrease in its internal energy due to chemical reactions and from the heat TΞS it absorbs in order to keep its temperature constant, which is the ideal maximum heat that can be absorbed. For any actual battery, the electrical work done would be less than the maximum work, and the heat absorbed would be correspondingly less than TΞS.
Changes in free energy can be used to judge whether changes of state can occur spontaneously. Under constant temperature and volume, the transformation will happen spontaneously, either slowly or rapidly, if the Helmholtz free energy is smaller in the final state than in the initial stateβthat is, if the difference ΞF between the final state and the initial state is negative. Under constant temperature and pressure, the transformation of state will occur spontaneously if the change in the Gibbs free energy, ΞG, is negative.
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Phase transitions provide instructive examples, as when ice melts to form water at 0.01 Β°C (T = 273.16 K), with the solid and liquid phases in equilibrium. Then ΞH = 79.71 calories per gram is the latent heat of fusion, and by definition ΞS = ΞH/T = 0.292 calories per gramβK is the entropy change. It follows immediately that ΞG = ΞH β TΞS is zero, indicating that the two phases are in equilibrium and that no useful work can be extracted from the phase transition (other than work against the atmosphere due to changes in pressure and volume). Furthermore, ΞG is negative for T > 273.16 K, indicating that the direction of spontaneous change is from ice to water, and ΞG is positive for T < 273.16 K, where the reverse reaction of freezing takes place.