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The basic thermodynamic potential is internal energy.In a simple fluid system, neglecting the effects of viscosity, the fundamental thermodynamic equation is written: = + where U is the internal energy, T is temperature, S is entropy, P is the hydrostatic pressure, V is the volume, is the chemical potential, and M mass.
The equilibrium constant for a full redox reaction can be obtained from the standard redox potentials of the constituent half-reactions. At equilibrium the potential for the two half-reactions must be equal to each other and, of course, the number of electrons exchanged must be the same in the two half reactions. [32]
At equilibrium, the chemical force driving the forward reaction must be equal to the chemical force driving the reverse reaction. Writing the initial active masses of A,B, A' and B' as p, q, p' and q' and the dissociated active mass at equilibrium as ξ {\displaystyle \xi } , this equality is represented by
The chemical system will attempt to partly oppose the change affected to the original state of equilibrium. In turn, the rate of reaction, extent, and yield of products will be altered corresponding to the impact on the system. This can be illustrated by the equilibrium of carbon monoxide and hydrogen gas, reacting to form methanol. C O + 2 H 2 ...
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
If a mixture is not at equilibrium, the liberation of the excess Gibbs energy (or Helmholtz energy at constant volume reactions) is the "driving force" for the composition of the mixture to change until equilibrium is reached. The equilibrium constant can be related to the standard Gibbs free energy change for the reaction by the equation
The fractional extent of the reaction (i.e. the percentage change in concentration of a measurable species) depends on the molar volume change (ΔV°) between the reactants and products and the equilibrium position. If K is the equilibrium constant and P is the pressure then the volume change is given by:
An equilibrium state is mathematically ascertained by seeking the extrema of a thermodynamic potential function, whose nature depends on the constraints imposed on the system. For example, a chemical reaction at constant temperature and pressure will reach equilibrium at a minimum of its components' Gibbs free energy and a maximum of their entropy.